##############ECHO OF PROBLEM################# ##############temp/mtest2postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 + 1.0; diff ( y2 , x , 1 ) = y1 - 1.0; ! // BEGIN FIRST INPUT BLOCK Digits=64; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=10.0; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); glob_look_poles=true; glob_max_iter=1000000; glob_display_interval=0.1; glob_max_minutes=10; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y1 (double x) { return(1.0 + cos(x)); } double exact_soln_y2 (double x) { return(1.0 + sin(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 9.9 estimated_steps = 9900000 step_error = 1.01010101010101e-17 est_needed_step_err = 1.01010101010101e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.467208605532302e-183 estimated_step_error = 2.467208605532302e-183 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.655715664606566e-175 estimated_step_error = 1.655715664606566e-175 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.111131969458436e-167 estimated_step_error = 1.111131969458436e-167 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.456680367024186e-160 estimated_step_error = 7.456680367024186e-160 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.004093412037817e-152 estimated_step_error = 5.004093412037817e-152 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.358190142481624e-144 estimated_step_error = 3.358190142481624e-144 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.25364312158092e-136 estimated_step_error = 2.25364312158092e-136 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.512394117654307e-128 estimated_step_error = 1.512394117654307e-128 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.014950270158055e-120 estimated_step_error = 1.014950270158055e-120 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.811212724408108e-113 estimated_step_error = 6.811212724408108e-113 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.570923134360025e-105 estimated_step_error = 4.570923134360025e-105 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.067488750234022e-97 estimated_step_error = 3.067488750234022e-97 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.05854901161809e-89 estimated_step_error = 2.05854901161809e-89 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.381458319740244e-81 estimated_step_error = 1.381458319740244e-81 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.270668118428105e-74 estimated_step_error = 9.270668118428105e-74 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.221249002016115e-66 estimated_step_error = 6.221249002016115e-66 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.174750875079241e-58 estimated_step_error = 4.174750875079241e-58 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.801274754399603e-50 estimated_step_error = 2.801274754399603e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y1[1] (analytic) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09579 Order of pole (three term test) = -1.134 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.11 y1[1] (analytic) = 1.993956097956697 y1[1] (numeric) = 1.993956097956697 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.109778300837175 y2[1] (numeric) = 1.109778300837175 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1052 Order of pole (three term test) = -1.184 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.12 y1[1] (analytic) = 1.992808635853866 y1[1] (numeric) = 1.992808635853866 absolute error = 2.220446049250313e-16 relative error = 1.114229439445855e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.119712207288919 y2[1] (numeric) = 1.119712207288919 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1146 Order of pole (three term test) = -1.239 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.13 y1[1] (analytic) = 1.991561893714788 y1[1] (numeric) = 1.991561893714788 absolute error = 2.220446049250313e-16 relative error = 1.114926960722569e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.129634142619695 y2[1] (numeric) = 1.129634142619695 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1239 Order of pole (three term test) = -1.299 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.14 y1[1] (analytic) = 1.990215996212637 y1[1] (numeric) = 1.990215996212637 absolute error = 2.220446049250313e-16 relative error = 1.115680937886039e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.139543114644237 y2[1] (numeric) = 1.139543114644237 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1332 Order of pole (three term test) = -1.364 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.15 y1[1] (analytic) = 1.988771077936042 y1[1] (numeric) = 1.988771077936042 absolute error = 4.440892098500626e-16 relative error = 2.232983045544593e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.149438132473599 y2[1] (numeric) = 1.149438132473599 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1425 Order of pole (three term test) = -1.433 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.16 y1[1] (analytic) = 1.987227283375627 y1[1] (numeric) = 1.987227283375627 absolute error = 4.440892098500626e-16 relative error = 2.234717757576804e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.159318206614246 y2[1] (numeric) = 1.159318206614246 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1517 Order of pole (three term test) = -1.507 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.17 y1[1] (analytic) = 1.985584766909561 y1[1] (numeric) = 1.98558476690956 absolute error = 4.440892098500626e-16 relative error = 2.236566361965296e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.169182349066996 y2[1] (numeric) = 1.169182349066996 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1608 Order of pole (three term test) = -1.585 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.18 y1[1] (analytic) = 1.983843692788121 y1[1] (numeric) = 1.983843692788121 absolute error = 2.220446049250313e-16 relative error = 1.119264616119866e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.179029573425824 y2[1] (numeric) = 1.179029573425824 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1698 Order of pole (three term test) = -1.668 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y1[1] (analytic) = 1.98200423511727 y1[1] (numeric) = 1.98200423511727 absolute error = 4.440892098500626e-16 relative error = 2.240606765523823e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.188858894976501 y2[1] (numeric) = 1.188858894976501 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1788 Order of pole (three term test) = -1.755 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y1[1] (analytic) = 1.980066577841242 y1[1] (numeric) = 1.980066577841241 absolute error = 4.440892098500626e-16 relative error = 2.242799382706761e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.198669330795061 y2[1] (numeric) = 1.198669330795061 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1877 Order of pole (three term test) = -1.847 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y1[1] (analytic) = 1.978030914724148 y1[1] (numeric) = 1.978030914724148 absolute error = 4.440892098500626e-16 relative error = 2.245107528625225e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.2084598998461 y2[1] (numeric) = 1.2084598998461 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1966 Order of pole (three term test) = -1.943 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y1[1] (analytic) = 1.975897449330605 y1[1] (numeric) = 1.975897449330605 absolute error = 4.440892098500626e-16 relative error = 2.247531672256124e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.218229623080869 y2[1] (numeric) = 1.218229623080869 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2054 Order of pole (three term test) = -2.044 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y1[1] (analytic) = 1.973666395005375 y1[1] (numeric) = 1.973666395005374 absolute error = 4.440892098500626e-16 relative error = 2.250072306920204e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.227977523535188 y2[1] (numeric) = 1.227977523535188 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.214 Order of pole (three term test) = -2.149 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y1[1] (analytic) = 1.97133797485203 y1[1] (numeric) = 1.971337974852029 absolute error = 6.661338147750939e-16 relative error = 3.379094925745011e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.237702626427135 y2[1] (numeric) = 1.237702626427135 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2226 Order of pole (three term test) = -2.259 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y1[1] (analytic) = 1.968912421710645 y1[1] (numeric) = 1.968912421710644 absolute error = 6.661338147750939e-16 relative error = 3.383257718473525e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.247403959254523 y2[1] (numeric) = 1.247403959254523 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2311 Order of pole (three term test) = -2.373 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y1[1] (analytic) = 1.966389978134513 y1[1] (numeric) = 1.966389978134513 absolute error = 4.440892098500626e-16 relative error = 2.258398460062149e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.257080551892155 y2[1] (numeric) = 1.257080551892155 absolute error = 2.220446049250313e-16 relative error = 1.766351444947662e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2395 Order of pole (three term test) = -2.491 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y1[1] (analytic) = 1.96377089636589 y1[1] (numeric) = 1.96377089636589 absolute error = 4.440892098500626e-16 relative error = 2.26141048669111e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.266731436688831 y2[1] (numeric) = 1.266731436688831 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2479 Order of pole (three term test) = -2.613 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y1[1] (analytic) = 1.961055438310771 y1[1] (numeric) = 1.96105543831077 absolute error = 6.661338147750939e-16 relative error = 3.396812766032221e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.276355648564114 y2[1] (numeric) = 1.276355648564114 absolute error = 2.220446049250313e-16 relative error = 1.739676595428782e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2561 Order of pole (three term test) = -2.739 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y1[1] (analytic) = 1.958243875512697 y1[1] (numeric) = 1.958243875512697 absolute error = 6.661338147750939e-16 relative error = 3.401689764512554e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.285952225104836 y2[1] (numeric) = 1.285952225104835 absolute error = 2.220446049250313e-16 relative error = 1.726694045005672e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2642 Order of pole (three term test) = -2.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y1[1] (analytic) = 1.955336489125606 y1[1] (numeric) = 1.955336489125605 absolute error = 6.661338147750939e-16 relative error = 3.40674773104131e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.29552020666134 y2[1] (numeric) = 1.295520206661339 absolute error = 4.440892098500626e-16 relative error = 3.427883313333386e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2722 Order of pole (three term test) = -3.004 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y1[1] (analytic) = 1.952333569885713 y1[1] (numeric) = 1.952333569885713 absolute error = 6.661338147750939e-16 relative error = 3.411987710758302e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.305058636443444 y2[1] (numeric) = 1.305058636443443 absolute error = 2.220446049250313e-16 relative error = 1.701414777271227e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2801 Order of pole (three term test) = -3.143 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y1[1] (analytic) = 1.949235418082441 y1[1] (numeric) = 1.94923541808244 absolute error = 4.440892098500626e-16 relative error = 2.278273859229047e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.314566560616118 y2[1] (numeric) = 1.314566560616118 absolute error = 2.220446049250313e-16 relative error = 1.689108878754396e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2879 Order of pole (three term test) = -3.285 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y1[1] (analytic) = 1.946042343528387 y1[1] (numeric) = 1.946042343528386 absolute error = 4.440892098500626e-16 relative error = 2.282012060667089e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.324043028394869 y2[1] (numeric) = 1.324043028394868 absolute error = 2.220446049250313e-16 relative error = 1.677019554222607e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2956 Order of pole (three term test) = -3.431 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y1[1] (analytic) = 1.942754665528346 y1[1] (numeric) = 1.942754665528346 absolute error = 4.440892098500626e-16 relative error = 2.285873855972902e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.333487092140815 y2[1] (numeric) = 1.333487092140814 absolute error = 2.220446049250313e-16 relative error = 1.665142514192283e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3031 Order of pole (three term test) = -3.581 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y1[1] (analytic) = 1.939372712847379 y1[1] (numeric) = 1.939372712847378 absolute error = 4.440892098500626e-16 relative error = 2.28986005066583e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.342897807455452 y2[1] (numeric) = 1.342897807455451 absolute error = 2.220446049250313e-16 relative error = 1.653473582965823e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3106 Order of pole (three term test) = -3.735 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y1[1] (analytic) = 1.935896823677935 y1[1] (numeric) = 1.935896823677934 absolute error = 4.440892098500626e-16 relative error = 2.293971478326799e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.35227423327509 y2[1] (numeric) = 1.35227423327509 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3179 Order of pole (three term test) = -3.893 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y1[1] (analytic) = 1.932327345606034 y1[1] (numeric) = 1.932327345606034 absolute error = 4.440892098500626e-16 relative error = 2.298209000974332e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.361615431964962 y2[1] (numeric) = 1.361615431964962 absolute error = 2.220446049250313e-16 relative error = 1.630743892235389e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.325 Order of pole (three term test) = -4.054 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y1[1] (analytic) = 1.92866463557651 y1[1] (numeric) = 1.92866463557651 absolute error = 4.440892098500626e-16 relative error = 2.302573509454726e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.370920469412983 y2[1] (numeric) = 1.370920469412983 absolute error = 2.220446049250313e-16 relative error = 1.619675319459699e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3321 Order of pole (three term test) = -4.219 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y1[1] (analytic) = 1.924909059857313 y1[1] (numeric) = 1.924909059857313 absolute error = 2.220446049250313e-16 relative error = 1.153532961923358e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.380188415123162 y2[1] (numeric) = 1.380188415123161 absolute error = 2.220446049250313e-16 relative error = 1.608799222570037e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.339 Order of pole (three term test) = -4.387 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y1[1] (analytic) = 1.921060994002885 y1[1] (numeric) = 1.921060994002885 absolute error = 2.220446049250313e-16 relative error = 1.155843596940462e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.389418342308651 y2[1] (numeric) = 1.38941834230865 absolute error = 4.440892098500626e-16 relative error = 3.196223889718961e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3458 Order of pole (three term test) = -4.559 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y1[1] (analytic) = 1.917120822816605 y1[1] (numeric) = 1.917120822816605 absolute error = 2.220446049250313e-16 relative error = 1.158219149687221e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.398609327984423 y2[1] (numeric) = 1.398609327984423 absolute error = 4.440892098500626e-16 relative error = 3.175219848490876e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3524 Order of pole (three term test) = -4.734 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y1[1] (analytic) = 1.913088940312308 y1[1] (numeric) = 1.913088940312308 absolute error = 2.220446049250313e-16 relative error = 1.16066012534045e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.40776045305957 y2[1] (numeric) = 1.40776045305957 absolute error = 4.440892098500626e-16 relative error = 3.15457938092306e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3589 Order of pole (three term test) = -4.912 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y1[1] (analytic) = 1.908965749674885 y1[1] (numeric) = 1.908965749674885 absolute error = 2.220446049250313e-16 relative error = 1.163167044578184e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.416870802429211 y2[1] (numeric) = 1.41687080242921 absolute error = 4.440892098500626e-16 relative error = 3.134295724696112e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3653 Order of pole (three term test) = -5.093 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y1[1] (analytic) = 1.904751663219963 y1[1] (numeric) = 1.904751663219963 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.425939465066 y2[1] (numeric) = 1.425939465065999 absolute error = 4.440892098500626e-16 relative error = 3.114362290474287e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3715 Order of pole (three term test) = -5.278 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y1[1] (analytic) = 1.900447102352677 y1[1] (numeric) = 1.900447102352677 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.43496553411123 y2[1] (numeric) = 1.43496553411123 absolute error = 4.440892098500626e-16 relative error = 3.09477265685769e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3776 Order of pole (three term test) = -5.466 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y1[1] (analytic) = 1.896052497525525 y1[1] (numeric) = 1.896052497525525 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.44394810696552 y2[1] (numeric) = 1.44394810696552 absolute error = 4.440892098500626e-16 relative error = 3.075520565509263e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3835 Order of pole (three term test) = -5.657 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y1[1] (analytic) = 1.891568288195329 y1[1] (numeric) = 1.891568288195329 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.452886285379068 y2[1] (numeric) = 1.452886285379068 absolute error = 4.440892098500626e-16 relative error = 3.056599916449735e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3892 Order of pole (three term test) = -5.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y1[1] (analytic) = 1.886994922779284 y1[1] (numeric) = 1.886994922779284 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.461779175541483 y2[1] (numeric) = 1.461779175541483 absolute error = 4.440892098500626e-16 relative error = 3.038004763514023e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3949 Order of pole (three term test) = -6.047 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y1[1] (analytic) = 1.882332858610121 y1[1] (numeric) = 1.882332858610122 absolute error = 2.220446049250313e-16 relative error = 1.179624548917373e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.470625888171158 y2[1] (numeric) = 1.470625888171158 absolute error = 4.440892098500626e-16 relative error = 3.019729309962871e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4003 Order of pole (three term test) = -6.246 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y1[1] (analytic) = 1.877582561890373 y1[1] (numeric) = 1.877582561890373 absolute error = 2.220446049250313e-16 relative error = 1.182609007091939e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.479425538604203 y2[1] (numeric) = 1.479425538604203 absolute error = 4.440892098500626e-16 relative error = 3.001767904243754e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4056 Order of pole (three term test) = -6.448 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y1[1] (analytic) = 1.872744507645751 y1[1] (numeric) = 1.872744507645751 absolute error = 2.220446049250313e-16 relative error = 1.18566416304254e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.488177246882908 y2[1] (numeric) = 1.488177246882907 absolute error = 4.440892098500626e-16 relative error = 2.984115035895346e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4107 Order of pole (three term test) = -6.653 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y1[1] (analytic) = 1.86781917967765 y1[1] (numeric) = 1.86781917967765 absolute error = 2.220446049250313e-16 relative error = 1.188790688846829e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.496880137843737 y2[1] (numeric) = 1.496880137843737 absolute error = 4.440892098500626e-16 relative error = 2.966765331590111e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4157 Order of pole (three term test) = -6.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y1[1] (analytic) = 1.862807070514761 y1[1] (numeric) = 1.862807070514761 absolute error = 2.220446049250313e-16 relative error = 1.191989274894004e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.505533341204847 y2[1] (numeric) = 1.505533341204847 absolute error = 4.440892098500626e-16 relative error = 2.949713551309778e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4205 Order of pole (three term test) = -7.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y1[1] (analytic) = 1.857708681363824 y1[1] (numeric) = 1.857708681363824 absolute error = 2.220446049250313e-16 relative error = 1.195260630219044e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.514135991653113 y2[1] (numeric) = 1.514135991653113 absolute error = 4.440892098500626e-16 relative error = 2.932954584648714e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4251 Order of pole (three term test) = -7.281 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y1[1] (analytic) = 1.852524522059505 y1[1] (numeric) = 1.852524522059506 absolute error = 2.220446049250313e-16 relative error = 1.198605482847686e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.522687228930659 y2[1] (numeric) = 1.522687228930659 absolute error = 4.440892098500626e-16 relative error = 2.916483447240403e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4295 Order of pole (three term test) = -7.496 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y1[1] (analytic) = 1.847255111013416 y1[1] (numeric) = 1.847255111013416 absolute error = 2.220446049250313e-16 relative error = 1.20202458015242e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.531186197920884 y2[1] (numeric) = 1.531186197920883 absolute error = 6.661338147750939e-16 relative error = 4.350442915953668e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4338 Order of pole (three term test) = -7.712 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y1[1] (analytic) = 1.841900975162269 y1[1] (numeric) = 1.841900975162269 absolute error = 2.220446049250313e-16 relative error = 1.205518689219813e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.53963204873397 y2[1] (numeric) = 1.539632048733969 absolute error = 6.661338147750939e-16 relative error = 4.326577998443536e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4379 Order of pole (three term test) = -7.931 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y1[1] (analytic) = 1.836462649915187 y1[1] (numeric) = 1.836462649915187 absolute error = 2.220446049250313e-16 relative error = 1.209088597229494e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.548023936791874 y2[1] (numeric) = 1.548023936791873 absolute error = 6.661338147750939e-16 relative error = 4.303123478539939e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4418 Order of pole (three term test) = -8.151 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y1[1] (analytic) = 1.830940679100163 y1[1] (numeric) = 1.830940679100164 absolute error = 4.440892098500626e-16 relative error = 2.425470223690236e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.556361022912784 y2[1] (numeric) = 1.556361022912784 absolute error = 6.661338147750939e-16 relative error = 4.280072585783478e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4456 Order of pole (three term test) = -8.373 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y1[1] (analytic) = 1.825335614909678 y1[1] (numeric) = 1.825335614909678 absolute error = 4.440892098500626e-16 relative error = 2.432918123235311e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.564642473395036 y2[1] (numeric) = 1.564642473395035 absolute error = 6.661338147750939e-16 relative error = 4.257418714511086e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4492 Order of pole (three term test) = -8.598 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y1[1] (analytic) = 1.819648017845479 y1[1] (numeric) = 1.81964801784548 absolute error = 4.440892098500626e-16 relative error = 2.440522592802746e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.572867460100482 y2[1] (numeric) = 1.572867460100481 absolute error = 6.661338147750939e-16 relative error = 4.235155419468964e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4526 Order of pole (three term test) = -8.824 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y1[1] (analytic) = 1.813878456662534 y1[1] (numeric) = 1.813878456662534 absolute error = 4.440892098500626e-16 relative error = 2.448285375565735e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.581035160537305 y2[1] (numeric) = 1.581035160537305 absolute error = 6.661338147750939e-16 relative error = 4.213276411567674e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4558 Order of pole (three term test) = -9.051 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y1[1] (analytic) = 1.808027508312152 y1[1] (numeric) = 1.808027508312152 absolute error = 4.440892098500626e-16 relative error = 2.456208259047084e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.58914475794227 y2[1] (numeric) = 1.589144757942269 absolute error = 6.661338147750939e-16 relative error = 4.191775553774271e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.85 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4588 Order of pole (three term test) = -9.281 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y1[1] (analytic) = 1.802095757884292 y1[1] (numeric) = 1.802095757884293 absolute error = 2.220446049250313e-16 relative error = 1.232146538015924e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.597195441362392 y2[1] (numeric) = 1.597195441362392 absolute error = 4.440892098500626e-16 relative error = 2.780431238091055e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4617 Order of pole (three term test) = -9.511 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y1[1] (analytic) = 1.796083798549056 y1[1] (numeric) = 1.796083798549056 absolute error = 2.220446049250313e-16 relative error = 1.236270852754239e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.60518640573604 y2[1] (numeric) = 1.605186405736039 absolute error = 4.440892098500626e-16 relative error = 2.766589651289942e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.44 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4643 Order of pole (three term test) = -9.743 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y1[1] (analytic) = 1.789992231497365 y1[1] (numeric) = 1.789992231497365 absolute error = 2.220446049250313e-16 relative error = 1.240478036819671e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.613116851973434 y2[1] (numeric) = 1.613116851973434 absolute error = 6.661338147750939e-16 relative error = 4.129482708956687e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4668 Order of pole (three term test) = -9.977 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y1[1] (analytic) = 1.783821665880849 y1[1] (numeric) = 1.783821665880849 absolute error = 2.220446049250313e-16 relative error = 1.244769077380759e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.62098598703656 y2[1] (numeric) = 1.620985987036559 absolute error = 6.661338147750939e-16 relative error = 4.109435985889678e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.05 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4691 Order of pole (three term test) = -10.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y1[1] (analytic) = 1.777572718750928 y1[1] (numeric) = 1.777572718750928 absolute error = 2.220446049250313e-16 relative error = 1.249144986209389e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.628793024018469 y2[1] (numeric) = 1.628793024018468 absolute error = 6.661338147750939e-16 relative error = 4.089738873829684e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4712 Order of pole (three term test) = -10.45 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y1[1] (analytic) = 1.771246014997106 y1[1] (numeric) = 1.771246014997107 absolute error = 2.220446049250313e-16 relative error = 1.253606800212866e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.636537182221968 y2[1] (numeric) = 1.636537182221968 absolute error = 6.661338147750939e-16 relative error = 4.070386068898642e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4731 Order of pole (three term test) = -10.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y1[1] (analytic) = 1.764842187284488 y1[1] (numeric) = 1.764842187284488 absolute error = 2.220446049250313e-16 relative error = 1.258155581982574e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.644217687237691 y2[1] (numeric) = 1.644217687237691 absolute error = 6.661338147750939e-16 relative error = 4.051372393969365e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4749 Order of pole (three term test) = -10.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y1[1] (analytic) = 1.758361875990508 y1[1] (numeric) = 1.758361875990508 absolute error = 4.440892098500626e-16 relative error = 2.525584840719442e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.651833771021537 y2[1] (numeric) = 1.651833771021537 absolute error = 6.661338147750939e-16 relative error = 4.032692795493213e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.33 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4764 Order of pole (three term test) = -11.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y1[1] (analytic) = 1.751805729140895 y1[1] (numeric) = 1.751805729140895 absolute error = 4.440892098500626e-16 relative error = 2.535036862037487e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.659384671971474 y2[1] (numeric) = 1.659384671971473 absolute error = 6.661338147750939e-16 relative error = 4.014342340427172e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4777 Order of pole (three term test) = -11.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y1[1] (analytic) = 1.74517440234487 y1[1] (numeric) = 1.745174402344871 absolute error = 4.440892098500626e-16 relative error = 2.544669514137788e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.666869635003698 y2[1] (numeric) = 1.666869635003698 absolute error = 6.661338147750939e-16 relative error = 3.996316213256929e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4789 Order of pole (three term test) = -11.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y1[1] (analytic) = 1.738468558729588 y1[1] (numeric) = 1.738468558729588 absolute error = 4.440892098500626e-16 relative error = 2.554485139349242e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.674287911628145 y2[1] (numeric) = 1.674287911628145 absolute error = 6.661338147750939e-16 relative error = 3.978609713112713e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.35 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4799 Order of pole (three term test) = -11.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y1[1] (analytic) = 1.731688868873821 y1[1] (numeric) = 1.731688868873821 absolute error = 4.440892098500626e-16 relative error = 2.564486137390661e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.681638760023335 y2[1] (numeric) = 1.681638760023334 absolute error = 6.661338147750939e-16 relative error = 3.961218250974725e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4806 Order of pole (three term test) = -12.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y1[1] (analytic) = 1.724836010740905 y1[1] (numeric) = 1.724836010740905 absolute error = 4.440892098500626e-16 relative error = 2.574674966690333e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.688921445110552 y2[1] (numeric) = 1.688921445110551 absolute error = 4.440892098500626e-16 relative error = 2.629424897976791e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.06 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4812 Order of pole (three term test) = -12.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y1[1] (analytic) = 1.717910669610943 y1[1] (numeric) = 1.717910669610943 absolute error = 4.440892098500626e-16 relative error = 2.585054145746915e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.696135238627357 y2[1] (numeric) = 1.696135238627357 absolute error = 4.440892098500626e-16 relative error = 2.61824175181605e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4816 Order of pole (three term test) = -12.6 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y1[1] (analytic) = 1.710913538012277 y1[1] (numeric) = 1.710913538012277 absolute error = 4.440892098500626e-16 relative error = 2.595626254533009e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.703279419200411 y2[1] (numeric) = 1.70327941920041 absolute error = 4.440892098500626e-16 relative error = 2.607259882577201e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4818 Order of pole (three term test) = -12.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y1[1] (analytic) = 1.703845315652236 y1[1] (numeric) = 1.703845315652236 absolute error = 2.220446049250313e-16 relative error = 1.303196967971427e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.710353272417608 y2[1] (numeric) = 1.710353272417608 absolute error = 4.440892098500626e-16 relative error = 2.596476511676072e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4818 Order of pole (three term test) = -13.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y1[1] (analytic) = 1.696706709347165 y1[1] (numeric) = 1.696706709347165 absolute error = 2.220446049250313e-16 relative error = 1.308679948642783e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.717356090899523 y2[1] (numeric) = 1.717356090899523 absolute error = 4.440892098500626e-16 relative error = 2.585888926608435e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4816 Order of pole (three term test) = -13.33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y1[1] (analytic) = 1.689498432951747 y1[1] (numeric) = 1.689498432951747 absolute error = 2.220446049250313e-16 relative error = 1.314263455912735e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.724287174370143 y2[1] (numeric) = 1.724287174370142 absolute error = 4.440892098500626e-16 relative error = 2.575494479405856e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4812 Order of pole (three term test) = -13.57 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y1[1] (analytic) = 1.682221207287613 y1[1] (numeric) = 1.682221207287613 absolute error = 4.440892098500626e-16 relative error = 2.63989782037111e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.731145829726896 y2[1] (numeric) = 1.731145829726896 absolute error = 4.440892098500626e-16 relative error = 2.565290585138755e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4806 Order of pole (three term test) = -13.81 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y1[1] (analytic) = 1.674875760071267 y1[1] (numeric) = 1.674875760071267 absolute error = 2.220446049250313e-16 relative error = 1.325737766457276e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.737931371109963 y2[1] (numeric) = 1.737931371109963 absolute error = 4.440892098500626e-16 relative error = 2.55527472046515e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4799 Order of pole (three term test) = -14.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y1[1] (analytic) = 1.667462825841308 y1[1] (numeric) = 1.667462825841308 absolute error = 4.440892098500626e-16 relative error = 2.663263030322732e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.74464311997086 y2[1] (numeric) = 1.744643119970859 absolute error = 4.440892098500626e-16 relative error = 2.545444422223613e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4789 Order of pole (three term test) = -14.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y1[1] (analytic) = 1.659983145884982 y1[1] (numeric) = 1.659983145884982 absolute error = 4.440892098500626e-16 relative error = 2.675263366082592e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.751280405140293 y2[1] (numeric) = 1.751280405140293 absolute error = 4.440892098500626e-16 relative error = 2.53579728606903e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4778 Order of pole (three term test) = -14.53 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y1[1] (analytic) = 1.652437468164051 y1[1] (numeric) = 1.652437468164052 absolute error = 2.220446049250313e-16 relative error = 1.343739834050937e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.757842562895277 y2[1] (numeric) = 1.757842562895277 absolute error = 4.440892098500626e-16 relative error = 2.526330965149801e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4764 Order of pole (three term test) = -14.77 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y1[1] (analytic) = 1.644826547240001 y1[1] (numeric) = 1.644826547240001 absolute error = 2.220446049250313e-16 relative error = 1.349957570283745e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.764328937025506 y2[1] (numeric) = 1.764328937025505 absolute error = 4.440892098500626e-16 relative error = 2.517043168825172e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4749 Order of pole (three term test) = -15.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y1[1] (analytic) = 1.63715114419858 y1[1] (numeric) = 1.63715114419858 absolute error = 2.220446049250313e-16 relative error = 1.356286532931734e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.77073887889897 y2[1] (numeric) = 1.770738878898969 absolute error = 4.440892098500626e-16 relative error = 2.507931661421437e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4732 Order of pole (three term test) = -15.24 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y1[1] (analytic) = 1.629412026573696 y1[1] (numeric) = 1.629412026573697 absolute error = 2.220446049250313e-16 relative error = 1.362728403275281e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.777071747526824 y2[1] (numeric) = 1.777071747526824 absolute error = 4.440892098500626e-16 relative error = 2.498994261025802e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4712 Order of pole (three term test) = -15.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y1[1] (analytic) = 1.621609968270664 y1[1] (numeric) = 1.621609968270664 absolute error = 2.220446049250313e-16 relative error = 1.369284903704845e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.783326909627484 y2[1] (numeric) = 1.783326909627483 absolute error = 4.440892098500626e-16 relative error = 2.490228838316737e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4691 Order of pole (three term test) = -15.72 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y1[1] (analytic) = 1.613745749488811 y1[1] (numeric) = 1.613745749488811 absolute error = 2.220446049250313e-16 relative error = 1.375957798775729e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.789503739689951 y2[1] (numeric) = 1.78950373968995 absolute error = 6.661338147750939e-16 relative error = 3.722449973144555e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4668 Order of pole (three term test) = -15.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y1[1] (analytic) = 1.605820156643462 y1[1] (numeric) = 1.605820156643462 absolute error = 2.220446049250313e-16 relative error = 1.382748896297056e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.795601620036366 y2[1] (numeric) = 1.795601620036366 absolute error = 6.661338147750939e-16 relative error = 3.709808497285732e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4644 Order of pole (three term test) = -16.18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y1[1] (analytic) = 1.597833982287298 y1[1] (numeric) = 1.597833982287298 absolute error = 2.220446049250313e-16 relative error = 1.38966004845619e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.801619940883778 y2[1] (numeric) = 1.801619940883777 absolute error = 6.661338147750939e-16 relative error = 3.697415862572683e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4617 Order of pole (three term test) = -16.42 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y1[1] (analytic) = 1.589788025031098 y1[1] (numeric) = 1.589788025031098 absolute error = 2.220446049250313e-16 relative error = 1.396693152979863e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.807558100405115 y2[1] (numeric) = 1.807558100405114 absolute error = 6.661338147750939e-16 relative error = 3.685269174063054e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4589 Order of pole (three term test) = -16.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y1[1] (analytic) = 1.581683089463883 y1[1] (numeric) = 1.581683089463883 absolute error = 2.220446049250313e-16 relative error = 1.403850154333344e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.813415504789374 y2[1] (numeric) = 1.813415504789373 absolute error = 6.661338147750939e-16 relative error = 3.673365607693227e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4558 Order of pole (three term test) = -16.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y1[1] (analytic) = 1.573519986072456 y1[1] (numeric) = 1.573519986072456 absolute error = 2.220446049250313e-16 relative error = 1.411133044959029e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.819191568300999 y2[1] (numeric) = 1.819191568300998 absolute error = 8.881784197001252e-16 relative error = 4.882269878425302e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4526 Order of pole (three term test) = -17.1 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y1[1] (analytic) = 1.565299531160354 y1[1] (numeric) = 1.565299531160354 absolute error = 2.220446049250313e-16 relative error = 1.418543866555879e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.82488571333845 y2[1] (numeric) = 1.82488571333845 absolute error = 8.881784197001252e-16 relative error = 4.86703585440038e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4492 Order of pole (three term test) = -17.33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y1[1] (analytic) = 1.557022546766217 y1[1] (numeric) = 1.557022546766217 absolute error = 2.220446049250313e-16 relative error = 1.426084711401233e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.830497370491971 y2[1] (numeric) = 1.83049737049197 absolute error = 1.110223024625157e-15 relative error = 6.06514405604838e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4457 Order of pole (three term test) = -17.55 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y1[1] (analytic) = 1.548689860581587 y1[1] (numeric) = 1.548689860581587 absolute error = 2.220446049250313e-16 relative error = 1.433757723716522e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.836025978600521 y2[1] (numeric) = 1.83602597860052 absolute error = 1.110223024625157e-15 relative error = 6.046880804330475e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4419 Order of pole (three term test) = -17.78 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y1[1] (analytic) = 1.540302305868139 y1[1] (numeric) = 1.540302305868139 absolute error = 2.220446049250313e-16 relative error = 1.44156510107854e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.841470984807897 y2[1] (numeric) = 1.841470984807896 absolute error = 1.110223024625157e-15 relative error = 6.029000911686781e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.438 Order of pole (three term test) = -18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.010000000000001 y1[1] (analytic) = 1.531860721374355 y1[1] (numeric) = 1.531860721374355 absolute error = 2.220446049250313e-16 relative error = 1.449509095877968e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.846831844618016 y2[1] (numeric) = 1.846831844618015 absolute error = 1.110223024625157e-15 relative error = 6.011500331557184e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4339 Order of pole (three term test) = -18.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.020000000000001 y1[1] (analytic) = 1.523365951251649 y1[1] (numeric) = 1.523365951251649 absolute error = 2.220446049250313e-16 relative error = 1.457592016826895e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.852108021949363 y2[1] (numeric) = 1.852108021949362 absolute error = 1.110223024625157e-15 relative error = 5.994375119959985e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4296 Order of pole (three term test) = -18.43 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.030000000000001 y1[1] (analytic) = 1.514818844969955 y1[1] (numeric) = 1.514818844969955 absolute error = 4.440892098500626e-16 relative error = 2.931632461034447e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.857298989188604 y2[1] (numeric) = 1.857298989188603 absolute error = 1.110223024625157e-15 relative error = 5.977621433532242e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4252 Order of pole (three term test) = -18.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.040000000000001 y1[1] (analytic) = 1.506220257232778 y1[1] (numeric) = 1.506220257232778 absolute error = 2.220446049250313e-16 relative error = 1.474184163031845e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.862404227243339 y2[1] (numeric) = 1.862404227243338 absolute error = 1.110223024625157e-15 relative error = 5.961235527630149e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4205 Order of pole (three term test) = -18.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.050000000000001 y1[1] (analytic) = 1.497571047891726 y1[1] (numeric) = 1.497571047891727 absolute error = 2.220446049250313e-16 relative error = 1.482698301610629e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.867423225594017 y2[1] (numeric) = 1.867423225594016 absolute error = 1.110223024625157e-15 relative error = 5.945213754487822e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4158 Order of pole (three term test) = -19.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.060000000000001 y1[1] (analytic) = 1.488872081860527 y1[1] (numeric) = 1.488872081860527 absolute error = 2.220446049250313e-16 relative error = 1.491361196373294e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.872355482344987 y2[1] (numeric) = 1.872355482344986 absolute error = 1.110223024625157e-15 relative error = 5.929552561432856e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4108 Order of pole (three term test) = -19.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.070000000000001 y1[1] (analytic) = 1.480124229028533 y1[1] (numeric) = 1.480124229028534 absolute error = 2.220446049250313e-16 relative error = 1.500175462101369e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.877200504274682 y2[1] (numeric) = 1.877200504274681 absolute error = 1.110223024625157e-15 relative error = 5.914248489157144e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4057 Order of pole (three term test) = -19.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.080000000000001 y1[1] (analytic) = 1.471328364173739 y1[1] (numeric) = 1.47132836417374 absolute error = 2.220446049250313e-16 relative error = 1.509143780081518e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.881957806884948 y2[1] (numeric) = 1.881957806884947 absolute error = 1.110223024625157e-15 relative error = 5.899298170041435e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4004 Order of pole (three term test) = -19.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.090000000000001 y1[1] (analytic) = 1.4624853668753 y1[1] (numeric) = 1.4624853668753 absolute error = 2.220446049250313e-16 relative error = 1.518268900012619e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.886626914449488 y2[1] (numeric) = 1.886626914449486 absolute error = 1.110223024625157e-15 relative error = 5.88469832653223e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.395 Order of pole (three term test) = -19.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.100000000000001 y1[1] (analytic) = 1.453596121425577 y1[1] (numeric) = 1.453596121425577 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.891207360061436 y2[1] (numeric) = 1.891207360061435 absolute error = 1.110223024625157e-15 relative error = 5.870445769569611e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3894 Order of pole (three term test) = -20.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.110000000000001 y1[1] (analytic) = 1.444661516741706 y1[1] (numeric) = 1.444661516741706 absolute error = 2.220446049250313e-16 relative error = 1.537000898493035e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.895698685680048 y2[1] (numeric) = 1.895698685680047 absolute error = 1.110223024625157e-15 relative error = 5.856537397064681e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3836 Order of pole (three term test) = -20.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.120000000000001 y1[1] (analytic) = 1.435682446276711 y1[1] (numeric) = 1.435682446276712 absolute error = 2.220446049250313e-16 relative error = 1.546613636608013e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.900100442176505 y2[1] (numeric) = 1.900100442176504 absolute error = 1.110223024625157e-15 relative error = 5.842970192425359e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3777 Order of pole (three term test) = -20.46 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.130000000000001 y1[1] (analytic) = 1.426659807930157 y1[1] (numeric) = 1.426659807930157 absolute error = 2.220446049250313e-16 relative error = 1.55639490010713e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.904412189378826 y2[1] (numeric) = 1.904412189378825 absolute error = 1.110223024625157e-15 relative error = 5.829741223129247e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3717 Order of pole (three term test) = -20.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.140000000000001 y1[1] (analytic) = 1.417594503958357 y1[1] (numeric) = 1.417594503958358 absolute error = 4.440892098500626e-16 relative error = 3.132695623537124e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.908633496115884 y2[1] (numeric) = 1.908633496115882 absolute error = 1.110223024625157e-15 relative error = 5.81684763934243e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3655 Order of pole (three term test) = -20.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.150000000000001 y1[1] (analytic) = 1.408487440884157 y1[1] (numeric) = 1.408487440884157 absolute error = 4.440892098500626e-16 relative error = 3.152951151423064e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.912763940260521 y2[1] (numeric) = 1.91276394026052 absolute error = 1.332267629550188e-15 relative error = 6.965144007099648e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3591 Order of pole (three term test) = -21.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.160000000000001 y1[1] (analytic) = 1.399339529406272 y1[1] (numeric) = 1.399339529406273 absolute error = 4.440892098500626e-16 relative error = 3.173562959652014e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.916803108771767 y2[1] (numeric) = 1.916803108771766 absolute error = 1.332267629550188e-15 relative error = 6.950466761314192e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3526 Order of pole (three term test) = -21.19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.170000000000001 y1[1] (analytic) = 1.39015168430823 y1[1] (numeric) = 1.39015168430823 absolute error = 4.440892098500626e-16 relative error = 3.194537796579021e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.920750597736136 y2[1] (numeric) = 1.920750597736135 absolute error = 1.332267629550188e-15 relative error = 6.936182298318404e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.346 Order of pole (three term test) = -21.37 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.180000000000001 y1[1] (analytic) = 1.380924824366881 y1[1] (numeric) = 1.380924824366881 absolute error = 4.440892098500626e-16 relative error = 3.215882588349197e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.924606012408021 y2[1] (numeric) = 1.924606012408019 absolute error = 1.332267629550188e-15 relative error = 6.922287579696828e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3392 Order of pole (three term test) = -21.54 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.190000000000001 y1[1] (analytic) = 1.371659872260532 y1[1] (numeric) = 1.371659872260533 absolute error = 4.440892098500626e-16 relative error = 3.237604444301426e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.928368967249167 y2[1] (numeric) = 1.928368967249166 absolute error = 1.332267629550188e-15 relative error = 6.908779658753157e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3323 Order of pole (three term test) = -21.71 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.200000000000001 y1[1] (analytic) = 1.362357754476673 y1[1] (numeric) = 1.362357754476673 absolute error = 6.661338147750939e-16 relative error = 4.889565993852901e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.932039085967227 y2[1] (numeric) = 1.932039085967225 absolute error = 1.332267629550188e-15 relative error = 6.895655679156313e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3253 Order of pole (three term test) = -21.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.210000000000001 y1[1] (analytic) = 1.35301940121933 y1[1] (numeric) = 1.35301940121933 absolute error = 6.661338147750939e-16 relative error = 4.923313103823787e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.935616001553386 y2[1] (numeric) = 1.935616001553385 absolute error = 1.332267629550188e-15 relative error = 6.882912873633022e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3181 Order of pole (three term test) = -22.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.220000000000001 y1[1] (analytic) = 1.343645746316046 y1[1] (numeric) = 1.343645746316047 absolute error = 6.661338147750939e-16 relative error = 4.957659536388016e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.939099356319068 y2[1] (numeric) = 1.939099356319067 absolute error = 1.332267629550188e-15 relative error = 6.870548562705885e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3108 Order of pole (three term test) = -22.19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.230000000000001 y1[1] (analytic) = 1.334237727124502 y1[1] (numeric) = 1.334237727124503 absolute error = 6.661338147750939e-16 relative error = 4.992617141854624e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.942488801931698 y2[1] (numeric) = 1.942488801931697 absolute error = 1.110223024625157e-15 relative error = 5.715466794563248e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3034 Order of pole (three term test) = -22.34 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.240000000000001 y1[1] (analytic) = 1.324796284438776 y1[1] (numeric) = 1.324796284438776 absolute error = 6.661338147750939e-16 relative error = 5.028198090525961e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.945783999449539 y2[1] (numeric) = 1.945783999449538 absolute error = 1.110223024625157e-15 relative error = 5.705787615373741e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2959 Order of pole (three term test) = -22.49 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.250000000000001 y1[1] (analytic) = 1.315322362395268 y1[1] (numeric) = 1.315322362395269 absolute error = 6.661338147750939e-16 relative error = 5.064414882767073e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.948984619355586 y2[1] (numeric) = 1.948984619355585 absolute error = 1.110223024625157e-15 relative error = 5.696417578668432e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2882 Order of pole (three term test) = -22.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.260000000000001 y1[1] (analytic) = 1.305816908378288 y1[1] (numeric) = 1.305816908378289 absolute error = 8.881784197001252e-16 relative error = 6.801707145936454e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.952090341590516 y2[1] (numeric) = 1.952090341590515 absolute error = 1.110223024625157e-15 relative error = 5.687354734415487e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2804 Order of pole (three term test) = -22.78 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.270000000000001 y1[1] (analytic) = 1.296280872925318 y1[1] (numeric) = 1.296280872925319 absolute error = 8.881784197001252e-16 relative error = 6.851743617074072e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.955100855584692 y2[1] (numeric) = 1.955100855584691 absolute error = 1.110223024625157e-15 relative error = 5.678597201028451e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2725 Order of pole (three term test) = -22.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.280000000000001 y1[1] (analytic) = 1.286715209631955 y1[1] (numeric) = 1.286715209631956 absolute error = 8.881784197001252e-16 relative error = 6.902680663533737e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.958015860289225 y2[1] (numeric) = 1.958015860289224 absolute error = 1.110223024625157e-15 relative error = 5.67014316452555e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2645 Order of pole (three term test) = -23.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.290000000000001 y1[1] (analytic) = 1.277120875056557 y1[1] (numeric) = 1.277120875056558 absolute error = 8.881784197001252e-16 relative error = 6.954536857451277e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.960835064206073 y2[1] (numeric) = 1.960835064206072 absolute error = 1.110223024625157e-15 relative error = 5.661990877721667e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2564 Order of pole (three term test) = -23.19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.300000000000001 y1[1] (analytic) = 1.267498828624587 y1[1] (numeric) = 1.267498828624587 absolute error = 8.881784197001252e-16 relative error = 7.007331286167129e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.963558185417193 y2[1] (numeric) = 1.963558185417192 absolute error = 1.110223024625157e-15 relative error = 5.654138659452404e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2482 Order of pole (three term test) = -23.31 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.310000000000001 y1[1] (analytic) = 1.257850032532669 y1[1] (numeric) = 1.25785003253267 absolute error = 8.881784197001252e-16 relative error = 7.061083569014874e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.966184951612734 y2[1] (numeric) = 1.966184951612733 absolute error = 1.110223024625157e-15 relative error = 5.646584893829608e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2399 Order of pole (three term test) = -23.43 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.320000000000001 y1[1] (analytic) = 1.248175451652372 y1[1] (numeric) = 1.248175451652373 absolute error = 8.881784197001252e-16 relative error = 7.115813874758778e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.968715100118265 y2[1] (numeric) = 1.968715100118264 absolute error = 1.110223024625157e-15 relative error = 5.639328029527801e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2315 Order of pole (three term test) = -23.55 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.330000000000001 y1[1] (analytic) = 1.238476053433722 y1[1] (numeric) = 1.238476053433723 absolute error = 8.881784197001252e-16 relative error = 7.17154293970898e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.971148377921045 y2[1] (numeric) = 1.971148377921044 absolute error = 1.110223024625157e-15 relative error = 5.632366579100962e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.223 Order of pole (three term test) = -23.67 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.340000000000001 y1[1] (analytic) = 1.228752807808458 y1[1] (numeric) = 1.228752807808459 absolute error = 8.881784197001252e-16 relative error = 7.22829208654453e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.97348454169532 y2[1] (numeric) = 1.973484541695318 absolute error = 1.110223024625157e-15 relative error = 5.62569911832915e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2145 Order of pole (three term test) = -23.78 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.350000000000001 y1[1] (analytic) = 1.219006687093041 y1[1] (numeric) = 1.219006687093041 absolute error = 6.661338147750939e-16 relative error = 5.46456243290691e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.975723357826659 y2[1] (numeric) = 1.975723357826658 absolute error = 1.332267629550188e-15 relative error = 6.743189142713344e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2058 Order of pole (three term test) = -23.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.360000000000001 y1[1] (analytic) = 1.209238665891418 y1[1] (numeric) = 1.209238665891419 absolute error = 6.661338147750939e-16 relative error = 5.508704224935098e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.977864602435316 y2[1] (numeric) = 1.977864602435315 absolute error = 1.332267629550188e-15 relative error = 6.735888937542973e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.197 Order of pole (three term test) = -23.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.370000000000001 y1[1] (analytic) = 1.199449720997572 y1[1] (numeric) = 1.199449720997573 absolute error = 6.661338147750939e-16 relative error = 5.553661842707972e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.979908061398614 y2[1] (numeric) = 1.979908061398613 absolute error = 1.332267629550188e-15 relative error = 6.728936840678698e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1882 Order of pole (three term test) = -24.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.380000000000001 y1[1] (analytic) = 1.189640831297833 y1[1] (numeric) = 1.189640831297834 absolute error = 8.881784197001252e-16 relative error = 7.465937586651015e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.98185353037236 y2[1] (numeric) = 1.981853530372359 absolute error = 1.332267629550188e-15 relative error = 6.722331439396913e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1793 Order of pole (three term test) = -24.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.390000000000001 y1[1] (analytic) = 1.179812977672998 y1[1] (numeric) = 1.179812977672999 absolute error = 8.881784197001252e-16 relative error = 7.52812891965235e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.983700814811277 y2[1] (numeric) = 1.983700814811275 absolute error = 1.332267629550188e-15 relative error = 6.71607139344214e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1703 Order of pole (three term test) = -24.26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.400000000000001 y1[1] (analytic) = 1.16996714290024 y1[1] (numeric) = 1.169967142900241 absolute error = 8.881784197001252e-16 relative error = 7.591481735960665e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.98544972998846 y2[1] (numeric) = 1.985449729988459 absolute error = 1.332267629550188e-15 relative error = 6.710155434446236e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1613 Order of pole (three term test) = -24.34 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.410000000000001 y1[1] (analytic) = 1.16010431155483 y1[1] (numeric) = 1.160104311554831 absolute error = 8.881784197001252e-16 relative error = 7.656022056410978e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.98710010101385 y2[1] (numeric) = 1.987100101013849 absolute error = 1.332267629550188e-15 relative error = 6.704582365379799e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1522 Order of pole (three term test) = -24.42 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.420000000000001 y1[1] (analytic) = 1.150225469911685 y1[1] (numeric) = 1.150225469911686 absolute error = 8.881784197001252e-16 relative error = 7.721776668432845e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.98865176285172 y2[1] (numeric) = 1.988651762851719 absolute error = 1.332267629550188e-15 relative error = 6.699351060035371e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.143 Order of pole (three term test) = -24.49 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.430000000000001 y1[1] (analytic) = 1.140331605846736 y1[1] (numeric) = 1.140331605846737 absolute error = 8.881784197001252e-16 relative error = 7.788773152881456e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.990104560337178 y2[1] (numeric) = 1.990104560337177 absolute error = 1.332267629550188e-15 relative error = 6.694460462542056e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1338 Order of pole (three term test) = -24.56 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.440000000000001 y1[1] (analytic) = 1.130423708738144 y1[1] (numeric) = 1.130423708738145 absolute error = 1.110223024625157e-15 relative error = 9.821299889971901e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.991458348191687 y2[1] (numeric) = 1.991458348191685 absolute error = 1.332267629550188e-15 relative error = 6.689909586911185e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1245 Order of pole (three term test) = -24.63 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.450000000000001 y1[1] (analytic) = 1.120502769367365 y1[1] (numeric) = 1.120502769367367 absolute error = 1.110223024625157e-15 relative error = 9.908257748010629e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.992712991037589 y2[1] (numeric) = 1.992712991037587 absolute error = 1.554312234475219e-15 relative error = 7.799980436048153e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1152 Order of pole (three term test) = -24.69 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.460000000000001 y1[1] (analytic) = 1.110569779820068 y1[1] (numeric) = 1.11056977982007 absolute error = 1.110223024625157e-15 relative error = 9.996877682058231e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.993868363411645 y2[1] (numeric) = 1.993868363411643 absolute error = 1.554312234475219e-15 relative error = 7.795460638212267e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1058 Order of pole (three term test) = -24.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.470000000000001 y1[1] (analytic) = 1.100625733386931 y1[1] (numeric) = 1.100625733386932 absolute error = 1.110223024625157e-15 relative error = 1.008719849942716e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.994924349777581 y2[1] (numeric) = 1.994924349777579 absolute error = 1.554312234475219e-15 relative error = 7.791334215999284e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09641 Order of pole (three term test) = -24.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.480000000000001 y1[1] (analytic) = 1.090671624464309 y1[1] (numeric) = 1.09067162446431 absolute error = 1.110223024625157e-15 relative error = 1.017926018906424e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.99588084453764 y2[1] (numeric) = 1.995880844537639 absolute error = 1.554312234475219e-15 relative error = 7.78760034061696e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08695 Order of pole (three term test) = -24.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.490000000000001 y1[1] (analytic) = 1.0807084484548 y1[1] (numeric) = 1.080708448454801 absolute error = 1.110223024625157e-15 relative error = 1.027310396446476e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.996737752043144 y2[1] (numeric) = 1.996737752043142 absolute error = 1.554312234475219e-15 relative error = 7.784258262682635e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07747 Order of pole (three term test) = -24.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.500000000000001 y1[1] (analytic) = 1.070737201667702 y1[1] (numeric) = 1.070737201667703 absolute error = 1.332267629550188e-15 relative error = 1.244252677010891e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.997494986604055 y2[1] (numeric) = 1.997494986604053 absolute error = 1.554312234475219e-15 relative error = 7.781307311903239e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06795 Order of pole (three term test) = -24.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.510000000000001 y1[1] (analytic) = 1.060758881219385 y1[1] (numeric) = 1.060758881219386 absolute error = 1.110223024625157e-15 relative error = 1.046630901971719e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.998152472497548 y2[1] (numeric) = 1.998152472497547 absolute error = 1.332267629550188e-15 relative error = 6.667497340105123e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0584 Order of pole (three term test) = -24.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.520000000000001 y1[1] (analytic) = 1.050774484933578 y1[1] (numeric) = 1.050774484933579 absolute error = 1.332267629550188e-15 relative error = 1.26789111141617e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.998710143975583 y2[1] (numeric) = 1.998710143975582 absolute error = 1.332267629550188e-15 relative error = 6.665637003773887e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04883 Order of pole (three term test) = -24.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.530000000000001 y1[1] (analytic) = 1.04078501124159 y1[1] (numeric) = 1.040785011241591 absolute error = 1.332267629550188e-15 relative error = 1.280060353637182e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.999167945271476 y2[1] (numeric) = 1.999167945271475 absolute error = 1.554312234475219e-15 relative error = 7.774795700138899e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03924 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.540000000000001 y1[1] (analytic) = 1.030791459082465 y1[1] (numeric) = 1.030791459082466 absolute error = 1.554312234475219e-15 relative error = 1.507882337188508e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.999525830605479 y2[1] (numeric) = 1.999525830605478 absolute error = 1.554312234475219e-15 relative error = 7.773404127540357e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02964 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.550000000000001 y1[1] (analytic) = 1.020794827803091 y1[1] (numeric) = 1.020794827803093 absolute error = 1.332267629550188e-15 relative error = 1.305127723283468e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.999783764189357 y2[1] (numeric) = 1.999783764189355 absolute error = 1.554312234475219e-15 relative error = 7.772401508146474e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02002 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.560000000000001 y1[1] (analytic) = 1.010796117058266 y1[1] (numeric) = 1.010796117058268 absolute error = 1.554312234475219e-15 relative error = 1.537710927302289e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.999941720229966 y2[1] (numeric) = 1.999941720229965 absolute error = 1.554312234475219e-15 relative error = 7.771787641374341e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0104 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.570000000000001 y1[1] (analytic) = 1.000796326710732 y1[1] (numeric) = 1.000796326710734 absolute error = 1.554312234475219e-15 relative error = 1.553075478987518e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.999999682931835 y2[1] (numeric) = 1.999999682931833 absolute error = 1.554312234475219e-15 relative error = 7.771562404433612e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0007668 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.580000000000001 y1[1] (analytic) = 0.9907964567311905 y1[1] (numeric) = 0.990796456731192 absolute error = 1.443289932012704e-15 relative error = 1.456696703149674e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.99995764649874 y2[1] (numeric) = 1.999957646498739 absolute error = 1.554312234475219e-15 relative error = 7.771725752274316e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008874 Order of pole (three term test) = -0.8949 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.590000000000001 y1[1] (analytic) = 0.9807975070983063 y1[1] (numeric) = 0.9807975070983077 absolute error = 1.443289932012704e-15 relative error = 1.471547308763746e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.999815615134291 y2[1] (numeric) = 1.999815615134289 absolute error = 1.554312234475219e-15 relative error = 7.7722777175677e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01851 Order of pole (three term test) = -0.9018 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.600000000000001 y1[1] (analytic) = 0.97080047769871 y1[1] (numeric) = 0.9708004776987116 absolute error = 1.554312234475219e-15 relative error = 1.601062494488804e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.999573603041505 y2[1] (numeric) = 1.999573603041504 absolute error = 1.554312234475219e-15 relative error = 7.77321841072012e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02814 Order of pole (three term test) = -0.9135 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.610000000000001 y1[1] (analytic) = 0.9608063682270112 y1[1] (numeric) = 0.9608063682270127 absolute error = 1.554312234475219e-15 relative error = 1.617716415996922e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.999231634421391 y2[1] (numeric) = 1.999231634421389 absolute error = 1.554312234475219e-15 relative error = 7.774548019919973e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03776 Order of pole (three term test) = -0.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.620000000000001 y1[1] (analytic) = 0.9508161780858283 y1[1] (numeric) = 0.9508161780858299 absolute error = 1.554312234475219e-15 relative error = 1.634713702078925e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.998789743470524 y2[1] (numeric) = 1.998789743470522 absolute error = 1.554312234475219e-15 relative error = 7.776266811217708e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04737 Order of pole (three term test) = -0.9513 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.630000000000001 y1[1] (analytic) = 0.9408309062858505 y1[1] (numeric) = 0.9408309062858521 absolute error = 1.554312234475219e-15 relative error = 1.652063324121897e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.998247974377632 y2[1] (numeric) = 1.998247974377631 absolute error = 1.554312234475219e-15 relative error = 7.778375128638976e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05696 Order of pole (three term test) = -0.9775 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.640000000000001 y1[1] (analytic) = 0.9308515513459368 y1[1] (numeric) = 0.9308515513459383 absolute error = 1.554312234475219e-15 relative error = 1.669774554522478e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.997606381319174 y2[1] (numeric) = 1.997606381319172 absolute error = 1.332267629550188e-15 relative error = 6.669320052283718e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06652 Order of pole (three term test) = -1.008 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.650000000000001 y1[1] (analytic) = 0.9208791111932648 y1[1] (numeric) = 0.9208791111932665 absolute error = 1.665334536937735e-15 relative error = 1.808418191590656e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.996865028453919 y2[1] (numeric) = 1.996865028453917 absolute error = 1.332267629550188e-15 relative error = 6.67179609320767e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07606 Order of pole (three term test) = -1.044 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.660000000000001 y1[1] (analytic) = 0.9109145830635397 y1[1] (numeric) = 0.9109145830635414 absolute error = 1.77635683940025e-15 relative error = 1.950080581020123e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.996023989916537 y2[1] (numeric) = 1.996023989916535 absolute error = 1.332267629550188e-15 relative error = 6.674607300716342e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08556 Order of pole (three term test) = -1.085 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.670000000000001 y1[1] (analytic) = 0.9009589634012707 y1[1] (numeric) = 0.9009589634012725 absolute error = 1.77635683940025e-15 relative error = 1.971629021475303e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.99508334981018 y2[1] (numeric) = 1.995083349810179 absolute error = 1.332267629550188e-15 relative error = 6.677754238573266e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09503 Order of pole (three term test) = -1.13 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.680000000000001 y1[1] (analytic) = 0.8910132477601276 y1[1] (numeric) = 0.8910132477601294 absolute error = 1.77635683940025e-15 relative error = 1.993636844194789e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.994043202198076 y2[1] (numeric) = 1.994043202198075 absolute error = 1.332267629550188e-15 relative error = 6.681237538292055e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1045 Order of pole (three term test) = -1.18 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.690000000000001 y1[1] (analytic) = 0.8810784307033864 y1[1] (numeric) = 0.8810784307033883 absolute error = 1.887379141862766e-15 relative error = 2.142123874665761e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.992903651094118 y2[1] (numeric) = 1.992903651094117 absolute error = 1.110223024625157e-15 relative error = 5.570881582838368e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1139 Order of pole (three term test) = -1.235 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.700000000000001 y1[1] (analytic) = 0.8711555057044741 y1[1] (numeric) = 0.8711555057044759 absolute error = 1.77635683940025e-15 relative error = 2.039081229204619e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.991664810452468 y2[1] (numeric) = 1.991664810452467 absolute error = 1.110223024625157e-15 relative error = 5.574346741472703e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1232 Order of pole (three term test) = -1.294 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.710000000000001 y1[1] (analytic) = 0.8612454650476211 y1[1] (numeric) = 0.861245465047623 absolute error = 1.887379141862766e-15 relative error = 2.191453213351209e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.990326804156158 y2[1] (numeric) = 1.990326804156157 absolute error = 1.332267629550188e-15 relative error = 6.693712945874894e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1325 Order of pole (three term test) = -1.358 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.720000000000001 y1[1] (analytic) = 0.851349299728635 y1[1] (numeric) = 0.8513492997286369 absolute error = 1.887379141862766e-15 relative error = 2.216926874156545e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.988889766004701 y2[1] (numeric) = 1.9888897660047 absolute error = 1.332267629550188e-15 relative error = 6.698549373233783e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1417 Order of pole (three term test) = -1.427 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.730000000000001 y1[1] (analytic) = 0.841467999355801 y1[1] (numeric) = 0.8414679993558029 absolute error = 1.887379141862766e-15 relative error = 2.24296009272804e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.987353839700716 y2[1] (numeric) = 1.987353839700715 absolute error = 1.110223024625157e-15 relative error = 5.586438622285549e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1509 Order of pole (three term test) = -1.5 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.740000000000001 y1[1] (analytic) = 0.8316025520509217 y1[1] (numeric) = 0.8316025520509236 absolute error = 1.887379141862766e-15 relative error = 2.269568722712621e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.985719178835553 y2[1] (numeric) = 1.985719178835552 absolute error = 1.110223024625157e-15 relative error = 5.591037425927482e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1601 Order of pole (three term test) = -1.578 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.750000000000001 y1[1] (analytic) = 0.8217539443505066 y1[1] (numeric) = 0.8217539443505085 absolute error = 1.887379141862766e-15 relative error = 2.296769190873191e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.983985946873937 y2[1] (numeric) = 1.983985946873936 absolute error = 1.110223024625157e-15 relative error = 5.595921817765277e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1691 Order of pole (three term test) = -1.661 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.760000000000001 y1[1] (analytic) = 0.8119231611071186 y1[1] (numeric) = 0.8119231611071205 absolute error = 1.887379141862766e-15 relative error = 2.324578522047803e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.982154317137618 y2[1] (numeric) = 1.982154317137617 absolute error = 8.881784197001252e-16 relative error = 4.480874228716574e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1781 Order of pole (three term test) = -1.748 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.770000000000001 y1[1] (analytic) = 0.8021111853908897 y1[1] (numeric) = 0.8021111853908915 absolute error = 1.887379141862766e-15 relative error = 2.353014365387508e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.980224472788045 y2[1] (numeric) = 1.980224472788044 absolute error = 8.881784197001252e-16 relative error = 4.485241102235343e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.187 Order of pole (three term test) = -1.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.780000000000001 y1[1] (analytic) = 0.7923189983912149 y1[1] (numeric) = 0.7923189983912168 absolute error = 1.887379141862766e-15 relative error = 2.382095021948288e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.978196606808044 y2[1] (numeric) = 1.978196606808043 absolute error = 8.881784197001252e-16 relative error = 4.489838960614041e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1959 Order of pole (three term test) = -1.936 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.790000000000001 y1[1] (analytic) = 0.7825475793186341 y1[1] (numeric) = 0.7825475793186359 absolute error = 1.887379141862766e-15 relative error = 2.41183947371751e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.976070921982524 y2[1] (numeric) = 1.976070921982523 absolute error = 8.881784197001252e-16 relative error = 4.49466873794715e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2047 Order of pole (three term test) = -2.036 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.800000000000001 y1[1] (analytic) = 0.7727979053069116 y1[1] (numeric) = 0.7727979053069135 absolute error = 1.887379141862766e-15 relative error = 2.442267414160764e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.973847630878195 y2[1] (numeric) = 1.973847630878194 absolute error = 8.881784197001252e-16 relative error = 4.499731416983595e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2133 Order of pole (three term test) = -2.141 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.810000000000001 y1[1] (analytic) = 0.763070951315324 y1[1] (numeric) = 0.763070951315326 absolute error = 1.998401444325282e-15 relative error = 2.61889335569725e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.971526955822315 y2[1] (numeric) = 1.971526955822314 absolute error = 6.661338147750939e-16 relative error = 3.378771022165672e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2219 Order of pole (three term test) = -2.25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.820000000000001 y1[1] (analytic) = 0.7533676900311647 y1[1] (numeric) = 0.7533676900311667 absolute error = 1.998401444325282e-15 relative error = 2.652624303867629e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.969109128880456 y2[1] (numeric) = 1.969109128880455 absolute error = 6.661338147750939e-16 relative error = 3.382919742766246e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2305 Order of pole (three term test) = -2.363 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.830000000000001 y1[1] (analytic) = 0.743689091772476 y1[1] (numeric) = 0.743689091772478 absolute error = 1.998401444325282e-15 relative error = 2.687146371291233e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.966594391833297 y2[1] (numeric) = 1.966594391833297 absolute error = 6.661338147750939e-16 relative error = 3.387245573064566e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2389 Order of pole (three term test) = -2.481 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.840000000000001 y1[1] (analytic) = 0.7340361243910184 y1[1] (numeric) = 0.7340361243910204 absolute error = 1.998401444325282e-15 relative error = 2.722483782365921e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.963982996152448 y2[1] (numeric) = 1.963982996152447 absolute error = 6.661338147750939e-16 relative error = 3.391749399460623e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2472 Order of pole (three term test) = -2.603 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.850000000000001 y1[1] (analytic) = 0.7244097531754857 y1[1] (numeric) = 0.7244097531754878 absolute error = 2.109423746787797e-15 relative error = 2.911920687899403e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.9612752029753 y2[1] (numeric) = 1.961275202975299 absolute error = 6.661338147750939e-16 relative error = 3.396432146618453e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2554 Order of pole (three term test) = -2.729 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.860000000000001 y1[1] (analytic) = 0.7148109407549779 y1[1] (numeric) = 0.71481094075498 absolute error = 2.109423746787797e-15 relative error = 2.95102330772923e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.958471283078914 y2[1] (numeric) = 1.958471283078913 absolute error = 6.661338147750939e-16 relative error = 3.401294777873202e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2636 Order of pole (three term test) = -2.859 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.870000000000001 y1[1] (analytic) = 0.7052406470027377 y1[1] (numeric) = 0.7052406470027398 absolute error = 2.109423746787797e-15 relative error = 2.991069439563385e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.955571516852944 y2[1] (numeric) = 1.955571516852943 absolute error = 6.661338147750939e-16 relative error = 3.40633829565634e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2716 Order of pole (three term test) = -2.993 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.880000000000001 y1[1] (analytic) = 0.6956998289401654 y1[1] (numeric) = 0.6956998289401675 absolute error = 2.109423746787797e-15 relative error = 3.032088925479988e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.952576194271595 y2[1] (numeric) = 1.952576194271594 absolute error = 6.661338147750939e-16 relative error = 3.411563741939372e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2795 Order of pole (three term test) = -3.131 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.890000000000001 y1[1] (analytic) = 0.6861894406411163 y1[1] (numeric) = 0.6861894406411184 absolute error = 2.109423746787797e-15 relative error = 3.074112805957686e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.94948561486463 y2[1] (numeric) = 1.949485614864629 absolute error = 6.661338147750939e-16 relative error = 3.41697219869637e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2873 Order of pole (three term test) = -3.273 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y1[1] (analytic) = 0.6767104331364951 y1[1] (numeric) = 0.6767104331364974 absolute error = 2.220446049250313e-15 relative error = 3.281235134736633e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.946300087687414 y2[1] (numeric) = 1.946300087687413 absolute error = 4.440892098500626e-16 relative error = 2.281709858923799e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.295 Order of pole (three term test) = -3.419 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.910000000000001 y1[1] (analytic) = 0.6672637543191534 y1[1] (numeric) = 0.6672637543191555 absolute error = 2.109423746787797e-15 relative error = 3.161304256575664e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.94301993129001 y2[1] (numeric) = 1.94301993129001 absolute error = 4.440892098500626e-16 relative error = 2.285561782967521e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3025 Order of pole (three term test) = -3.569 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.920000000000001 y1[1] (analytic) = 0.6578503488491003 y1[1] (numeric) = 0.6578503488491025 absolute error = 2.220446049250313e-15 relative error = 3.375305725891841e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.939645473685324 y2[1] (numeric) = 1.939645473685324 absolute error = 4.440892098500626e-16 relative error = 2.289538041229223e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.31 Order of pole (three term test) = -3.723 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.930000000000001 y1[1] (analytic) = 0.6484711580590387 y1[1] (numeric) = 0.6484711580590409 absolute error = 2.220446049250313e-15 relative error = 3.424124607016303e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.936177052316306 y2[1] (numeric) = 1.936177052316305 absolute error = 4.440892098500626e-16 relative error = 2.293639465041617e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3173 Order of pole (three term test) = -3.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.940000000000002 y1[1] (analytic) = 0.6391271198602314 y1[1] (numeric) = 0.6391271198602336 absolute error = 2.220446049250313e-15 relative error = 3.474185307198191e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.9326150140222 y2[1] (numeric) = 1.9326150140222 absolute error = 4.440892098500626e-16 relative error = 2.297866914144554e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3245 Order of pole (three term test) = -4.041 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.950000000000002 y1[1] (analytic) = 0.6298191686487117 y1[1] (numeric) = 0.6298191686487139 absolute error = 2.220446049250313e-15 relative error = 3.525529484938224e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.928959715003869 y2[1] (numeric) = 1.928959715003868 absolute error = 2.220446049250313e-16 relative error = 1.151110638537031e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3315 Order of pole (three term test) = -4.205 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.960000000000002 y1[1] (analytic) = 0.6205482352118441 y1[1] (numeric) = 0.6205482352118463 absolute error = 2.220446049250313e-15 relative error = 3.578200570487953e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.925211520788168 y2[1] (numeric) = 1.925211520788167 absolute error = 4.440892098500626e-16 relative error = 2.306703471565845e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3385 Order of pole (three term test) = -4.373 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.970000000000002 y1[1] (analytic) = 0.6113152466352465 y1[1] (numeric) = 0.6113152466352488 absolute error = 2.331468351712829e-15 relative error = 3.813856049796752e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.921370806191395 y2[1] (numeric) = 1.921370806191394 absolute error = 4.440892098500626e-16 relative error = 2.31131444497354e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3453 Order of pole (three term test) = -4.545 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.980000000000002 y1[1] (analytic) = 0.6021211262100826 y1[1] (numeric) = 0.602121126210085 absolute error = 2.331468351712829e-15 relative error = 3.87209192673198e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.917437955281809 y2[1] (numeric) = 1.917437955281809 absolute error = 4.440892098500626e-16 relative error = 2.316055174702089e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3519 Order of pole (three term test) = -4.719 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.990000000000002 y1[1] (analytic) = 0.5929667933407331 y1[1] (numeric) = 0.5929667933407354 absolute error = 2.331468351712829e-15 relative error = 3.93187001008522e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.913413361341225 y2[1] (numeric) = 1.913413361341224 absolute error = 4.440892098500626e-16 relative error = 2.320926668656553e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3584 Order of pole (three term test) = -4.898 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.000000000000001 y1[1] (analytic) = 0.5838531634528564 y1[1] (numeric) = 0.5838531634528586 absolute error = 2.220446049250313e-15 relative error = 3.80308986615537e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.909297426825681 y2[1] (numeric) = 1.909297426825681 absolute error = 4.440892098500626e-16 relative error = 2.325929965706742e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3648 Order of pole (three term test) = -5.079 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.010000000000001 y1[1] (analytic) = 0.5747811479018466 y1[1] (numeric) = 0.5747811479018486 absolute error = 1.998401444325282e-15 relative error = 3.476804087295051e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.9050905633252 y2[1] (numeric) = 1.9050905633252 absolute error = 6.661338147750939e-16 relative error = 3.496599204252026e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.371 Order of pole (three term test) = -5.263 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.020000000000001 y1[1] (analytic) = 0.5657516538816988 y1[1] (numeric) = 0.5657516538817006 absolute error = 1.77635683940025e-15 relative error = 3.139817315976764e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.900793191522627 y2[1] (numeric) = 1.900793191522626 absolute error = 6.661338147750939e-16 relative error = 3.504504423448027e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3771 Order of pole (three term test) = -5.451 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.030000000000001 y1[1] (analytic) = 0.5567655843342902 y1[1] (numeric) = 0.5567655843342919 absolute error = 1.665334536937735e-15 relative error = 2.99108742313685e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.89640574115156 y2[1] (numeric) = 1.896405741151559 absolute error = 8.881784197001252e-16 relative error = 4.683483077628705e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.383 Order of pole (three term test) = -5.641 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.04 y1[1] (analytic) = 0.5478238378590876 y1[1] (numeric) = 0.5478238378590891 absolute error = 1.443289932012704e-15 relative error = 2.634587676310554e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.891928650953379 y2[1] (numeric) = 1.891928650953378 absolute error = 1.110223024625157e-15 relative error = 5.868207683549238e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3888 Order of pole (three term test) = -5.835 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.05 y1[1] (analytic) = 0.5389273086232869 y1[1] (numeric) = 0.5389273086232881 absolute error = 1.221245327087672e-15 relative error = 2.266066884247147e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.887362368633375 y2[1] (numeric) = 1.887362368633374 absolute error = 1.110223024625157e-15 relative error = 5.882405218395133e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3944 Order of pole (three term test) = -6.031 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.06 y1[1] (analytic) = 0.5300768862723978 y1[1] (numeric) = 0.5300768862723988 absolute error = 9.992007221626409e-16 relative error = 1.885010925847403e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.882707350815974 y2[1] (numeric) = 1.882707350815973 absolute error = 1.110223024625157e-15 relative error = 5.896949539948313e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3999 Order of pole (three term test) = -6.23 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.07 y1[1] (analytic) = 0.5212734558412802 y1[1] (numeric) = 0.521273455841281 absolute error = 8.881784197001252e-16 relative error = 1.703862741805449e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.877964062999078 y2[1] (numeric) = 1.877964062999077 absolute error = 1.332267629550188e-15 relative error = 7.094212587979868e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4052 Order of pole (three term test) = -6.432 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.08 y1[1] (analytic) = 0.512517897665641 y1[1] (numeric) = 0.5125178976656417 absolute error = 6.661338147750939e-16 relative error = 1.29972790766747e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.873132979507517 y2[1] (numeric) = 1.873132979507515 absolute error = 1.332267629550188e-15 relative error = 7.112509598226534e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4103 Order of pole (three term test) = -6.636 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.089999999999999 y1[1] (analytic) = 0.5038110872940015 y1[1] (numeric) = 0.503811087294002 absolute error = 5.551115123125783e-16 relative error = 1.101824724211836e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.868214583445613 y2[1] (numeric) = 1.868214583445611 absolute error = 1.332267629550188e-15 relative error = 7.131234502479049e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4153 Order of pole (three term test) = -6.843 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.099999999999999 y1[1] (analytic) = 0.4951538954001433 y1[1] (numeric) = 0.4951538954001436 absolute error = 3.33066907387547e-16 relative error = 6.726533113879459e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.863209366648874 y2[1] (numeric) = 1.863209366648873 absolute error = 1.554312234475219e-15 relative error = 8.34212333995921e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4201 Order of pole (three term test) = -7.053 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.109999999999999 y1[1] (analytic) = 0.4865471876960413 y1[1] (numeric) = 0.4865471876960414 absolute error = 1.665334536937735e-16 relative error = 3.422760585306502e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.858117829634809 y2[1] (numeric) = 1.858117829634808 absolute error = 1.554312234475219e-15 relative error = 8.364982078562265e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4247 Order of pole (three term test) = -7.265 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.119999999999999 y1[1] (analytic) = 0.4779918248452938 y1[1] (numeric) = 0.4779918248452938 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.852940481552877 y2[1] (numeric) = 1.852940481552875 absolute error = 1.77635683940025e-15 relative error = 9.586691300044107e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4292 Order of pole (three term test) = -7.479 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.129999999999999 y1[1] (analytic) = 0.4694886623770564 y1[1] (numeric) = 0.4694886623770562 absolute error = 1.665334536937735e-16 relative error = 3.547124074319539e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.847677840133571 y2[1] (numeric) = 1.847677840133569 absolute error = 1.77635683940025e-15 relative error = 9.613996557277733e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4335 Order of pole (three term test) = -7.695 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.139999999999998 y1[1] (analytic) = 0.46103855060049 y1[1] (numeric) = 0.4610385506004896 absolute error = 3.33066907387547e-16 relative error = 7.22427456345541e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.842330431636647 y2[1] (numeric) = 1.842330431636645 absolute error = 1.998401444325282e-15 relative error = 1.084713909084153e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4376 Order of pole (three term test) = -7.913 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.149999999999998 y1[1] (analytic) = 0.4526423345197305 y1[1] (numeric) = 0.45264233451973 absolute error = 4.440892098500626e-16 relative error = 9.811040107886882e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 1.836898790798499 y2[1] (numeric) = 1.836898790798497 absolute error = 2.220446049250313e-15 relative error = 1.208801519372271e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4415 Order of pole (three term test) = -8.133 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.159999999999998 y1[1] (analytic) = 0.4443008537493891 y1[1] (numeric) = 0.4443008537493885 absolute error = 6.106226635438361e-16 relative error = 1.374345015074542e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.831383460778684 y2[1] (numeric) = 1.831383460778682 absolute error = 2.220446049250313e-15 relative error = 1.212441903513863e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4453 Order of pole (three term test) = -8.356 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.169999999999998 y1[1] (analytic) = 0.4360149424305917 y1[1] (numeric) = 0.436014942430591 absolute error = 7.771561172376096e-16 relative error = 1.782407072806509e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.825784993105609 y2[1] (numeric) = 1.825784993105607 absolute error = 2.442490654175344e-15 relative error = 1.33777562166328e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4489 Order of pole (three term test) = -8.58 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.179999999999997 y1[1] (analytic) = 0.4277854291475653 y1[1] (numeric) = 0.4277854291475644 absolute error = 9.436895709313831e-16 relative error = 2.20598811140399e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.820103947621376 y2[1] (numeric) = 1.820103947621373 absolute error = 2.442490654175344e-15 relative error = 1.341951187660102e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4523 Order of pole (three term test) = -8.806 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.189999999999997 y1[1] (analytic) = 0.4196131368447803 y1[1] (numeric) = 0.4196131368447792 absolute error = 1.110223024625157e-15 relative error = 2.645825230766883e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.814340892425798 y2[1] (numeric) = 1.814340892425795 absolute error = 2.664535259100376e-15 relative error = 1.468596816741454e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4555 Order of pole (three term test) = -9.033 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.199999999999997 y1[1] (analytic) = 0.4114988827446567 y1[1] (numeric) = 0.4114988827446554 absolute error = 1.27675647831893e-15 relative error = 3.102697314274807e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.808496403819592 y2[1] (numeric) = 1.808496403819589 absolute error = 2.664535259100376e-15 relative error = 1.47334285734426e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.83 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4586 Order of pole (three term test) = -9.262 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.209999999999997 y1[1] (analytic) = 0.4034434782658426 y1[1] (numeric) = 0.4034434782658412 absolute error = 1.387778780781446e-15 relative error = 3.439834463917127e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.802571066246749 y2[1] (numeric) = 1.802571066246746 absolute error = 2.886579864025407e-15 relative error = 1.601368133593614e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.12 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4615 Order of pole (three term test) = -9.493 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.219999999999997 y1[1] (analytic) = 0.3954477289420731 y1[1] (numeric) = 0.3954477289420716 absolute error = 1.498801083243961e-15 relative error = 3.790137035945684e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.796565472236089 y2[1] (numeric) = 1.796565472236086 absolute error = 3.108624468950438e-15 relative error = 1.730315158000504e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4641 Order of pole (three term test) = -9.725 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.229999999999996 y1[1] (analytic) = 0.3875124343416176 y1[1] (numeric) = 0.387512434341616 absolute error = 1.665334536937735e-15 relative error = 4.297499613830799e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.790480222342007 y2[1] (numeric) = 1.790480222342004 absolute error = 3.108624468950438e-15 relative error = 1.736195926746544e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4666 Order of pole (three term test) = -9.958 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.239999999999996 y1[1] (analytic) = 0.3796383879873234 y1[1] (numeric) = 0.3796383879873215 absolute error = 1.831867990631508e-15 relative error = 4.825297042122824e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.784315925084422 y2[1] (numeric) = 1.784315925084419 absolute error = 3.33066907387547e-15 relative error = 1.866636410655744e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4689 Order of pole (three term test) = -10.19 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.249999999999996 y1[1] (analytic) = 0.371826377277264 y1[1] (numeric) = 0.3718263772772621 absolute error = 1.942890293094024e-15 relative error = 5.22526214337195e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.778073196887924 y2[1] (numeric) = 1.77807319688792 absolute error = 3.552713678800501e-15 relative error = 1.998069418637346e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.34 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4711 Order of pole (three term test) = -10.43 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.259999999999996 y1[1] (analytic) = 0.3640771834060007 y1[1] (numeric) = 0.3640771834059987 absolute error = 2.05391259555654e-15 relative error = 5.641420800781461e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.771752662020128 y2[1] (numeric) = 1.771752662020125 absolute error = 3.774758283725532e-15 relative error = 2.130522146032282e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.473 Order of pole (three term test) = -10.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.269999999999996 y1[1] (analytic) = 0.3563915812864629 y1[1] (numeric) = 0.3563915812864607 absolute error = 2.164934898019055e-15 relative error = 6.074596067068456e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.765354952529256 y2[1] (numeric) = 1.765354952529252 absolute error = 3.996802888650564e-15 relative error = 2.264022248287389e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.98 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4747 Order of pole (three term test) = -10.9 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.279999999999995 y1[1] (analytic) = 0.3487703394724578 y1[1] (numeric) = 0.3487703394724556 absolute error = 2.275957200481571e-15 relative error = 6.525661568366543e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.758880708180925 y2[1] (numeric) = 1.758880708180921 absolute error = 4.218847493575595e-15 relative error = 2.398597854847601e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4763 Order of pole (three term test) = -11.14 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.289999999999995 y1[1] (analytic) = 0.341214220081816 y1[1] (numeric) = 0.3412142200818136 absolute error = 2.386979502944087e-15 relative error = 6.995545210195927e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.752330576394174 y2[1] (numeric) = 1.75233057639417 absolute error = 4.218847493575595e-15 relative error = 2.407563704250856e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4776 Order of pole (three term test) = -11.38 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.299999999999995 y1[1] (analytic) = 0.3337239787201796 y1[1] (numeric) = 0.3337239787201771 absolute error = 2.498001805406602e-15 relative error = 7.485233200761769e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.745705212176724 y2[1] (numeric) = 1.745705212176719 absolute error = 4.440892098500626e-15 relative error = 2.54389576632086e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.98 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4788 Order of pole (three term test) = -11.62 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.309999999999995 y1[1] (analytic) = 0.326300364405443 y1[1] (numeric) = 0.3263003644054404 absolute error = 2.609024107869118e-15 relative error = 7.995774422817644e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.739005278059474 y2[1] (numeric) = 1.73900527805947 absolute error = 4.662936703425657e-15 relative error = 2.681381570404977e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.32 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4798 Order of pole (three term test) = -11.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.319999999999995 y1[1] (analytic) = 0.3189441194928514 y1[1] (numeric) = 0.3189441194928487 absolute error = 2.720046410331634e-15 relative error = 8.528285188818472e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.732231444030255 y2[1] (numeric) = 1.73223144403025 absolute error = 4.884981308350689e-15 relative error = 2.820051168789064e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4806 Order of pole (three term test) = -12.1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.329999999999994 y1[1] (analytic) = 0.3116559796007659 y1[1] (numeric) = 0.311655979600763 absolute error = 2.831068712794149e-15 relative error = 9.083954418011725e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.725384387466824 y2[1] (numeric) = 1.725384387466818 absolute error = 5.10702591327572e-15 relative error = 2.959935160172486e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4812 Order of pole (three term test) = -12.34 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.339999999999994 y1[1] (analytic) = 0.3044366735371021 y1[1] (numeric) = 0.3044366735370992 absolute error = 2.942091015256665e-15 relative error = 9.664049278537752e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.71846479306913 y2[1] (numeric) = 1.718464793069125 absolute error = 5.10702591327572e-15 relative error = 2.97185367653341e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -12.58 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.349999999999994 y1[1] (analytic) = 0.2972869232264505 y1[1] (numeric) = 0.2972869232264475 absolute error = 3.05311331771918e-15 relative error = 1.02699213425999e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.711473352790849 y2[1] (numeric) = 1.711473352790843 absolute error = 5.329070518200751e-15 relative error = 3.113732685063892e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.359999999999994 y1[1] (analytic) = 0.2902074436378839 y1[1] (numeric) = 0.2902074436378808 absolute error = 3.108624468950438e-15 relative error = 1.071173237316865e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.704410765770181 y2[1] (numeric) = 1.704410765770175 absolute error = 5.329070518200751e-15 relative error = 3.126635095966833e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.07 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.86 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.369999999999993 y1[1] (analytic) = 0.2831989427134617 y1[1] (numeric) = 0.2831989427134585 absolute error = 3.219646771412954e-15 relative error = 1.136885166506629e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.697277738259942 y2[1] (numeric) = 1.697277738259937 absolute error = 5.551115123125783e-15 relative error = 3.270599147088804e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -13.31 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.379999999999993 y1[1] (analytic) = 0.276262121297436 y1[1] (numeric) = 0.2762621212974327 absolute error = 3.33066907387547e-15 relative error = 1.205619162784001e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.690074983556941 y2[1] (numeric) = 1.690074983556936 absolute error = 5.773159728050814e-15 relative error = 3.415919284185007e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.07 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4813 Order of pole (three term test) = -13.55 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.389999999999993 y1[1] (analytic) = 0.2693976730661676 y1[1] (numeric) = 0.2693976730661642 absolute error = 3.441691376337985e-15 relative error = 1.277550521192757e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.682803221930645 y2[1] (numeric) = 1.682803221930639 absolute error = 5.773159728050814e-15 relative error = 3.430680220250226e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4807 Order of pole (three term test) = -13.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.399999999999993 y1[1] (analytic) = 0.2626062844587594 y1[1] (numeric) = 0.2626062844587558 absolute error = 3.552713678800501e-15 relative error = 1.352866968177386e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.675463180551156 y2[1] (numeric) = 1.67546318055115 absolute error = 5.995204332975845e-15 relative error = 3.578236992951214e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.32 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4799 Order of pole (three term test) = -14.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.409999999999993 y1[1] (analytic) = 0.2558886346084125 y1[1] (numeric) = 0.2558886346084089 absolute error = 3.552713678800501e-15 relative error = 1.388382756521107e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.668055593416497 y2[1] (numeric) = 1.66805559341649 absolute error = 6.439293542825908e-15 relative error = 3.860359072108025e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.96 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.479 Order of pole (three term test) = -14.27 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.419999999999992 y1[1] (analytic) = 0.2492453952745141 y1[1] (numeric) = 0.2492453952745105 absolute error = 3.635980405647388e-15 relative error = 1.458795417922481e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.660581201279206 y2[1] (numeric) = 1.6605812012792 absolute error = 6.661338147750939e-15 relative error = 4.01144981204139e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4779 Order of pole (three term test) = -14.51 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.429999999999992 y1[1] (analytic) = 0.2426772307754615 y1[1] (numeric) = 0.2426772307754577 absolute error = 3.719247132494274e-15 relative error = 1.532590066488574e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.653040751572271 y2[1] (numeric) = 1.653040751572264 absolute error = 6.883382752675971e-15 relative error = 4.164073236627058e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.25 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4765 Order of pole (three term test) = -14.75 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.439999999999992 y1[1] (analytic) = 0.2361847979222311 y1[1] (numeric) = 0.2361847979222273 absolute error = 3.774758283725532e-15 relative error = 1.598222373722991e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.645434998334377 y2[1] (numeric) = 1.64543499833437 absolute error = 6.883382752675971e-15 relative error = 4.183320981773092e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.475 Order of pole (three term test) = -14.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.449999999999992 y1[1] (analytic) = 0.2297687459526979 y1[1] (numeric) = 0.2297687459526941 absolute error = 3.83026943495679e-15 relative error = 1.66701063674923e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.63776470213451 y2[1] (numeric) = 1.637764702134503 absolute error = 7.105427357601002e-15 relative error = 4.338490961699473e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4733 Order of pole (three term test) = -15.22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.459999999999992 y1[1] (analytic) = 0.2234297164667123 y1[1] (numeric) = 0.2234297164667084 absolute error = 3.885780586188048e-15 relative error = 1.739151196016924e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.630030629995899 y2[1] (numeric) = 1.630030629995891 absolute error = 7.327471962526033e-15 relative error = 4.495297099137621e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.23 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4714 Order of pole (three term test) = -15.46 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.469999999999991 y1[1] (analytic) = 0.2171683433619402 y1[1] (numeric) = 0.2171683433619362 absolute error = 3.941291737419306e-15 relative error = 1.814855552335551e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.622233555319312 y2[1] (numeric) = 1.622233555319304 absolute error = 7.771561172376096e-15 relative error = 4.790654925669063e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4693 Order of pole (three term test) = -15.7 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.479999999999991 y1[1] (analytic) = 0.2109852527704743 y1[1] (numeric) = 0.2109852527704703 absolute error = 3.996802888650564e-15 relative error = 1.894351778699238e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.614374257805719 y2[1] (numeric) = 1.614374257805711 absolute error = 7.993605777301127e-15 relative error = 4.951519598786315e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.467 Order of pole (three term test) = -15.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.489999999999991 y1[1] (analytic) = 0.2048810629962214 y1[1] (numeric) = 0.2048810629962173 absolute error = 4.052314039881821e-15 relative error = 1.977886086991143e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.606453523378322 y2[1] (numeric) = 1.606453523378314 absolute error = 8.215650382226158e-15 relative error = 5.114153794470754e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.25 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4646 Order of pole (three term test) = -16.16 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.499999999999991 y1[1] (analytic) = 0.1988563844530719 y1[1] (numeric) = 0.1988563844530677 absolute error = 4.107825191113079e-15 relative error = 2.065724569221706e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.598472144103964 y2[1] (numeric) = 1.598472144103956 absolute error = 8.43769498715119e-15 relative error = 5.278599954509063e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.94 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4619 Order of pole (three term test) = -16.4 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.50999999999999 y1[1] (analytic) = 0.1929118196038596 y1[1] (numeric) = 0.1929118196038555 absolute error = 4.135580766728708e-15 relative error = 2.143767434893848e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.59043091811392 y2[1] (numeric) = 1.590430918113912 absolute error = 8.659739592076221e-15 relative error = 5.444901437370029e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4591 Order of pole (three term test) = -16.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.51999999999999 y1[1] (analytic) = 0.1870479629001157 y1[1] (numeric) = 0.1870479629001115 absolute error = 4.163336342344337e-15 relative error = 2.225812180893718e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.58233064952409 y2[1] (numeric) = 1.582330649524081 absolute error = 8.881784197001252e-15 relative error = 5.61310254571166e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4561 Order of pole (three term test) = -16.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.52999999999999 y1[1] (analytic) = 0.181265400722624 y1[1] (numeric) = 0.1812654007226198 absolute error = 4.218847493575595e-15 relative error = 2.327442234842909e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.574172148354581 y2[1] (numeric) = 1.574172148354572 absolute error = 9.103828801926284e-15 relative error = 5.783248554767121e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4529 Order of pole (three term test) = -17.08 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.53999999999999 y1[1] (analytic) = 0.1755647113227835 y1[1] (numeric) = 0.1755647113227793 absolute error = 4.246603069191224e-15 relative error = 2.418824966130953e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.565956230448711 y2[1] (numeric) = 1.565956230448702 absolute error = 9.103828801926284e-15 relative error = 5.813590843032478e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4495 Order of pole (three term test) = -17.31 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.54999999999999 y1[1] (analytic) = 0.1699464647647836 y1[1] (numeric) = 0.1699464647647793 absolute error = 4.274358644806853e-15 relative error = 2.515120659157476e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.557683717391426 y2[1] (numeric) = 1.557683717391416 absolute error = 9.325873406851315e-15 relative error = 5.987013475668145e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.446 Order of pole (three term test) = -17.54 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.559999999999989 y1[1] (analytic) = 0.1644112228685982 y1[1] (numeric) = 0.1644112228685939 absolute error = 4.302114220422482e-15 relative error = 2.616679169074026e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.549355436427136 y2[1] (numeric) = 1.549355436427126 absolute error = 9.547918011776346e-15 relative error = 6.162509768445488e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4422 Order of pole (three term test) = -17.76 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.569999999999989 y1[1] (analytic) = 0.1589595391538043 y1[1] (numeric) = 0.1589595391538 absolute error = 4.302114220422482e-15 relative error = 2.706420919011277e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.540972220376998 y2[1] (numeric) = 1.540972220376988 absolute error = 9.769962616701378e-15 relative error = 6.340128970210225e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4383 Order of pole (three term test) = -17.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.579999999999989 y1[1] (analytic) = 0.1535919587842303 y1[1] (numeric) = 0.153591958784226 absolute error = 4.329869796038111e-15 relative error = 2.819073231640216e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.53253490755563 y2[1] (numeric) = 1.53253490755562 absolute error = 9.992007221626409e-15 relative error = 6.519921453249966e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4342 Order of pole (three term test) = -18.2 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.589999999999989 y1[1] (analytic) = 0.1483090185134402 y1[1] (numeric) = 0.1483090185134359 absolute error = 4.329869796038111e-15 relative error = 2.919491909148953e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.524044341687286 y2[1] (numeric) = 1.524044341687275 absolute error = 1.021405182655144e-14 relative error = 6.701938747558588e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.43 Order of pole (three term test) = -18.41 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.599999999999989 y1[1] (analytic) = 0.1431112466310587 y1[1] (numeric) = 0.1431112466310543 absolute error = 4.329869796038111e-15 relative error = 3.025527271941478e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.515501371821474 y2[1] (numeric) = 1.515501371821464 absolute error = 1.043609643147647e-14 relative error = 6.886233576241093e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4255 Order of pole (three term test) = -18.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.609999999999988 y1[1] (analytic) = 0.1379991629099424 y1[1] (numeric) = 0.1379991629099381 absolute error = 4.329869796038111e-15 relative error = 3.137605841032357e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.506906852248064 y2[1] (numeric) = 1.506906852248053 absolute error = 1.088018564132653e-14 relative error = 7.220211139855819e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4209 Order of pole (three term test) = -18.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.619999999999988 y1[1] (analytic) = 0.1329732785542035 y1[1] (numeric) = 0.1329732785541992 absolute error = 4.329869796038111e-15 relative error = 3.256195412428775e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.498261642411849 y2[1] (numeric) = 1.498261642411838 absolute error = 1.088018564132653e-14 relative error = 7.26187291547556e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4161 Order of pole (three term test) = -19.05 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.629999999999988 y1[1] (analytic) = 0.1280340961480894 y1[1] (numeric) = 0.128034096148085 absolute error = 4.329869796038111e-15 relative error = 3.381809944618197e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.48956660682661 y2[1] (numeric) = 1.489566606826599 absolute error = 1.13242748511766e-14 relative error = 7.602395756777848e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4112 Order of pole (three term test) = -19.26 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.639999999999988 y1[1] (analytic) = 0.1231821096057245 y1[1] (numeric) = 0.1231821096057202 absolute error = 4.315992008230296e-15 relative error = 3.50374906067506e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.480822614988659 y2[1] (numeric) = 1.480822614988648 absolute error = 1.154631945610163e-14 relative error = 7.797233334520661e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4061 Order of pole (three term test) = -19.46 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.649999999999987 y1[1] (analytic) = 0.11841780412172 y1[1] (numeric) = 0.1184178041217157 absolute error = 4.288236432614667e-15 relative error = 3.621276770346838e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.472030541289894 y2[1] (numeric) = 1.472030541289882 absolute error = 1.154631945610163e-14 relative error = 7.843804277310683e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4008 Order of pole (three term test) = -19.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.659999999999987 y1[1] (analytic) = 0.1137416561226539 y1[1] (numeric) = 0.1137416561226496 absolute error = 4.274358644806853e-15 relative error = 3.757953585797604e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.463191264930357 y2[1] (numeric) = 1.463191264930345 absolute error = 1.199040866595169e-14 relative error = 8.194696724438412e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3954 Order of pole (three term test) = -19.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.669999999999987 y1[1] (analytic) = 0.1091541332194294 y1[1] (numeric) = 0.1091541332194251 absolute error = 4.246603069191224e-15 relative error = 3.890464743698162e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.454305669830318 y2[1] (numeric) = 1.454305669830306 absolute error = 1.199040866595169e-14 relative error = 8.244765123793184e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3898 Order of pole (three term test) = -20.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.679999999999987 y1[1] (analytic) = 0.1046556941605138 y1[1] (numeric) = 0.1046556941605096 absolute error = 4.218847493575595e-15 relative error = 4.031168611910415e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.445374644541883 y2[1] (numeric) = 1.445374644541871 absolute error = 1.243449787580175e-14 relative error = 8.602958355992825e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3841 Order of pole (three term test) = -20.25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.689999999999987 y1[1] (analytic) = 0.1002467887860645 y1[1] (numeric) = 0.1002467887860603 absolute error = 4.191091917959966e-15 relative error = 4.180774235974907e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.436399082160138 y2[1] (numeric) = 1.436399082160126 absolute error = 1.243449787580175e-14 relative error = 8.656715275188043e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3782 Order of pole (three term test) = -20.44 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.699999999999986 y1[1] (analytic) = 0.09592785798294466 y1[1] (numeric) = 0.0959278579829405 absolute error = 4.163336342344337e-15 relative error = 4.340070163022457e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.427379880233842 y2[1] (numeric) = 1.42737988023383 absolute error = 1.265654248072678e-14 relative error = 8.866975537481523e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3722 Order of pole (three term test) = -20.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.709999999999986 y1[1] (analytic) = 0.09169933364063559 y1[1] (numeric) = 0.09169933364063147 absolute error = 4.121702978920894e-15 relative error = 4.494801450873798e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.418317940675671 y2[1] (numeric) = 1.418317940675659 absolute error = 1.287858708565182e-14 relative error = 9.080183445692435e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.366 Order of pole (three term test) = -20.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.719999999999986 y1[1] (analytic) = 0.08756163860804778 y1[1] (numeric) = 0.08756163860804368 absolute error = 4.093947403305265e-15 relative error = 4.675503414949787e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.40921416967203 y2[1] (numeric) = 1.409214169672017 absolute error = 1.310063169057685e-14 relative error = 9.296409284350149e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3596 Order of pole (three term test) = -21 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.729999999999986 y1[1] (analytic) = 0.08351518665123638 y1[1] (numeric) = 0.08351518665123232 absolute error = 4.052314039881821e-15 relative error = 4.852188209558207e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.400069477592432 y2[1] (numeric) = 1.400069477592419 absolute error = 1.332267629550188e-14 relative error = 9.515725118450284e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3532 Order of pole (three term test) = -21.18 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.739999999999986 y1[1] (analytic) = 0.07956038241202504 y1[1] (numeric) = 0.07956038241202104 absolute error = 3.996802888650564e-15 relative error = 5.023609449175388e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.390884778898466 y2[1] (numeric) = 1.390884778898452 absolute error = 1.354472090042691e-14 relative error = 9.738204850551228e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3465 Order of pole (three term test) = -21.35 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.749999999999985 y1[1] (analytic) = 0.07569762136754205 y1[1] (numeric) = 0.0756976213675381 absolute error = 3.941291737419306e-15 relative error = 5.206625606216565e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.381660992052345 y2[1] (numeric) = 1.381660992052332 absolute error = 1.376676550535194e-14 relative error = 9.963924279936809e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3398 Order of pole (three term test) = -21.52 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.759999999999985 y1[1] (analytic) = 0.07192728979067288 y1[1] (numeric) = 0.07192728979066899 absolute error = 3.885780586188048e-15 relative error = 5.402373143068062e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.372399039425069 y2[1] (numeric) = 1.372399039425055 absolute error = 1.398881011027697e-14 relative error = 1.019296116393175e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3329 Order of pole (three term test) = -21.69 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.769999999999985 y1[1] (analytic) = 0.06824976471143331 y1[1] (numeric) = 0.06824976471142948 absolute error = 3.83026943495679e-15 relative error = 5.612135735780987e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.363099847204182 y2[1] (numeric) = 1.363099847204168 absolute error = 1.4210854715202e-14 relative error = 1.042539528146049e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3258 Order of pole (three term test) = -21.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.779999999999985 y1[1] (analytic) = 0.06466541387926662 y1[1] (numeric) = 0.06466541387926288 absolute error = 3.747002708109903e-15 relative error = 5.794446340520969e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.353764345301157 y2[1] (numeric) = 1.353764345301143 absolute error = 1.443289932012704e-14 relative error = 1.066130849894433e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3187 Order of pole (three term test) = -22.02 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.789999999999984 y1[1] (analytic) = 0.06117459572626913 y1[1] (numeric) = 0.06117459572626546 absolute error = 3.677613769070831e-15 relative error = 6.01166828388474e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.344393467258405 y2[1] (numeric) = 1.34439346725839 absolute error = 1.465494392505207e-14 relative error = 1.090078483863627e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3114 Order of pole (three term test) = -22.18 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.799999999999984 y1[1] (analytic) = 0.05777765933134711 y1[1] (numeric) = 0.05777765933134351 absolute error = 3.601285936127852e-15 relative error = 6.23300766733204e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.33498815015592 y2[1] (numeric) = 1.334988150155905 absolute error = 1.48769885299771e-14 relative error = 1.114391054949779e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.304 Order of pole (three term test) = -22.33 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.809999999999984 y1[1] (analytic) = 0.05447494438530929 y1[1] (numeric) = 0.05447494438530576 absolute error = 3.524958103184872e-15 relative error = 6.470787887826604e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.325549334517575 y2[1] (numeric) = 1.32554933451756 absolute error = 1.509903313490213e-14 relative error = 1.139077418072661e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2965 Order of pole (three term test) = -22.48 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.819999999999984 y1[1] (analytic) = 0.05126678115689801 y1[1] (numeric) = 0.05126678115689457 absolute error = 3.434752482434078e-15 relative error = 6.699762311821927e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.316077964217069 y2[1] (numeric) = 1.316077964217053 absolute error = 1.554312234475219e-14 relative error = 1.181018356613755e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2888 Order of pole (three term test) = -22.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.829999999999984 y1[1] (analytic) = 0.04815349045976265 y1[1] (numeric) = 0.04815349045975931 absolute error = 3.344546861683284e-15 relative error = 6.945595905405876e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.306574986383539 y2[1] (numeric) = 1.306574986383523 absolute error = 1.576516694967722e-14 relative error = 1.206602538237284e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.281 Order of pole (three term test) = -22.77 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.839999999999983 y1[1] (analytic) = 0.04513538362037854 y1[1] (numeric) = 0.04513538362037529 absolute error = 3.25434124093249e-15 relative error = 7.210177425994362e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.297041351306848 y2[1] (numeric) = 1.297041351306832 absolute error = 1.620925615952729e-14 relative error = 1.249710053052316e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2732 Order of pole (three term test) = -22.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.849999999999983 y1[1] (analytic) = 0.04221276244691452 y1[1] (numeric) = 0.04221276244691137 absolute error = 3.150257832373882e-15 relative error = 7.462808993691302e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.287478012342561 y2[1] (numeric) = 1.287478012342544 absolute error = 1.643130076445232e-14 relative error = 1.276239330453158e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2652 Order of pole (three term test) = -23.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.859999999999983 y1[1] (analytic) = 0.03938591919905243 y1[1] (numeric) = 0.03938591919904939 absolute error = 3.046174423815273e-15 relative error = 7.73417121083354e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.277885925816603 y2[1] (numeric) = 1.277885925816586 absolute error = 1.665334536937735e-14 relative error = 1.303194990486762e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2571 Order of pole (three term test) = -23.17 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.869999999999983 y1[1] (analytic) = 0.03665513655876138 y1[1] (numeric) = 0.03665513655875843 absolute error = 2.942091015256665e-15 relative error = 8.026408551336964e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.268266050929635 y2[1] (numeric) = 1.268266050929618 absolute error = 1.687538997430238e-14 relative error = 1.330587534211199e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2489 Order of pole (three term test) = -23.3 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.879999999999983 y1[1] (analytic) = 0.03402068760202973 y1[1] (numeric) = 0.03402068760202689 absolute error = 2.831068712794149e-15 relative error = 8.321609327570566e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.258619349661128 y2[1] (numeric) = 1.25861934966111 absolute error = 1.709743457922741e-14 relative error = 1.358427755288424e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2406 Order of pole (three term test) = -23.42 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.889999999999982 y1[1] (analytic) = 0.03148283577155779 y1[1] (numeric) = 0.03148283577155508 absolute error = 2.713107516427726e-15 relative error = 8.617735505512501e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.24894678667317 y2[1] (numeric) = 1.248946786673153 absolute error = 1.731947918415244e-14 relative error = 1.386726750007219e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2322 Order of pole (three term test) = -23.54 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.899999999999982 y1[1] (analytic) = 0.02904183485041375 y1[1] (numeric) = 0.02904183485041116 absolute error = 2.59167687310935e-15 relative error = 8.923943292351678e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.239249329214 y2[1] (numeric) = 1.239249329213982 absolute error = 1.754152378907747e-14 relative error = 1.415495927700302e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2237 Order of pole (three term test) = -23.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.909999999999982 y1[1] (analytic) = 0.02669792893665555 y1[1] (numeric) = 0.02669792893665309 absolute error = 2.463307335887066e-15 relative error = 9.226585858894132e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.229527947021282 y2[1] (numeric) = 1.229527947021264 absolute error = 1.77635683940025e-14 relative error = 1.444747021573397e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2151 Order of pole (three term test) = -23.77 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.919999999999982 y1[1] (analytic) = 0.02445135241892134 y1[1] (numeric) = 0.024451352418919 absolute error = 2.334937798664782e-15 relative error = 9.549319639505598e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.219783612225135 y2[1] (numeric) = 1.219783612225117 absolute error = 1.798561299892754e-14 relative error = 1.474492099965018e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2065 Order of pole (three term test) = -23.87 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.929999999999982 y1[1] (analytic) = 0.02230232995299072 y1[1] (numeric) = 0.02230232995298853 absolute error = 2.196159920586638e-15 relative error = 9.847221905584509e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.210017299250917 y2[1] (numeric) = 1.210017299250899 absolute error = 1.820765760385257e-14 relative error = 1.50474357805664e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1977 Order of pole (three term test) = -23.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.939999999999981 y1[1] (analytic) = 0.02025107643931947 y1[1] (numeric) = 0.02025107643931741 absolute error = 2.05391259555654e-15 relative error = 1.014223911361406e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.200229984721789 y2[1] (numeric) = 1.20022998472177 absolute error = 1.84297022087776e-14 relative error = 1.535514230053965e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1889 Order of pole (three term test) = -24.07 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.949999999999981 y1[1] (analytic) = 0.01829779700154956 y1[1] (numeric) = 0.01829779700154765 absolute error = 1.911665270526441e-15 relative error = 1.044751600624136e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.190422647361046 y2[1] (numeric) = 1.190422647361027 absolute error = 1.865174681370263e-14 relative error = 1.566817201861055e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.18 Order of pole (three term test) = -24.16 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.959999999999981 y1[1] (analytic) = 0.01644268696599705 y1[1] (numeric) = 0.01644268696599529 absolute error = 1.762479051592436e-15 relative error = 1.071892358735033e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.180596267894252 y2[1] (numeric) = 1.180596267894233 absolute error = 1.887379141862766e-14 relative error = 1.598666024270223e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1711 Order of pole (three term test) = -24.25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.969999999999981 y1[1] (analytic) = 0.01468593184211957 y1[1] (numeric) = 0.01468593184211797 absolute error = 1.6080886622305e-15 relative error = 1.094985786069405e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.170751828951164 y2[1] (numeric) = 1.170751828951145 absolute error = 1.909583602355269e-14 relative error = 1.631074626691806e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.162 Order of pole (three term test) = -24.33 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.97999999999998 y1[1] (analytic) = 0.01302770730396556 y1[1] (numeric) = 0.01302770730396411 absolute error = 1.450228825916611e-15 relative error = 1.113188063010265e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.160890314967475 y2[1] (numeric) = 1.160890314967456 absolute error = 1.931788062847772e-14 relative error = 1.664057351449173e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1529 Order of pole (three term test) = -24.41 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.98999999999998 y1[1] (analytic) = 0.01146817917260698 y1[1] (numeric) = 0.01146817917260569 absolute error = 1.288899542650768e-15 relative error = 1.123892052305433e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.151012712086364 y2[1] (numeric) = 1.151012712086344 absolute error = 1.953992523340276e-14 relative error = 1.697628968665693e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1438 Order of pole (three term test) = -24.49 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.99999999999998 y1[1] (analytic) = 0.01000750339955736 y1[1] (numeric) = 0.01000750339955624 absolute error = 1.122366088956994e-15 relative error = 1.121524564265087e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.141120008059887 y2[1] (numeric) = 1.141120008059867 absolute error = 1.998401444325282e-14 relative error = 1.751263171454622e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1345 Order of pole (three term test) = -24.56 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.00999999999998 y1[1] (analytic) = 0.008645826051176787 y1[1] (numeric) = 0.008645826051175835 absolute error = 9.523631883112671e-16 relative error = 1.101529434751513e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.131213192150204 y2[1] (numeric) = 1.131213192150184 absolute error = 1.998401444325282e-14 relative error = 1.766600193661754e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1253 Order of pole (three term test) = -24.62 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.01999999999998 y1[1] (analytic) = 0.007383283294065367 y1[1] (numeric) = 0.007383283294064588 absolute error = 7.788908407135864e-16 relative error = 1.054938310899778e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.12129325503065 y2[1] (numeric) = 1.12129325503063 absolute error = 2.020605904817785e-14 relative error = 1.802031623531484e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1159 Order of pole (three term test) = -24.68 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.029999999999979 y1[1] (analytic) = 0.006220001381446695 y1[1] (numeric) = 0.006220001381446095 absolute error = 6.002143226879753e-16 relative error = 9.649745809998083e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.11136118868667 y2[1] (numeric) = 1.11136118868665 absolute error = 2.042810365310288e-14 relative error = 1.8381156244302e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1066 Order of pole (three term test) = -24.74 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.039999999999979 y1[1] (analytic) = 0.005156096640542635 y1[1] (numeric) = 0.005156096640542217 absolute error = 4.180683577104105e-16 relative error = 8.108233550611115e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.101417986316623 y2[1] (numeric) = 1.101417986316602 absolute error = 2.065014825802791e-14 relative error = 1.874869351560748e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09716 Order of pole (three term test) = -24.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.049999999999979 y1[1] (analytic) = 0.004191675460940694 y1[1] (numeric) = 0.004191675460940463 absolute error = 2.315855840429037e-16 relative error = 5.524892998059812e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.091464642232458 y2[1] (numeric) = 1.091464642232437 absolute error = 2.065014825802791e-14 relative error = 1.891966762733656e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08771 Order of pole (three term test) = -24.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.059999999999979 y1[1] (analytic) = 0.003326834283955151 y1[1] (numeric) = 0.003326834283955109 absolute error = 4.163336342344337e-17 relative error = 1.251440855477388e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.08150215176029 y2[1] (numeric) = 1.081502151760269 absolute error = 2.087219286295294e-14 relative error = 1.929926152156114e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07822 Order of pole (three term test) = -24.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.069999999999979 y1[1] (analytic) = 0.002561659592983005 y1[1] (numeric) = 0.002561659592983157 absolute error = 1.522219850169648e-16 relative error = 5.942319012016157e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.071531511140865 y2[1] (numeric) = 1.071531511140844 absolute error = 2.109423746787797e-14 relative error = 1.968606359081203e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06871 Order of pole (three term test) = -24.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.079999999999978 y1[1] (analytic) = 0.00189622790485571 y1[1] (numeric) = 0.00189622790485606 absolute error = 3.499804612783208e-16 relative error = 1.845666654214499e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.061553717429935 y2[1] (numeric) = 1.061553717429914 absolute error = 2.109423746787797e-14 relative error = 1.987109754459528e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05916 Order of pole (three term test) = -24.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.089999999999978 y1[1] (analytic) = 0.001330605762187555 y1[1] (numeric) = 0.001330605762188105 absolute error = 5.507747036226363e-16 relative error = 4.139277908410276e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.051569768398556 y2[1] (numeric) = 1.051569768398535 absolute error = 2.131628207280301e-14 relative error = 2.027091564762815e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04959 Order of pole (three term test) = -24.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.099999999999978 y1[1] (analytic) = 0.0008648497267214551 y1[1] (numeric) = 0.0008648497267222106 absolute error = 7.554720737878995e-16 relative error = 8.735298751284877e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.041580662433313 y2[1] (numeric) = 1.041580662433291 absolute error = 2.153832667772804e-14 relative error = 2.067850091169202e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04001 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.109999999999978 y1[1] (analytic) = 0.0004990063736728292 y1[1] (numeric) = 0.000499006373673794 absolute error = 9.648315132948504e-16 relative error = 1.933505390308776e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.031587398436476 y2[1] (numeric) = 1.031587398436454 absolute error = 2.176037128265307e-14 relative error = 2.109406465766657e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0304 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.119999999999977 y1[1] (analytic) = 0.0002331122870721134 y1[1] (numeric) = 0.0002331122870732915 absolute error = 1.178094080622749e-15 relative error = 5.053762268045122e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.021590975726119 y2[1] (numeric) = 1.021590975726097 absolute error = 2.19824158875781e-14 relative error = 2.151782504926065e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02079 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.129999999999977 y1[1] (analytic) = 6.719405610639012e-05 y1[1] (numeric) = 6.719405610778586e-05 absolute error = 1.395747666749214e-15 relative error = 2.077189185512615e-09 % Correct digits = 11 h = 0.01 y2[1] (analytic) = 1.011592393936181 y2[1] (numeric) = 1.011592393936159 absolute error = 2.220446049250313e-14 relative error = 2.195000736028069e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01116 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.139999999999977 y1[1] (analytic) = 1.268272460491304e-06 y1[1] (numeric) = 1.268272462109557e-06 absolute error = 1.618253057597552e-15 relative error = 1.275950639952138e-07 % Correct digits = 9 h = 0.01 y2[1] (analytic) = 1.00159265291651 y2[1] (numeric) = 1.001592652916487 absolute error = 2.264854970235319e-14 relative error = 2.261253578129143e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001534 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.149999999999977 y1[1] (analytic) = 3.534152865784345e-05 y1[1] (numeric) = 3.534152865968906e-05 absolute error = 1.845610253167762e-15 relative error = 5.222213988070265e-09 % Correct digits = 11 h = 0.01 y2[1] (analytic) = 0.9915927526328745 y2[1] (numeric) = 0.9915927526328517 absolute error = 2.275957200481571e-14 relative error = 2.295253968363983e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.008107 Order of pole (three term test) = -0.8946 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.159999999999977 y1[1] (analytic) = 0.0001694104174012212 y1[1] (numeric) = 0.000169410417403298 absolute error = 2.076816366450296e-15 relative error = 1.225908299093374e-09 % Correct digits = 11 h = 0.01 y2[1] (analytic) = 0.9815936930669698 y2[1] (numeric) = 0.9815936930669468 absolute error = 2.298161660974074e-14 relative error = 2.34125552884668e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.01775 Order of pole (three term test) = -0.901 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.169999999999976 y1[1] (analytic) = 0.0004034615319134739 y1[1] (numeric) = 0.0004034615319157862 absolute error = 2.312277973259835e-15 relative error = 5.731098978119493e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9715964741164197 y2[1] (numeric) = 0.9715964741163966 absolute error = 2.309263891220326e-14 relative error = 2.376772613672147e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02738 Order of pole (three term test) = -0.9124 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.179999999999976 y1[1] (analytic) = 0.0007374714672781922 y1[1] (numeric) = 0.000737471467280744 absolute error = 2.551778233161883e-15 relative error = 3.460172150903419e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9616020954947886 y2[1] (numeric) = 0.9616020954947653 absolute error = 2.331468351712829e-14 relative error = 2.42456662962364e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.037 Order of pole (three term test) = -0.9285 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.189999999999976 y1[1] (analytic) = 0.00117140682278018 y1[1] (numeric) = 0.001171406822782975 absolute error = 2.79507320066763e-15 relative error = 2.386082397944286e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9516115566316098 y2[1] (numeric) = 0.9516115566315864 absolute error = 2.34257058195908e-14 relative error = 2.461687823812276e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04661 Order of pole (three term test) = -0.9495 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.199999999999976 y1[1] (analytic) = 0.0017052242052455 y1[1] (numeric) = 0.001705224205248542 absolute error = 3.041837615125331e-15 relative error = 1.783834410611947e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9416258565724442 y2[1] (numeric) = 0.9416258565724207 absolute error = 2.353672812205332e-14 relative error = 2.499583880133448e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05619 Order of pole (three term test) = -0.9752 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.209999999999976 y1[1] (analytic) = 0.00233887023338075 y1[1] (numeric) = 0.002338870233384043 absolute error = 3.29250515740398e-15 relative error = 1.407733148429011e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9316459938789766 y2[1] (numeric) = 0.9316459938789529 absolute error = 2.375877272697835e-14 relative error = 2.550193193882255e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06576 Order of pole (three term test) = -1.006 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.219999999999975 y1[1] (analytic) = 0.003072281543111155 y1[1] (numeric) = 0.003072281543114701 absolute error = 3.546208465765588e-15 relative error = 1.154258949254537e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9216729665291595 y2[1] (numeric) = 0.9216729665291356 absolute error = 2.398081733190338e-14 relative error = 2.601879213427563e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0753 Order of pole (three term test) = -1.041 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.229999999999975 y1[1] (analytic) = 0.003905384793916915 y1[1] (numeric) = 0.003905384793920719 absolute error = 3.804248582817138e-15 relative error = 9.741033940478008e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9117077718174171 y2[1] (numeric) = 0.911707771817393 absolute error = 2.40918396343659e-14 relative error = 2.642495806122254e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08481 Order of pole (three term test) = -1.081 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.239999999999975 y1[1] (analytic) = 0.0048380966761672 y1[1] (numeric) = 0.004838096676171266 absolute error = 4.066191827689636e-15 relative error = 8.404527854352268e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9017514062549165 y2[1] (numeric) = 0.9017514062548923 absolute error = 2.420286193682841e-14 relative error = 2.683983830681878e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09428 Order of pole (three term test) = -1.126 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.249999999999975 y1[1] (analytic) = 0.005870323919451042 y1[1] (numeric) = 0.005870323919455373 absolute error = 4.331604519514087e-15 relative error = 7.378816874417304e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8918048654699168 y2[1] (numeric) = 0.8918048654698923 absolute error = 2.442490654175344e-14 relative error = 2.738817367730247e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1037 Order of pole (three term test) = -1.176 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.259999999999974 y1[1] (analytic) = 0.007001963301904299 y1[1] (numeric) = 0.007001963301908901 absolute error = 4.601354020028481e-15 relative error = 6.571519760432145e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8818691441082077 y2[1] (numeric) = 0.8818691441081832 absolute error = 2.453592884421596e-14 relative error = 2.782264127069326e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1131 Order of pole (three term test) = -1.23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.269999999999974 y1[1] (analytic) = 0.008232901660531757 y1[1] (numeric) = 0.008232901660536631 absolute error = 4.874572967494828e-15 relative error = 5.920844397866867e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8719452357336459 y2[1] (numeric) = 0.8719452357336211 absolute error = 2.475797344914099e-14 relative error = 2.839395461380081e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1225 Order of pole (three term test) = -1.289 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.279999999999974 y1[1] (analytic) = 0.00956301590252333 y1[1] (numeric) = 0.00956301590252848 absolute error = 5.15039400017514e-15 relative error = 5.385742377377141e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8620341327287987 y2[1] (numeric) = 0.8620341327287738 absolute error = 2.486899575160351e-14 relative error = 2.884920075366371e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1318 Order of pole (three term test) = -1.353 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.289999999999974 y1[1] (analytic) = 0.01099217301756324 y1[1] (numeric) = 0.01099217301756867 absolute error = 5.429684479807406e-15 relative error = 4.939591535842714e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8521368261957074 y2[1] (numeric) = 0.8521368261956824 absolute error = 2.498001805406602e-14 relative error = 2.931456226999037e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.141 Order of pole (three term test) = -1.421 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.299999999999974 y1[1] (analytic) = 0.01252023009113096 y1[1] (numeric) = 0.01252023009113667 absolute error = 5.712444406391626e-15 relative error = 4.562571426253732e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8422543058567776 y2[1] (numeric) = 0.8422543058567525 absolute error = 2.509104035652854e-14 relative error = 2.979033788495132e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1502 Order of pole (three term test) = -1.494 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.309999999999973 y1[1] (analytic) = 0.01414703431879248 y1[1] (numeric) = 0.01414703431879848 absolute error = 5.998673779927799e-15 relative error = 4.240234133000827e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8323875599558079 y2[1] (numeric) = 0.8323875599557826 absolute error = 2.531308496145357e-14 relative error = 3.041021536025534e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1593 Order of pole (three term test) = -1.572 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.319999999999973 y1[1] (analytic) = 0.01587242302148073 y1[1] (numeric) = 0.01587242302148702 absolute error = 6.290107323891903e-15 relative error = 3.962915627550545e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.822537575159166 y2[1] (numeric) = 0.8225375751591406 absolute error = 2.542410726391608e-14 relative error = 3.090935664428019e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1684 Order of pole (three term test) = -1.654 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.329999999999973 y1[1] (analytic) = 0.01769622366176324 y1[1] (numeric) = 0.01769622366176983 absolute error = 6.58501031480796e-15 relative error = 3.721138724662702e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8127053364571234 y2[1] (numeric) = 0.8127053364570979 absolute error = 2.55351295663786e-14 relative error = 3.141991127767841e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1774 Order of pole (three term test) = -1.741 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.339999999999973 y1[1] (analytic) = 0.01961825386109583 y1[1] (numeric) = 0.01961825386110271 absolute error = 6.879913305724017e-15 relative error = 3.506893811465707e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8028918270653567 y2[1] (numeric) = 0.802891827065331 absolute error = 2.564615186884112e-14 relative error = 3.194222559542069e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1863 Order of pole (three term test) = -1.832 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.349999999999973 y1[1] (analytic) = 0.02163832141806023 y1[1] (numeric) = 0.02163832141806741 absolute error = 7.181755190543981e-15 relative error = 3.318998295565475e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.7930980283266272 y2[1] (numeric) = 0.7930980283266014 absolute error = 2.586819647376615e-14 relative error = 3.261664453806039e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1952 Order of pole (three term test) = -1.928 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.359999999999972 y1[1] (analytic) = 0.02375622432758414 y1[1] (numeric) = 0.02375622432759162 absolute error = 7.487066522315899e-15 relative error = 3.151623094256784e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.7833249196126473 y2[1] (numeric) = 0.7833249196126213 absolute error = 2.597921877622866e-14 relative error = 3.316531636587706e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.204 Order of pole (three term test) = -2.028 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.369999999999972 y1[1] (analytic) = 0.02597175080114152 y1[1] (numeric) = 0.02597175080114931 absolute error = 7.795847301039771e-15 relative error = 3.00166413913733e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.7735734782261441 y2[1] (numeric) = 0.773573478226118 absolute error = 2.609024107869118e-14 relative error = 3.372690741481708e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2127 Order of pole (three term test) = -2.132 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.379999999999972 y1[1] (analytic) = 0.02828467928793128 y1[1] (numeric) = 0.02828467928793938 absolute error = 8.108097526715596e-15 relative error = 2.866604017028831e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.7638446793031302 y2[1] (numeric) = 0.763844679303104 absolute error = 2.620126338115369e-14 relative error = 3.430182089512962e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2213 Order of pole (three term test) = -2.241 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.389999999999972 y1[1] (analytic) = 0.03069477849703217 y1[1] (numeric) = 0.03069477849704059 absolute error = 8.420347752391422e-15 relative error = 2.743250860469826e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.7541394957153905 y2[1] (numeric) = 0.7541394957153642 absolute error = 2.631228568361621e-14 relative error = 3.489047561241425e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2298 Order of pole (three term test) = -2.354 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.399999999999971 y1[1] (analytic) = 0.0332018074205317 y1[1] (numeric) = 0.03320180742054044 absolute error = 8.736067425019201e-15 relative error = 2.631202366295545e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.7444588979731962 y2[1] (numeric) = 0.7444588979731698 absolute error = 2.642330798607873e-14 relative error = 3.549330669297753e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2382 Order of pole (three term test) = -2.472 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.409999999999971 y1[1] (analytic) = 0.0358055153576267 y1[1] (numeric) = 0.03580551535763575 absolute error = 9.055256544598933e-15 relative error = 2.529011649226306e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.7348038541282544 y2[1] (numeric) = 0.7348038541282278 absolute error = 2.664535259100376e-14 relative error = 3.626185742127723e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2465 Order of pole (three term test) = -2.593 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.419999999999971 y1[1] (analytic) = 0.0385056419396932 y1[1] (numeric) = 0.03850564193970258 absolute error = 9.381384558082573e-15 relative error = 2.436366227259766e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.7251753296769038 y2[1] (numeric) = 0.725175329676877 absolute error = 2.675637489346627e-14 relative error = 3.689642186998745e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2548 Order of pole (three term test) = -2.719 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.429999999999971 y1[1] (analytic) = 0.0413019171563231 y1[1] (numeric) = 0.04130191715633281 absolute error = 9.707512571566213e-15 relative error = 2.350378200320429e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.7155742874635656 y2[1] (numeric) = 0.7155742874635388 absolute error = 2.675637489346627e-14 relative error = 3.739147054641564e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2629 Order of pole (three term test) = -2.849 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.439999999999971 y1[1] (analytic) = 0.04419406138232496 y1[1] (numeric) = 0.044194061382335 absolute error = 1.003364058504985e-14 relative error = 2.270359471660308e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.7060016875844604 y2[1] (numeric) = 0.7060016875844335 absolute error = 2.686739719592879e-14 relative error = 3.805571242733693e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2709 Order of pole (three term test) = -2.982 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.44999999999997 y1[1] (analytic) = 0.04718178540568629 y1[1] (numeric) = 0.04718178540569666 absolute error = 1.03667074924374e-14 relative error = 2.197184231859953e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.696458487291599 y2[1] (numeric) = 0.696458487291572 absolute error = 2.69784194983913e-14 relative error = 3.873657940950005e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2789 Order of pole (three term test) = -3.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.45999999999997 y1[1] (analytic) = 0.05026479045649452 y1[1] (numeric) = 0.05026479045650523 absolute error = 1.070671329372885e-14 relative error = 2.130062255605301e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.686945640897058 y2[1] (numeric) = 0.6869456408970309 absolute error = 2.708944180085382e-14 relative error = 3.943462217109155e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2867 Order of pole (three term test) = -3.262 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.46999999999997 y1[1] (analytic) = 0.05344276823681372 y1[1] (numeric) = 0.05344276823682477 absolute error = 1.104671909502031e-14 relative error = 2.067018505866027e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.6774640996775496 y2[1] (numeric) = 0.6774640996775224 absolute error = 2.720046410331634e-14 relative error = 4.015041404594406e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2944 Order of pole (three term test) = -3.408 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.47999999999997 y1[1] (analytic) = 0.05671540095151417 y1[1] (numeric) = 0.05671540095152557 absolute error = 1.139366379021567e-14 relative error = 2.008918847273262e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.6680148117792943 y2[1] (numeric) = 0.6680148117792671 absolute error = 2.720046410331634e-14 relative error = 4.071835477849121e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3019 Order of pole (three term test) = -3.557 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.48999999999997 y1[1] (analytic) = 0.06008236134005159 y1[1] (numeric) = 0.06008236134006333 absolute error = 1.173366959150712e-14 relative error = 1.952930831912115e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.6585987221232078 y2[1] (numeric) = 0.6585987221231805 absolute error = 2.731148640577885e-14 relative error = 4.146908502605557e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3094 Order of pole (three term test) = -3.71 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.499999999999969 y1[1] (analytic) = 0.06354331270919292 y1[1] (numeric) = 0.06354331270920499 absolute error = 1.207367539279858e-14 relative error = 1.900070184891676e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.6492167723104089 y2[1] (numeric) = 0.6492167723103814 absolute error = 2.742250870824137e-14 relative error = 4.223937192911875e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3167 Order of pole (three term test) = -3.867 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.509999999999969 y1[1] (analytic) = 0.06709790896668534 y1[1] (numeric) = 0.06709790896669776 absolute error = 1.242062008799394e-14 relative error = 1.851118802250735e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.6398699005280605 y2[1] (numeric) = 0.6398699005280329 absolute error = 2.753353101070388e-14 relative error = 4.302988933841317e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3239 Order of pole (three term test) = -4.028 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.519999999999969 y1[1] (analytic) = 0.07074579465586528 y1[1] (numeric) = 0.07074579465587805 absolute error = 1.27675647831893e-14 relative error = 1.804710067262038e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.6305590414555517 y2[1] (numeric) = 0.6305590414555242 absolute error = 2.753353101070388e-14 relative error = 4.366527034034247e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.331 Order of pole (three term test) = -4.192 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.529999999999969 y1[1] (analytic) = 0.0744866049912037 y1[1] (numeric) = 0.07448660499121683 absolute error = 1.312838726619248e-14 relative error = 1.762516531360617e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.6212851261710312 y2[1] (numeric) = 0.6212851261710035 absolute error = 2.76445533131664e-14 relative error = 4.449575911069894e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3379 Order of pole (three term test) = -4.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.539999999999969 y1[1] (analytic) = 0.0783199658947844 y1[1] (numeric) = 0.07831996589479789 absolute error = 1.348920974919565e-14 relative error = 1.72232068733497e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.6120490820582988 y2[1] (numeric) = 0.612049082058271 absolute error = 2.775557561562891e-14 relative error = 4.534861080468893e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3447 Order of pole (three term test) = -4.531 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.549999999999968 y1[1] (analytic) = 0.08224549403371149 y1[1] (numeric) = 0.08224549403372534 absolute error = 1.385003223219883e-14 relative error = 1.683986751483535e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.6028518327140692 y2[1] (numeric) = 0.6028518327140414 absolute error = 2.775557561562891e-14 relative error = 4.604045987663655e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3514 Order of pole (three term test) = -4.705 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.559999999999968 y1[1] (analytic) = 0.08626279685844233 y1[1] (numeric) = 0.08626279685845654 absolute error = 1.4210854715202e-14 relative error = 1.647390906942431e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5936942978556125 y2[1] (numeric) = 0.5936942978555847 absolute error = 2.775557561562891e-14 relative error = 4.675061848476624e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3579 Order of pole (three term test) = -4.883 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.569999999999968 y1[1] (analytic) = 0.09037147264204221 y1[1] (numeric) = 0.09037147264205678 absolute error = 1.457167719820518e-14 relative error = 1.612420022845374e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5845773932287832 y2[1] (numeric) = 0.5845773932287555 absolute error = 2.775557561562891e-14 relative error = 4.747972798319683e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3643 Order of pole (three term test) = -5.064 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.579999999999968 y1[1] (analytic) = 0.0945711105203566 y1[1] (numeric) = 0.09457111052037155 absolute error = 1.494637746901617e-14 relative error = 1.580437978022785e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5755020305164468 y2[1] (numeric) = 0.5755020305164189 absolute error = 2.786659791809143e-14 relative error = 4.84213720203287e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3705 Order of pole (three term test) = -5.249 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.589999999999967 y1[1] (analytic) = 0.09886129053309742 y1[1] (numeric) = 0.09886129053311273 absolute error = 1.530719995201935e-14 relative error = 1.548351217091861e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5664691172473115 y2[1] (numeric) = 0.5664691172472837 absolute error = 2.786659791809143e-14 relative error = 4.919349893866379e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3766 Order of pole (three term test) = -5.436 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.599999999999967 y1[1] (analytic) = 0.1032415836658385 y1[1] (numeric) = 0.1032415836658542 absolute error = 1.568190022283034e-14 relative error = 1.518951924796879e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.557479556705177 y2[1] (numeric) = 0.5574795567051491 absolute error = 2.786659791809143e-14 relative error = 4.9986761994985e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3826 Order of pole (three term test) = -5.626 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.609999999999967 y1[1] (analytic) = 0.1077115518929168 y1[1] (numeric) = 0.1077115518929328 absolute error = 1.605660049364133e-14 relative error = 1.490703662835e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5485342478386062 y2[1] (numeric) = 0.5485342478385783 absolute error = 2.786659791809143e-14 relative error = 5.080192900970979e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3883 Order of pole (three term test) = -5.819 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.619999999999967 y1[1] (analytic) = 0.1122707482212346 y1[1] (numeric) = 0.112270748221251 absolute error = 1.643130076445232e-14 relative error = 1.463542465404586e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5396340851710313 y2[1] (numeric) = 0.5396340851710034 absolute error = 2.786659791809143e-14 relative error = 5.16398031255928e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.394 Order of pole (three term test) = -6.015 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.629999999999967 y1[1] (analytic) = 0.1169187167349583 y1[1] (numeric) = 0.1169187167349751 absolute error = 1.681987882307112e-14 relative error = 1.43859591456173e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5307799587113023 y2[1] (numeric) = 0.5307799587112744 absolute error = 2.797762022055394e-14 relative error = 5.27103930006734e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3994 Order of pole (three term test) = -6.214 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.639999999999966 y1[1] (analytic) = 0.1216549926411099 y1[1] (numeric) = 0.1216549926411271 absolute error = 1.719457909388211e-14 relative error = 1.413388692119462e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5219727538646868 y2[1] (numeric) = 0.5219727538646588 absolute error = 2.797762022055394e-14 relative error = 5.359977127811292e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4048 Order of pole (three term test) = -6.416 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.649999999999966 y1[1] (analytic) = 0.1264791023160457 y1[1] (numeric) = 0.1264791023160633 absolute error = 1.75692793646931e-14 relative error = 1.389105318030407e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5132133513443301 y2[1] (numeric) = 0.5132133513443021 absolute error = 2.797762022055394e-14 relative error = 5.451459933236017e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4099 Order of pole (three term test) = -6.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.659999999999966 y1[1] (analytic) = 0.1313905633528182 y1[1] (numeric) = 0.1313905633528362 absolute error = 1.795785742331191e-14 relative error = 1.366753971142535e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5045026270831847 y2[1] (numeric) = 0.5045026270831569 absolute error = 2.786659791809143e-14 relative error = 5.523578356609163e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4149 Order of pole (three term test) = -6.827 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.669999999999966 y1[1] (analytic) = 0.1363888846094166 y1[1] (numeric) = 0.136388884609435 absolute error = 1.834643548193071e-14 relative error = 1.345156207888222e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.495841452146418 y2[1] (numeric) = 0.4958414521463901 absolute error = 2.792210906932269e-14 relative error = 5.631257521623568e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4197 Order of pole (three term test) = -7.036 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.679999999999966 y1[1] (analytic) = 0.1414735662578806 y1[1] (numeric) = 0.1414735662578993 absolute error = 1.873501354054952e-14 relative error = 1.32427661478463e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.4872306926443059 y2[1] (numeric) = 0.487230692644278 absolute error = 2.792210906932269e-14 relative error = 5.730777943766923e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4244 Order of pole (three term test) = -7.248 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.689999999999965 y1[1] (analytic) = 0.1466440998342825 y1[1] (numeric) = 0.1466440998343016 absolute error = 1.912359159916832e-14 relative error = 1.304081897654201e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.478671209645623 y2[1] (numeric) = 0.4786712096455951 absolute error = 2.792210906932269e-14 relative error = 5.833254331296507e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4288 Order of pole (three term test) = -7.461 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.699999999999965 y1[1] (analytic) = 0.1518999682895733 y1[1] (numeric) = 0.1518999682895929 absolute error = 1.953992523340276e-14 relative error = 1.286367960008587e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.4701638590915364 y2[1] (numeric) = 0.4701638590915085 absolute error = 2.792210906932269e-14 relative error = 5.938803787104044e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4331 Order of pole (three term test) = -7.677 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.709999999999965 y1[1] (analytic) = 0.1572406460412876 y1[1] (numeric) = 0.1572406460413075 absolute error = 1.992850329202156e-14 relative error = 1.26738879505677e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.461709491710012 y2[1] (numeric) = 0.461709491709984 absolute error = 2.792210906932269e-14 relative error = 6.047549286004251e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4373 Order of pole (three term test) = -7.896 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.719999999999965 y1[1] (analytic) = 0.1626655990261006 y1[1] (numeric) = 0.1626655990261209 absolute error = 2.031708135064036e-14 relative error = 1.249009100404836e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.4533089529307426 y2[1] (numeric) = 0.4533089529307147 absolute error = 2.792210906932269e-14 relative error = 6.159620031503918e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4412 Order of pole (three term test) = -8.116 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.729999999999964 y1[1] (analytic) = 0.1681742847532346 y1[1] (numeric) = 0.1681742847532554 absolute error = 2.070565940925917e-14 relative error = 1.231202465920457e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.4449630828006058 y2[1] (numeric) = 0.4449630828005779 absolute error = 2.786659791809143e-14 relative error = 6.262676387150717e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.445 Order of pole (three term test) = -8.338 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.739999999999964 y1[1] (analytic) = 0.1737661523587076 y1[1] (numeric) = 0.1737661523587287 absolute error = 2.11219930434936e-14 relative error = 1.215541275258902e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.4366727158996597 y2[1] (numeric) = 0.4366727158996318 absolute error = 2.786659791809143e-14 relative error = 6.381575240092336e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4486 Order of pole (three term test) = -8.562 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.749999999999964 y1[1] (analytic) = 0.1794406426604187 y1[1] (numeric) = 0.1794406426604402 absolute error = 2.151057110211241e-14 relative error = 1.198756913884886e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.4284386812576857 y2[1] (numeric) = 0.4284386812576579 absolute error = 2.781108676686017e-14 relative error = 6.49126420733545e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.452 Order of pole (three term test) = -8.788 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.759999999999964 y1[1] (analytic) = 0.1851971882140666 y1[1] (numeric) = 0.1851971882140886 absolute error = 2.192690473634684e-14 relative error = 1.183976114745428e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.4202618022712866 y2[1] (numeric) = 0.4202618022712588 absolute error = 2.775557561562891e-14 relative error = 6.604353635192424e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4553 Order of pole (three term test) = -9.015 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.769999999999964 y1[1] (analytic) = 0.1910352133698931 y1[1] (numeric) = 0.1910352133699154 absolute error = 2.231548279496565e-14 relative error = 1.168134523542378e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.4121428966215467 y2[1] (numeric) = 0.412142896621519 absolute error = 2.770006446439766e-14 relative error = 6.72098553474123e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.81 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4584 Order of pole (three term test) = -9.244 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.779999999999963 y1[1] (analytic) = 0.1969541343302474 y1[1] (numeric) = 0.1969541343302701 absolute error = 2.273181642920008e-14 relative error = 1.154168025286739e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.4040827761922653 y2[1] (numeric) = 0.4040827761922377 absolute error = 2.76445533131664e-14 relative error = 6.841309489522248e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.1 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4612 Order of pole (three term test) = -9.474 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.789999999999963 y1[1] (analytic) = 0.2029533592079661 y1[1] (numeric) = 0.2029533592079892 absolute error = 2.314815006343451e-14 relative error = 1.140565012265435e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.3960822469887688 y2[1] (numeric) = 0.3960822469887412 absolute error = 2.76445533131664e-14 relative error = 6.979498203551213e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4639 Order of pole (three term test) = -9.706 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.799999999999963 y1[1] (analytic) = 0.2090322880855607 y1[1] (numeric) = 0.2090322880855842 absolute error = 2.353672812205332e-14 relative error = 1.125985288570315e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.3881421090573102 y2[1] (numeric) = 0.3881421090572826 absolute error = 2.758904216193514e-14 relative error = 7.10797450679631e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4664 Order of pole (three term test) = -9.939 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.809999999999963 y1[1] (analytic) = 0.2151903130752091 y1[1] (numeric) = 0.215190313075233 absolute error = 2.398081733190338e-14 relative error = 1.114400410929375e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.380263156405066 y2[1] (numeric) = 0.3802631564050385 absolute error = 2.747801985947262e-14 relative error = 7.226053693774722e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4688 Order of pole (three term test) = -10.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.819999999999963 y1[1] (analytic) = 0.2214268183795441 y1[1] (numeric) = 0.2214268183795685 absolute error = 2.436939539052219e-14 relative error = 1.100562053362073e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.3724461769207357 y2[1] (numeric) = 0.3724461769207083 absolute error = 2.736699755701011e-14 relative error = 7.347906691718942e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.31 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4709 Order of pole (three term test) = -10.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.829999999999962 y1[1] (analytic) = 0.2277411803532323 y1[1] (numeric) = 0.2277411803532571 absolute error = 2.478572902475662e-14 relative error = 1.088328820739109e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.3646919522957535 y2[1] (numeric) = 0.3646919522957262 absolute error = 2.731148640577885e-14 relative error = 7.488919410985551e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4728 Order of pole (three term test) = -10.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.839999999999962 y1[1] (analytic) = 0.2341327675653384 y1[1] (numeric) = 0.2341327675653636 absolute error = 2.520206265899105e-14 relative error = 1.076400493662555e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.3570012579461201 y2[1] (numeric) = 0.3570012579460929 absolute error = 2.720046410331634e-14 relative error = 7.619150772690422e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4746 Order of pole (three term test) = -10.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.849999999999962 y1[1] (analytic) = 0.2406009408624673 y1[1] (numeric) = 0.2406009408624929 absolute error = 2.561839629322549e-14 relative error = 1.064767087002769e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.3493748629348616 y2[1] (numeric) = 0.3493748629348346 absolute error = 2.708944180085382e-14 relative error = 7.753689424961418e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.28 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4762 Order of pole (three term test) = -11.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.859999999999962 y1[1] (analytic) = 0.2471450534326795 y1[1] (numeric) = 0.2471450534327055 absolute error = 2.600697435184429e-14 relative error = 1.052295969133301e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.3418135298951239 y2[1] (numeric) = 0.3418135298950968 absolute error = 2.703393064962256e-14 relative error = 7.90897032598949e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4775 Order of pole (three term test) = -11.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.869999999999961 y1[1] (analytic) = 0.2537644508701715 y1[1] (numeric) = 0.2537644508701979 absolute error = 2.642330798607873e-14 relative error = 1.041253331405239e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.3343180149539097 y2[1] (numeric) = 0.3343180149538827 absolute error = 2.692290834716005e-14 relative error = 8.053083334702062e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4787 Order of pole (three term test) = -11.6 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.879999999999961 y1[1] (analytic) = 0.2604584712407155 y1[1] (numeric) = 0.2604584712407423 absolute error = 2.686739719592879e-14 relative error = 1.031542459262074e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.3268890676564669 y2[1] (numeric) = 0.3268890676564401 absolute error = 2.681188604469753e-14 relative error = 8.20213604478036e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.29 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4797 Order of pole (three term test) = -11.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.889999999999961 y1[1] (analytic) = 0.2672264451478529 y1[1] (numeric) = 0.2672264451478802 absolute error = 2.725597525454759e-14 relative error = 1.019958007504355e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.3195274308913346 y2[1] (numeric) = 0.3195274308913079 absolute error = 2.670086374223501e-14 relative error = 8.356360412547957e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4805 Order of pole (three term test) = -12.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.899999999999961 y1[1] (analytic) = 0.2740676957998329 y1[1] (numeric) = 0.2740676957998606 absolute error = 2.770006446439766e-14 relative error = 1.01070154888406e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.3122338408160546 y2[1] (numeric) = 0.312233840816028 absolute error = 2.65898414397725e-14 relative error = 8.51600241994182e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4811 Order of pole (three term test) = -12.32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.909999999999961 y1[1] (analytic) = 0.2809815390772914 y1[1] (numeric) = 0.2809815390773195 absolute error = 2.808864252301646e-14 relative error = 9.996614943193808e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3050090267835565 y2[1] (numeric) = 0.30500902678353 absolute error = 2.647881913730998e-14 relative error = 8.681323112479602e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.37 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4815 Order of pole (three term test) = -12.56 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.91999999999996 y1[1] (analytic) = 0.2879672836016621 y1[1] (numeric) = 0.2879672836016906 absolute error = 2.853273173286652e-14 relative error = 9.908324090154331e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2978537112692227 y2[1] (numeric) = 0.2978537112691964 absolute error = 2.636779683484747e-14 relative error = 8.852599728399642e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4818 Order of pole (three term test) = -12.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.92999999999996 y1[1] (analytic) = 0.295024230804314 y1[1] (numeric) = 0.2950242308043429 absolute error = 2.892130979148533e-14 relative error = 9.803028623322971e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2907686097986421 y2[1] (numeric) = 0.2907686097986159 absolute error = 2.620126338115369e-14 relative error = 9.011035750832295e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4818 Order of pole (three term test) = -13.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.93999999999996 y1[1] (analytic) = 0.3021516749964076 y1[1] (numeric) = 0.302151674996437 absolute error = 2.936539900133539e-14 relative error = 9.718760950666425e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2837544308760574 y2[1] (numeric) = 0.2837544308760313 absolute error = 2.609024107869118e-14 relative error = 9.194655039620253e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4816 Order of pole (three term test) = -13.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.94999999999996 y1[1] (analytic) = 0.3093489034394632 y1[1] (numeric) = 0.309348903439493 absolute error = 2.980948821118545e-14 relative error = 9.636202966860977e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2768118759135157 y2[1] (numeric) = 0.2768118759134898 absolute error = 2.592370762499741e-14 relative error = 9.365099506459304e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4813 Order of pole (three term test) = -13.53 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.95999999999996 y1[1] (analytic) = 0.3166151964166343 y1[1] (numeric) = 0.3166151964166645 absolute error = 3.019806626980426e-14 relative error = 9.537781702071744e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2699416391607281 y2[1] (numeric) = 0.2699416391607022 absolute error = 2.581268532253489e-14 relative error = 9.56232073080269e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4807 Order of pole (three term test) = -13.77 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.969999999999959 y1[1] (analytic) = 0.3239498273046781 y1[1] (numeric) = 0.3239498273047088 absolute error = 3.064215547965432e-14 relative error = 9.458920146555614e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2631444076356443 y2[1] (numeric) = 0.2631444076356186 absolute error = 2.564615186884112e-14 relative error = 9.746037204161816e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.48 Order of pole (three term test) = -14.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.979999999999959 y1[1] (analytic) = 0.3313520626466184 y1[1] (numeric) = 0.3313520626466494 absolute error = 3.103073353827313e-14 relative error = 9.36488316699175e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2564208610557527 y2[1] (numeric) = 0.2564208610557272 absolute error = 2.55351295663786e-14 relative error = 9.958288674815182e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4791 Order of pole (three term test) = -14.25 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.989999999999959 y1[1] (analytic) = 0.3388211622250891 y1[1] (numeric) = 0.3388211622251206 absolute error = 3.147482274812319e-14 relative error = 9.28950911490396e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2497716717701083 y2[1] (numeric) = 0.249771671770083 absolute error = 2.53408405370692e-14 relative error = 1.014560232450744e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.478 Order of pole (three term test) = -14.49 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.999999999999959 y1[1] (analytic) = 0.3463563791363568 y1[1] (numeric) = 0.3463563791363887 absolute error = 3.191891195797325e-14 relative error = 9.215626990201072e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2431975046920987 y2[1] (numeric) = 0.2431975046920736 absolute error = 2.517430708337542e-14 relative error = 1.035138379205307e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4766 Order of pole (three term test) = -14.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.009999999999959 y1[1] (analytic) = 0.35395695986501 y1[1] (numeric) = 0.353956959865042 absolute error = 3.197442310920451e-14 relative error = 9.033421216353176e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.236699017232953 y2[1] (numeric) = 0.2366990172329283 absolute error = 2.470246229790973e-14 relative error = 1.043623357066929e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4751 Order of pole (three term test) = -14.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.019999999999959 y1[1] (analytic) = 0.361622144359309 y1[1] (numeric) = 0.3616221443593414 absolute error = 3.236300116782331e-14 relative error = 8.949396952767174e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2302768592360022 y2[1] (numeric) = 0.2302768592359777 absolute error = 2.453592884421596e-14 relative error = 1.065496938147397e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4734 Order of pole (three term test) = -15.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.029999999999959 y1[1] (analytic) = 0.3693511661071923 y1[1] (numeric) = 0.3693511661072251 absolute error = 3.280709037767338e-14 relative error = 8.882357330409017e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2239316729116941 y2[1] (numeric) = 0.2239316729116697 absolute error = 2.434163981490656e-14 relative error = 1.087011921913588e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4716 Order of pole (three term test) = -15.44 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.039999999999958 y1[1] (analytic) = 0.3771432522129259 y1[1] (numeric) = 0.3771432522129591 absolute error = 3.319566843629218e-14 relative error = 8.801872562087023e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2176640927733732 y2[1] (numeric) = 0.2176640927733491 absolute error = 2.414735078559715e-14 relative error = 1.10938604883897e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4695 Order of pole (three term test) = -15.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.049999999999958 y1[1] (analytic) = 0.3849976234743926 y1[1] (numeric) = 0.3849976234744262 absolute error = 3.358424649491099e-14 relative error = 8.723234754498368e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2114747455738307 y2[1] (numeric) = 0.2114747455738067 absolute error = 2.395306175628775e-14 relative error = 1.132667718374211e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4672 Order of pole (three term test) = -15.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.059999999999958 y1[1] (analytic) = 0.3929134944610116 y1[1] (numeric) = 0.3929134944610457 absolute error = 3.402833570476105e-14 relative error = 8.660515911127007e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2053642502426285 y2[1] (numeric) = 0.2053642502426048 absolute error = 2.375877272697835e-14 relative error = 1.156908892317355e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4648 Order of pole (three term test) = -16.15 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.069999999999958 y1[1] (analytic) = 0.4008900735922808 y1[1] (numeric) = 0.4008900735923153 absolute error = 3.441691376337985e-14 relative error = 8.585124958315394e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1993332178242079 y2[1] (numeric) = 0.1993332178241843 absolute error = 2.356448369766895e-14 relative error = 1.182165419034698e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4621 Order of pole (three term test) = -16.38 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.079999999999957 y1[1] (analytic) = 0.4089265632169342 y1[1] (numeric) = 0.408926563216969 absolute error = 3.480549182199866e-14 relative error = 8.511428445291399e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1933822514167847 y2[1] (numeric) = 0.1933822514167614 absolute error = 2.334243909274392e-14 relative error = 1.207062122905758e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4593 Order of pole (three term test) = -16.61 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.089999999999957 y1[1] (analytic) = 0.4170221596927063 y1[1] (numeric) = 0.4170221596927415 absolute error = 3.519406988061746e-14 relative error = 8.439376436626565e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1875119461120406 y2[1] (numeric) = 0.1875119461120175 absolute error = 2.312039448781888e-14 relative error = 1.233009147801398e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4563 Order of pole (three term test) = -16.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.099999999999957 y1[1] (analytic) = 0.4251760534666959 y1[1] (numeric) = 0.4251760534667315 absolute error = 3.563815909046752e-14 relative error = 8.381977018670236e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1817228889356142 y2[1] (numeric) = 0.1817228889355913 absolute error = 2.287059430727822e-14 relative error = 1.258542302581457e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4531 Order of pole (three term test) = -17.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.109999999999957 y1[1] (analytic) = 0.4333874291563204 y1[1] (numeric) = 0.4333874291563565 absolute error = 3.602673714908633e-14 relative error = 8.312824674961138e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1760156587883989 y2[1] (numeric) = 0.1760156587883763 absolute error = 2.264854970235319e-14 relative error = 1.286734933599325e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4498 Order of pole (three term test) = -17.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.119999999999957 y1[1] (analytic) = 0.4416554656308538 y1[1] (numeric) = 0.4416554656308902 absolute error = 3.635980405647388e-14 relative error = 8.232617251671072e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1703908263886535 y2[1] (numeric) = 0.170390826388631 absolute error = 2.242650509742816e-14 relative error = 1.316180311625132e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4462 Order of pole (three term test) = -17.52 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.129999999999956 y1[1] (analytic) = 0.4499793360935385 y1[1] (numeric) = 0.4499793360935753 absolute error = 3.680389326632394e-14 relative error = 8.179018526902623e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1648489542149305 y2[1] (numeric) = 0.1648489542149083 absolute error = 2.21767049168875e-14 relative error = 1.345274225274942e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4425 Order of pole (three term test) = -17.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.139999999999956 y1[1] (analytic) = 0.4583582081642648 y1[1] (numeric) = 0.4583582081643021 absolute error = 3.7247982476174e-14 relative error = 8.126391501824093e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1593905964498291 y2[1] (numeric) = 0.1593905964498071 absolute error = 2.192690473634684e-14 relative error = 1.375671164092087e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4386 Order of pole (three term test) = -17.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.149999999999956 y1[1] (analytic) = 0.4667912439628081 y1[1] (numeric) = 0.4667912439628457 absolute error = 3.763656053479281e-14 relative error = 8.062824875479353e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1540162989245772 y2[1] (numeric) = 0.1540162989245555 absolute error = 2.167710455580618e-14 relative error = 1.407455230853301e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4345 Order of pole (three term test) = -18.18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.159999999999956 y1[1] (analytic) = 0.4752776001926159 y1[1] (numeric) = 0.4752776001926539 absolute error = 3.802513859341161e-14 relative error = 8.000616603433688e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1487265990644488 y2[1] (numeric) = 0.1487265990644274 absolute error = 2.142730437526552e-14 relative error = 1.44071770013246e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4303 Order of pole (three term test) = -18.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.169999999999956 y1[1] (analytic) = 0.4838164282251372 y1[1] (numeric) = 0.4838164282251756 absolute error = 3.841371665203042e-14 relative error = 7.939729701397227e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1435220258350218 y2[1] (numeric) = 0.1435220258350006 absolute error = 2.114974861910923e-14 relative error = 1.473623891250031e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4259 Order of pole (three term test) = -18.61 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.179999999999955 y1[1] (analytic) = 0.4924068741846845 y1[1] (numeric) = 0.4924068741847233 absolute error = 3.880229471064922e-14 relative error = 7.880128557282457e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.138403099689282 y2[1] (numeric) = 0.1384030996892612 absolute error = 2.084443728733731e-14 relative error = 1.506067229284137e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4213 Order of pole (three term test) = -18.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.189999999999955 y1[1] (analytic) = 0.5010480790338204 y1[1] (numeric) = 0.5010480790338596 absolute error = 3.919087276926803e-14 relative error = 7.821778868974103e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1333703325155783 y2[1] (numeric) = 0.1333703325155577 absolute error = 2.056688153118102e-14 relative error = 1.542088194822391e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4165 Order of pole (three term test) = -19.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.199999999999955 y1[1] (analytic) = 0.5097391786592611 y1[1] (numeric) = 0.5097391786593006 absolute error = 3.952393967665557e-14 relative error = 7.753757476639959e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1284242275864341 y2[1] (numeric) = 0.1284242275864138 absolute error = 2.028932577502474e-14 relative error = 1.579867456190795e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4116 Order of pole (three term test) = -19.24 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.209999999999955 y1[1] (analytic) = 0.5184793039582866 y1[1] (numeric) = 0.5184793039583264 absolute error = 3.985700658404312e-14 relative error = 7.687289787607367e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1235652795082204 y2[1] (numeric) = 0.1235652795082004 absolute error = 1.999789223106063e-14 relative error = 1.618407072816133e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4065 Order of pole (three term test) = -19.44 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.219999999999954 y1[1] (analytic) = 0.5272675809256502 y1[1] (numeric) = 0.5272675809256905 absolute error = 4.030109579389318e-14 relative error = 7.643385873097331e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1187939741716961 y2[1] (numeric) = 0.1187939741716764 absolute error = 1.969258089928871e-14 relative error = 1.657708737888211e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4013 Order of pole (three term test) = -19.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.229999999999954 y1[1] (analytic) = 0.5361031307409789 y1[1] (numeric) = 0.5361031307410196 absolute error = 4.063416270128073e-14 relative error = 7.579542138677295e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1141107887034188 y2[1] (numeric) = 0.1141107887033994 absolute error = 1.93872695675168e-14 relative error = 1.698986554015112e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3959 Order of pole (three term test) = -19.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.239999999999954 y1[1] (analytic) = 0.5449850698566542 y1[1] (numeric) = 0.5449850698566951 absolute error = 4.096722960866828e-14 relative error = 7.517128793903246e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1095161914180325 y2[1] (numeric) = 0.1095161914180134 absolute error = 1.908195823574488e-14 relative error = 1.742386946502498e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3903 Order of pole (three term test) = -20.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.249999999999954 y1[1] (analytic) = 0.5539125100861658 y1[1] (numeric) = 0.5539125100862072 absolute error = 4.141131881851834e-14 relative error = 7.47614795919241e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1050106417714371 y2[1] (numeric) = 0.1050106417714183 absolute error = 1.877664690397296e-14 relative error = 1.788070864745464e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3846 Order of pole (three term test) = -20.24 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.259999999999954 y1[1] (analytic) = 0.5628845586929306 y1[1] (numeric) = 0.5628845586929724 absolute error = 4.174438572590589e-14 relative error = 7.416154001957376e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1005945903148425 y2[1] (numeric) = 0.1005945903148241 absolute error = 1.844357999658541e-14 relative error = 1.833456445208476e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3787 Order of pole (three term test) = -20.43 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.269999999999953 y1[1] (analytic) = 0.5719003184795645 y1[1] (numeric) = 0.5719003184796065 absolute error = 4.207745263329343e-14 relative error = 7.357480189057978e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.09626847864971445 y2[1] (numeric) = 0.09626847864969633 absolute error = 1.812439087700568e-14 relative error = 1.882692147130907e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3727 Order of pole (three term test) = -20.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.279999999999953 y1[1] (analytic) = 0.5809588878776017 y1[1] (numeric) = 0.5809588878776442 absolute error = 4.241051954068098e-14 relative error = 7.300089632093926e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.09203273938361432 y2[1] (numeric) = 0.09203273938359653 absolute error = 1.779132396961813e-14 relative error = 1.933151625038528e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3665 Order of pole (three term test) = -20.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.289999999999953 y1[1] (analytic) = 0.5900593610376514 y1[1] (numeric) = 0.5900593610376943 absolute error = 4.285460875053104e-14 relative error = 7.262762288046559e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.08788779608693897 y2[1] (numeric) = 0.08788779608692152 absolute error = 1.745825706223059e-14 relative error = 1.986425628987306e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3601 Order of pole (three term test) = -20.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.299999999999953 y1[1] (analytic) = 0.5992008279199814 y1[1] (numeric) = 0.5992008279200246 absolute error = 4.318767565791859e-14 relative error = 7.207546058946027e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.08383406325056396 y2[1] (numeric) = 0.08383406325054683 absolute error = 1.712519015484304e-14 relative error = 2.04274843552067e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3537 Order of pole (three term test) = -21.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.309999999999953 y1[1] (analytic) = 0.6083823743855211 y1[1] (numeric) = 0.6083823743855648 absolute error = 4.363176486776865e-14 relative error = 7.17176675472192e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.07987194624439481 y2[1] (numeric) = 0.07987194624437803 absolute error = 1.677824545964768e-14 relative error = 2.100643122969491e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3471 Order of pole (three term test) = -21.34 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.319999999999952 y1[1] (analytic) = 0.6176030822872755 y1[1] (numeric) = 0.6176030822873194 absolute error = 4.39648317751562e-14 relative error = 7.118622467416078e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.07600184127683039 y2[1] (numeric) = 0.07600184127681398 absolute error = 1.64174229766445e-14 relative error = 2.160134899475054e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3403 Order of pole (three term test) = -21.51 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.329999999999952 y1[1] (analytic) = 0.6268620295621379 y1[1] (numeric) = 0.6268620295621823 absolute error = 4.440892098500626e-14 relative error = 7.08432141216558e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.07222413535514238 y2[1] (numeric) = 0.07222413535512634 absolute error = 1.604272270583351e-14 relative error = 2.221241227319347e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3334 Order of pole (three term test) = -21.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.339999999999952 y1[1] (analytic) = 0.6361582903230969 y1[1] (numeric) = 0.6361582903231416 absolute error = 4.474198789239381e-14 relative error = 7.03315331623988e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.06853920624677488 y2[1] (numeric) = 0.06853920624675922 absolute error = 1.566802243502252e-14 relative error = 2.285994147438756e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3264 Order of pole (three term test) = -21.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.349999999999952 y1[1] (analytic) = 0.6454909349518232 y1[1] (numeric) = 0.6454909349518683 absolute error = 4.507505479978136e-14 relative error = 6.983065502406408e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.06494742244156797 y2[1] (numeric) = 0.06494742244155267 absolute error = 1.529332216421153e-14 relative error = 2.354723496220448e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3193 Order of pole (three term test) = -22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.359999999999951 y1[1] (analytic) = 0.6548590301916311 y1[1] (numeric) = 0.6548590301916765 absolute error = 4.54081217071689e-14 relative error = 6.93403001465539e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.061449143114909 y2[1] (numeric) = 0.06144914311489409 absolute error = 1.491862189340054e-14 relative error = 2.427799825540762e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.312 Order of pole (three term test) = -22.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.369999999999951 y1[1] (analytic) = 0.6642616392408033 y1[1] (numeric) = 0.664261639240849 absolute error = 4.574118861455645e-14 relative error = 6.886019892227239e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.05804471809181544 y2[1] (numeric) = 0.0580447180918009 absolute error = 1.453698272868564e-14 relative error = 2.504445401163112e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3046 Order of pole (three term test) = -22.32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.379999999999951 y1[1] (analytic) = 0.6736978218462703 y1[1] (numeric) = 0.6736978218463164 absolute error = 4.618527782440651e-14 relative error = 6.855488666689713e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.05473448781195257 y2[1] (numeric) = 0.05473448781193842 absolute error = 1.414840467006684e-14 relative error = 2.584915879486352e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2971 Order of pole (three term test) = -22.47 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.389999999999951 y1[1] (analytic) = 0.6831666343976351 y1[1] (numeric) = 0.6831666343976817 absolute error = 4.651834473179406e-14 relative error = 6.809223751509825e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.05151878329558987 y2[1] (numeric) = 0.05151878329557612 absolute error = 1.375288771754413e-14 relative error = 2.669490006904221e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2894 Order of pole (three term test) = -22.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.399999999999951 y1[1] (analytic) = 0.6926671300215334 y1[1] (numeric) = 0.6926671300215802 absolute error = 4.685141163918161e-14 relative error = 6.763914383771193e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.04839792611049922 y2[1] (numeric) = 0.04839792611048587 absolute error = 1.335043187111751e-14 relative error = 2.758471890022024e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2817 Order of pole (three term test) = -22.76 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.40999999999995 y1[1] (analytic) = 0.7021983586763195 y1[1] (numeric) = 0.7021983586763667 absolute error = 4.718447854656915e-14 relative error = 6.719537003121789e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.04537222833979844 y2[1] (numeric) = 0.04537222833978549 absolute error = 1.294797602469089e-14 relative error = 2.853722750340105e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2738 Order of pole (three term test) = -22.9 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.41999999999995 y1[1] (analytic) = 0.7117593672470708 y1[1] (numeric) = 0.7117593672471183 absolute error = 4.75175454539567e-14 relative error = 6.676068857055461e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.04244199255074318 y2[1] (numeric) = 0.04244199255073065 absolute error = 1.253164239045645e-14 relative error = 2.952651757684035e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2658 Order of pole (three term test) = -23.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.42999999999995 y1[1] (analytic) = 0.7213491996408976 y1[1] (numeric) = 0.7213491996409455 absolute error = 4.785061236134425e-14 relative error = 6.63348796743176e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.03960751176447049 y2[1] (numeric) = 0.03960751176445838 absolute error = 1.211530875622202e-14 relative error = 3.058841168379058e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2577 Order of pole (three term test) = -23.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.43999999999995 y1[1] (analytic) = 0.7309668968825522 y1[1] (numeric) = 0.7309668968826003 absolute error = 4.807265696626928e-14 relative error = 6.57658468137078e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.03686906942669695 y2[1] (numeric) = 0.03686906942668525 absolute error = 1.169897512198759e-14 relative error = 3.173113751961513e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2495 Order of pole (three term test) = -23.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.44999999999995 y1[1] (analytic) = 0.7406114972103249 y1[1] (numeric) = 0.7406114972103734 absolute error = 4.851674617611934e-14 relative error = 6.55090372737505e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.03422693937937431 y2[1] (numeric) = 0.03422693937936303 absolute error = 1.127570259384925e-14 relative error = 3.294394064531567e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2413 Order of pole (three term test) = -23.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.459999999999949 y1[1] (analytic) = 0.7502820361722203 y1[1] (numeric) = 0.7502820361722692 absolute error = 4.884981308350689e-14 relative error = 6.51086001375273e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.03168138583330551 y2[1] (numeric) = 0.03168138583329468 absolute error = 1.083855227790309e-14 relative error = 3.421110533147482e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2329 Order of pole (three term test) = -23.53 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.469999999999949 y1[1] (analytic) = 0.7599775467224009 y1[1] (numeric) = 0.7599775467224501 absolute error = 4.918287999089443e-14 relative error = 6.471622773989611e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.0292326633417239 y2[1] (numeric) = 0.0292326633417135 absolute error = 1.040140196195694e-14 relative error = 3.558143792909547e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2244 Order of pole (three term test) = -23.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.479999999999949 y1[1] (analytic) = 0.7696970593178912 y1[1] (numeric) = 0.7696970593179406 absolute error = 4.940492459581947e-14 relative error = 6.418749298536013e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.02688101677483802 y2[1] (numeric) = 0.02688101677482806 absolute error = 9.960782199058826e-15 relative error = 3.705507973337756e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2158 Order of pole (three term test) = -23.76 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.489999999999949 y1[1] (analytic) = 0.7794396020155312 y1[1] (numeric) = 0.7794396020155809 absolute error = 4.973799150320701e-14 relative error = 6.381250243712396e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.02462668129534488 y2[1] (numeric) = 0.02462668129533536 absolute error = 9.51322354225681e-15 relative error = 3.862974238455375e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2072 Order of pole (three term test) = -23.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.499999999999948 y1[1] (analytic) = 0.78920420056917 y1[1] (numeric) = 0.7892042005692199 absolute error = 4.996003610813204e-14 relative error = 6.330432107697999e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.02246988233491381 y2[1] (numeric) = 0.02246988233490474 absolute error = 9.06219543850284e-15 relative error = 4.033040896000581e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1984 Order of pole (three term test) = -23.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.509999999999948 y1[1] (analytic) = 0.7989898785270891 y1[1] (numeric) = 0.7989898785271394 absolute error = 5.029310301551959e-14 relative error = 6.294585747222884e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.02041083557164352 y2[1] (numeric) = 0.02041083557163492 absolute error = 8.604228440844963e-15 relative error = 4.215519943141717e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1896 Order of pole (three term test) = -24.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.519999999999948 y1[1] (analytic) = 0.8087956573296479 y1[1] (numeric) = 0.8087956573296984 absolute error = 5.051514762044462e-14 relative error = 6.245724388188169e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.01844974690849448 y2[1] (numeric) = 0.01844974690848634 absolute error = 8.139322549283179e-15 relative error = 4.411617454511389e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1807 Order of pole (three term test) = -24.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.529999999999948 y1[1] (analytic) = 0.818620556407137 y1[1] (numeric) = 0.8186205564071879 absolute error = 5.084821452783217e-14 relative error = 6.211450974429605e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.01658681245269877 y2[1] (numeric) = 0.0165868124526911 absolute error = 7.674416657721395e-15 relative error = 4.626818250707791e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1718 Order of pole (three term test) = -24.24 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.539999999999948 y1[1] (analytic) = 0.8284635932778366 y1[1] (numeric) = 0.8284635932778877 absolute error = 5.10702591327572e-14 relative error = 6.164454243631451e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.01482221849614953 y2[1] (numeric) = 0.01482221849614233 absolute error = 7.202571872255703e-15 relative error = 4.859307582145523e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1627 Order of pole (three term test) = -24.33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.549999999999947 y1[1] (analytic) = 0.8383237836462618 y1[1] (numeric) = 0.8383237836463131 absolute error = 5.129230373768223e-14 relative error = 6.11843594781339e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.01315614149677193 y2[1] (numeric) = 0.0131561414967652 absolute error = 6.725522916362081e-15 relative error = 5.112078581712046e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1536 Order of pole (three term test) = -24.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.559999999999947 y1[1] (analytic) = 0.8482001415015926 y1[1] (numeric) = 0.8482001415016442 absolute error = 5.162537064506978e-14 relative error = 6.086460980031898e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.0115887480608775 y2[1] (numeric) = 0.01158874806087125 absolute error = 6.243269790040529e-15 relative error = 5.387354835262327e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1445 Order of pole (three term test) = -24.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.569999999999947 y1[1] (analytic) = 0.8580916792162738 y1[1] (numeric) = 0.8580916792163258 absolute error = 5.195843755245733e-14 relative error = 6.055114949944841e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.01012019492650368 y2[1] (numeric) = 0.01012019492649792 absolute error = 5.757547216767023e-15 relative error = 5.689166323949592e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1353 Order of pole (three term test) = -24.55 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.579999999999947 y1[1] (analytic) = 0.867997407644777 y1[1] (numeric) = 0.8679974076448291 absolute error = 5.218048215738236e-14 relative error = 6.011594239546039e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.008750628947740114 y2[1] (numeric) = 0.008750628947734849 absolute error = 5.26488574958961e-15 relative error = 6.016579815042082e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.126 Order of pole (three term test) = -24.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.589999999999947 y1[1] (analytic) = 0.8779163362225136 y1[1] (numeric) = 0.8779163362225662 absolute error = 5.25135490647699e-14 relative error = 5.981612016781061e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.007480187080043385 y2[1] (numeric) = 0.007480187080038616 absolute error = 4.769622197198231e-15 relative error = 6.376340786881185e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1167 Order of pole (three term test) = -24.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.599999999999946 y1[1] (analytic) = 0.8878474730648922 y1[1] (numeric) = 0.8878474730649449 absolute error = 5.273559366969494e-14 relative error = 5.939713213087055e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.00630899636654156 y2[1] (numeric) = 0.006308996366537292 absolute error = 4.268287112640934e-15 relative error = 6.765397956601941e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1073 Order of pole (three term test) = -24.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.609999999999946 y1[1] (analytic) = 0.8977898250665041 y1[1] (numeric) = 0.897789825066557 absolute error = 5.295763827461997e-14 relative error = 5.898667683240575e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.005237173925330001 y2[1] (numeric) = 0.005237173925326239 absolute error = 3.762615219393695e-15 relative error = 7.184438158899997e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09791 Order of pole (three term test) = -24.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.619999999999946 y1[1] (analytic) = 0.9077423980004344 y1[1] (numeric) = 0.9077423980004876 absolute error = 5.3179682879545e-14 relative error = 5.858455327930992e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.004264826937759646 y2[1] (numeric) = 0.004264826937756394 absolute error = 3.252606517456513e-15 relative error = 7.626585005498812e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08846 Order of pole (three term test) = -24.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.629999999999946 y1[1] (analytic) = 0.9177041966176837 y1[1] (numeric) = 0.9177041966177371 absolute error = 5.340172748447003e-14 relative error = 5.819056694007605e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.003392052637718966 y2[1] (numeric) = 0.003392052637716228 absolute error = 2.737393645091402e-15 relative error = 8.070021127184516e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07898 Order of pole (three term test) = -24.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.639999999999946 y1[1] (analytic) = 0.9276742247466915 y1[1] (numeric) = 0.9276742247467451 absolute error = 5.362377208939506e-14 relative error = 5.780452949852891e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.002618938301910655 y2[1] (numeric) = 0.002618938301908437 absolute error = 2.218277644905342e-15 relative error = 8.47014090895914e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06947 Order of pole (three term test) = -24.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.649999999999945 y1[1] (analytic) = 0.9376514853929534 y1[1] (numeric) = 0.9376514853930072 absolute error = 5.384581669432009e-14 relative error = 5.74262586186319e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.001945561241124035 y2[1] (numeric) = 0.001945561241122339 absolute error = 1.695475357332832e-15 relative error = 8.714582309181295e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05992 Order of pole (three term test) = -24.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.659999999999945 y1[1] (analytic) = 0.9476349808387191 y1[1] (numeric) = 0.9476349808387732 absolute error = 5.406786129924512e-14 relative error = 5.705557771980042e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.001371988792504038 y2[1] (numeric) = 0.00137198879250287 absolute error = 1.167685739766888e-15 relative error = 8.510898530269531e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05036 Order of pole (three term test) = -24.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.669999999999945 y1[1] (analytic) = 0.9576237127427635 y1[1] (numeric) = 0.9576237127428179 absolute error = 5.440092820663267e-14 relative error = 5.680825096824417e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.0008982783128175507 y2[1] (numeric) = 0.000898278312816915 absolute error = 6.356677337282512e-16 relative error = 7.076512086041664e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04077 Order of pole (three term test) = -24.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.679999999999945 y1[1] (analytic) = 0.9676166822402202 y1[1] (numeric) = 0.9676166822402749 absolute error = 5.46229728115577e-14 relative error = 5.645104493764507e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.0005244771727177849 y2[1] (numeric) = 0.0005244771727176859 absolute error = 9.898765834792655e-17 relative error = 1.887358754528496e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03117 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.689999999999944 y1[1] (analytic) = 0.9776128900424669 y1[1] (numeric) = 0.9776128900425217 absolute error = 5.484501741648273e-14 relative error = 5.61009556800139e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.0002506227520072503 y2[1] (numeric) = 0.0002506227520076929 absolute error = 4.425713268085829e-16 relative error = 1.765886469859606e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02155 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.699999999999944 y1[1] (analytic) = 0.9876113365370535 y1[1] (numeric) = 0.9876113365371085 absolute error = 5.506706202140776e-14 relative error = 5.575782697522908e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 7.674243589980684e-05 y2[1] (numeric) = 7.674243590079479e-05 absolute error = 9.879521246231038e-16 relative error = 1.287360914517949e-09 % Correct digits = 11 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.01193 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.709999999999944 y1[1] (analytic) = 0.9976110218876625 y1[1] (numeric) = 0.9976110218877178 absolute error = 5.52891066263328e-14 relative error = 5.542150739445089e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 2.853612282165325e-06 y2[1] (numeric) = 2.853612283703157e-06 absolute error = 1.537832361453439e-15 relative error = 5.389072548729465e-08 % Correct digits = 10 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0023 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.719999999999944 y1[1] (analytic) = 1.007610946134092 y1[1] (numeric) = 1.007610946134147 absolute error = 5.551115123125783e-14 relative error = 5.509185012750989e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 2.896366997511381e-05 y2[1] (numeric) = 2.896366997720585e-05 absolute error = 2.09203924257835e-15 relative error = 7.222977075680926e-09 % Correct digits = 11 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007339 Order of pole (three term test) = -0.8943 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.729999999999944 y1[1] (analytic) = 1.01761010929225 y1[1] (numeric) = 1.017610109292306 absolute error = 5.551115123125783e-14 relative error = 5.455051077456957e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.0001550699979946412 y2[1] (numeric) = 0.0001550699979972911 absolute error = 2.649925634826134e-15 relative error = 1.708857721735256e-09 % Correct digits = 11 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01698 Order of pole (three term test) = -0.9004 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.739999999999943 y1[1] (analytic) = 1.027607511454155 y1[1] (numeric) = 1.02760751145421 absolute error = 5.573319583618286e-14 relative error = 5.423587820734738e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.000381159985813034 y2[1] (numeric) = 0.0003811599858162454 absolute error = 3.211461045010688e-15 relative error = 8.425493662878793e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02661 Order of pole (three term test) = -0.9113 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.749999999999943 y1[1] (analytic) = 1.03760215288792 y1[1] (numeric) = 1.037602152887976 absolute error = 5.595524044110789e-14 relative error = 5.392745214085161e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.0007072110246199178 y2[1] (numeric) = 0.0007072110246236949 absolute error = 3.777143528505e-15 relative error = 5.340900236297902e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03623 Order of pole (three term test) = -0.927 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.759999999999943 y1[1] (analytic) = 1.047593034137731 y1[1] (numeric) = 1.047593034137787 absolute error = 5.617728504603292e-14 relative error = 5.362510365704386e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.001133190509583121 y2[1] (numeric) = 0.001133190509587467 absolute error = 4.346783349928884e-15 relative error = 3.835880474791467e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04584 Order of pole (three term test) = -0.9476 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.769999999999943 y1[1] (analytic) = 1.057579156123789 y1[1] (numeric) = 1.057579156123846 absolute error = 5.639932965095795e-14 relative error = 5.332870766635687e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.001659055843109127 y2[1] (numeric) = 0.001659055843114048 absolute error = 4.921193660911705e-15 relative error = 2.966261612803352e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05543 Order of pole (three term test) = -0.973 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.779999999999943 y1[1] (analytic) = 1.067559520242218 y1[1] (numeric) = 1.067559520242274 absolute error = 5.639932965095795e-14 relative error = 5.283015005866985e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.002284754439102805 y2[1] (numeric) = 0.002284754439108304 absolute error = 5.499073418846478e-15 relative error = 2.406855338469502e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.065 Order of pole (three term test) = -1.003 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.789999999999942 y1[1] (analytic) = 1.077533128464921 y1[1] (numeric) = 1.077533128464978 absolute error = 5.662137425588298e-14 relative error = 5.254722361673196e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.003010223728225968 y2[1] (numeric) = 0.003010223728232049 absolute error = 6.080205783298709e-15 relative error = 2.019851789183121e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07454 Order of pole (three term test) = -1.038 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.799999999999942 y1[1] (analytic) = 1.087498983439389 y1[1] (numeric) = 1.087498983439446 absolute error = 5.684341886080801e-14 relative error = 5.226985930693162e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.003835391164154261 y2[1] (numeric) = 0.003835391164160927 absolute error = 6.665674956440881e-15 relative error = 1.737938758043399e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08405 Order of pole (three term test) = -1.078 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.809999999999942 y1[1] (analytic) = 1.097456088588428 y1[1] (numeric) = 1.097456088588485 absolute error = 5.684341886080801e-14 relative error = 5.179562030032677e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.004760174230831727 y2[1] (numeric) = 0.004760174230838981 absolute error = 7.254613576535007e-15 relative error = 1.524022698485857e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09353 Order of pole (three term test) = -1.122 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.819999999999942 y1[1] (analytic) = 1.107403448209822 y1[1] (numeric) = 1.107403448209879 absolute error = 5.706546346573305e-14 relative error = 5.153087030565281e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.005784480450722349 y2[1] (numeric) = 0.005784480450730194 absolute error = 7.84528692010511e-15 relative error = 1.356264747878163e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.103 Order of pole (three term test) = -1.172 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.829999999999941 y1[1] (analytic) = 1.117340067575897 y1[1] (numeric) = 1.117340067575955 absolute error = 5.728750807065808e-14 relative error = 5.127132708571441e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.006908207394057723 y2[1] (numeric) = 0.006908207394066165 absolute error = 8.442031795841132e-15 relative error = 1.222029292737038e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1124 Order of pole (three term test) = -1.226 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.839999999999941 y1[1] (analytic) = 1.127264953032998 y1[1] (numeric) = 1.127264953033055 absolute error = 5.750955267558311e-14 relative error = 5.101689050196139e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.008131242689079951 y2[1] (numeric) = 0.008131242689088995 absolute error = 9.043113480267095e-15 relative error = 1.112144087448252e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1217 Order of pole (three term test) = -1.284 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.849999999999941 y1[1] (analytic) = 1.137177112100849 y1[1] (numeric) = 1.137177112100907 absolute error = 5.750955267558311e-14 relative error = 5.05722038050331e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.009453464033278725 y2[1] (numeric) = 0.00945346403328837 absolute error = 9.645062526431047e-15 relative error = 1.020267543461089e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.131 Order of pole (three term test) = -1.348 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.859999999999941 y1[1] (analytic) = 1.147075553571804 y1[1] (numeric) = 1.147075553571862 absolute error = 5.750955267558311e-14 relative error = 5.013580186283967e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.01087473920562147 y2[1] (numeric) = 0.01087473920563172 absolute error = 1.024874629607098e-14 relative error = 9.42436053158231e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1403 Order of pole (three term test) = -1.416 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.869999999999941 y1[1] (analytic) = 1.156959287609965 y1[1] (numeric) = 1.156959287610022 absolute error = 5.773159728050814e-14 relative error = 4.989941988345115e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.01239492607977535 y2[1] (numeric) = 0.01239492607978621 absolute error = 1.085763423613884e-14 relative error = 8.759741015200653e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1495 Order of pole (three term test) = -1.488 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.87999999999994 y1[1] (analytic) = 1.166827325850163 y1[1] (numeric) = 1.166827325850221 absolute error = 5.773159728050814e-14 relative error = 4.94774128112266e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.01401387263831976 y2[1] (numeric) = 0.01401387263833123 absolute error = 1.146825689968267e-14 relative error = 8.18350301566441e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1586 Order of pole (three term test) = -1.566 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.88999999999994 y1[1] (analytic) = 1.176678681496799 y1[1] (numeric) = 1.176678681496857 absolute error = 5.795364188543317e-14 relative error = 4.925188396522407e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.01573141698794797 y2[1] (numeric) = 0.01573141698796005 absolute error = 1.208408373365444e-14 relative error = 7.681497313886094e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1677 Order of pole (three term test) = -1.648 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.89999999999994 y1[1] (analytic) = 1.186512369422516 y1[1] (numeric) = 1.186512369422574 absolute error = 5.795364188543317e-14 relative error = 4.884368960573045e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.01754738737565629 y2[1] (numeric) = 0.01754738737566899 absolute error = 1.270511473805414e-14 relative error = 7.240459486111363e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1767 Order of pole (three term test) = -1.734 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.90999999999994 y1[1] (analytic) = 1.196327406266718 y1[1] (numeric) = 1.196327406266776 absolute error = 5.795364188543317e-14 relative error = 4.84429610003539e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.01946160220591926 y2[1] (numeric) = 0.01946160220593258 absolute error = 1.332267629550188e-14 relative error = 6.845621524136269e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1856 Order of pole (three term test) = -1.825 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.91999999999994 y1[1] (analytic) = 1.206122810533899 y1[1] (numeric) = 1.206122810533957 absolute error = 5.81756864903582e-14 relative error = 4.82336342387939e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.02147387005884903 y2[1] (numeric) = 0.02147387005886298 absolute error = 1.394717674685353e-14 relative error = 6.49495256729754e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1945 Order of pole (three term test) = -1.92 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.929999999999939 y1[1] (analytic) = 1.215897602691795 y1[1] (numeric) = 1.215897602691853 absolute error = 5.81756864903582e-14 relative error = 4.78458764632539e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.02358398970933718 y2[1] (numeric) = 0.02358398970935176 absolute error = 1.457514664515713e-14 relative error = 6.180102189998268e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2033 Order of pole (three term test) = -2.02 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.939999999999939 y1[1] (analytic) = 1.225650805269336 y1[1] (numeric) = 1.225650805269394 absolute error = 5.81756864903582e-14 relative error = 4.746513953260458e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.02579175014717711 y2[1] (numeric) = 0.02579175014719231 absolute error = 1.520311654346074e-14 relative error = 5.894565687363682e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.212 Order of pole (three term test) = -2.124 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.949999999999939 y1[1] (analytic) = 1.235381442954392 y1[1] (numeric) = 1.23538144295445 absolute error = 5.81756864903582e-14 relative error = 4.709127437695044e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.0280969305981648 y2[1] (numeric) = 0.02809693059818064 absolute error = 1.58345558887163e-14 relative error = 5.635688864089145e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2206 Order of pole (three term test) = -2.232 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.959999999999939 y1[1] (analytic) = 1.245088542691302 y1[1] (numeric) = 1.245088542691361 absolute error = 5.839773109528323e-14 relative error = 4.690247246919042e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.03049930054617615 y2[1] (numeric) = 0.03049930054619262 absolute error = 1.646946468092381e-14 relative error = 5.399948322089853e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2291 Order of pole (three term test) = -2.345 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.969999999999938 y1[1] (analytic) = 1.254771133778184 y1[1] (numeric) = 1.254771133778242 absolute error = 5.839773109528323e-14 relative error = 4.654054394720136e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.03299861975621832 y2[1] (numeric) = 0.03299861975623544 absolute error = 1.711131236703523e-14 relative error = 5.185463056772469e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2375 Order of pole (three term test) = -2.462 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.979999999999938 y1[1] (analytic) = 1.264428247963996 y1[1] (numeric) = 1.264428247964054 absolute error = 5.839773109528323e-14 relative error = 4.618508894381019e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.03559463829845308 y2[1] (numeric) = 0.03559463829847082 absolute error = 1.774275171229078e-14 relative error = 4.984669759395159e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2459 Order of pole (three term test) = -2.583 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.989999999999938 y1[1] (analytic) = 1.274058919545368 y1[1] (numeric) = 1.274058919545426 absolute error = 5.839773109528323e-14 relative error = 4.583597367390336e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.03828709657318952 y2[1] (numeric) = 0.03828709657320791 absolute error = 1.838806884535416e-14 relative error = 4.802680404402973e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2541 Order of pole (three term test) = -2.709 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.999999999999938 y1[1] (analytic) = 1.283662185463167 y1[1] (numeric) = 1.283662185463225 absolute error = 5.839773109528323e-14 relative error = 4.549306800232054e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.04107572533684389 y2[1] (numeric) = 0.04107572533686293 absolute error = 1.903338597841753e-14 relative error = 4.633730949930435e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2623 Order of pole (three term test) = -2.838 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.009999999999938 y1[1] (analytic) = 1.293237085398804 y1[1] (numeric) = 1.293237085398862 absolute error = 5.839773109528323e-14 relative error = 4.515624532780449e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.04396024572886368 y2[1] (numeric) = 0.04396024572888336 absolute error = 1.96787031114809e-14 relative error = 4.476477049936083e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2703 Order of pole (three term test) = -2.972 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.019999999999937 y1[1] (analytic) = 1.302782661870264 y1[1] (numeric) = 1.302782661870323 absolute error = 5.839773109528323e-14 relative error = 4.482538247127723e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.04694036929961344 y2[1] (numeric) = 0.04694036929963376 absolute error = 2.032402024454427e-14 relative error = 4.329752949922284e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2782 Order of pole (three term test) = -3.109 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.029999999999937 y1[1] (analytic) = 1.312297960327856 y1[1] (numeric) = 1.312297960327914 absolute error = 5.839773109528323e-14 relative error = 4.450035956825958e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.05001579803921952 y2[1] (numeric) = 0.05001579803924049 absolute error = 2.097627627151155e-14 relative error = 4.193930136846594e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.286 Order of pole (three term test) = -3.251 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.039999999999937 y1[1] (analytic) = 1.321782029249662 y1[1] (numeric) = 1.321782029249721 absolute error = 5.861977570020827e-14 relative error = 4.434904878642134e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.05318622440737081 y2[1] (numeric) = 0.05318622440739244 absolute error = 2.162853229847883e-14 relative error = 4.066566585516351e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2937 Order of pole (three term test) = -3.396 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.049999999999937 y1[1] (analytic) = 1.331233920236694 y1[1] (numeric) = 1.331233920236753 absolute error = 5.839773109528323e-14 relative error = 4.386737011997116e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.05645133136407251 y2[1] (numeric) = 0.05645133136409479 absolute error = 2.228078832544611e-14 relative error = 3.946902187611883e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3013 Order of pole (three term test) = -3.545 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.059999999999937 y1[1] (analytic) = 1.34065268810773 y1[1] (numeric) = 1.340652688107788 absolute error = 5.861977570020827e-14 relative error = 4.372480376177621e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.05981079240134986 y2[1] (numeric) = 0.0598107924013728 absolute error = 2.293304435241339e-14 relative error = 3.834265260778557e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3088 Order of pole (three term test) = -3.698 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.069999999999936 y1[1] (analytic) = 1.350037390993831 y1[1] (numeric) = 1.35003739099389 absolute error = 5.839773109528323e-14 relative error = 4.325638051572311e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.06326427157589869 y2[1] (numeric) = 0.06326427157592228 absolute error = 2.359223927328458e-14 relative error = 3.729156866206981e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3161 Order of pole (three term test) = -3.855 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.079999999999936 y1[1] (analytic) = 1.35938709043253 y1[1] (numeric) = 1.359387090432588 absolute error = 5.839773109528323e-14 relative error = 4.29588683799419e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.0668114235426794 y2[1] (numeric) = 0.06681142354270365 absolute error = 2.425837308805967e-14 relative error = 3.630872057764692e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3233 Order of pole (three term test) = -4.015 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.089999999999936 y1[1] (analytic) = 1.368700851461674 y1[1] (numeric) = 1.368700851461732 absolute error = 5.81756864903582e-14 relative error = 4.250431087861951e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.07045189358945129 y2[1] (numeric) = 0.07045189358947621 absolute error = 2.491062911502695e-14 relative error = 3.535835283603619e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3304 Order of pole (three term test) = -4.179 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.099999999999936 y1[1] (analytic) = 1.377977742712921 y1[1] (numeric) = 1.377977742712979 absolute error = 5.839773109528323e-14 relative error = 4.23792992333182e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.0741853176722434 y2[1] (numeric) = 0.07418531767226898 absolute error = 2.557676292980204e-14 relative error = 3.447685301126862e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3374 Order of pole (three term test) = -4.346 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.109999999999935 y1[1] (analytic) = 1.387216836504877 y1[1] (numeric) = 1.387216836504936 absolute error = 5.839773109528323e-14 relative error = 4.209704608431482e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.07801132245175861 y2[1] (numeric) = 0.07801132245178485 absolute error = 2.624289674457714e-14 relative error = 3.36398562667688e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3442 Order of pole (three term test) = -4.517 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.119999999999935 y1[1] (analytic) = 1.396417208935863 y1[1] (numeric) = 1.396417208935921 absolute error = 5.839773109528323e-14 relative error = 4.181968735531777e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.08192952533070731 y2[1] (numeric) = 0.08192952533073422 absolute error = 2.690903055935223e-14 relative error = 3.284411871145882e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3509 Order of pole (three term test) = -4.691 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.129999999999935 y1[1] (analytic) = 1.405577939976302 y1[1] (numeric) = 1.40557793997636 absolute error = 5.81756864903582e-14 relative error = 4.138915732509224e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.08593953449206675 y2[1] (numeric) = 0.08593953449209434 absolute error = 2.758904216193514e-14 relative error = 3.210285269171657e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3574 Order of pole (three term test) = -4.869 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.139999999999935 y1[1] (analytic) = 1.414698113560723 y1[1] (numeric) = 1.414698113560781 absolute error = 5.81756864903582e-14 relative error = 4.112233269607816e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.09004094893826246 y2[1] (numeric) = 0.09004094893829072 absolute error = 2.825517597671023e-14 relative error = 3.138036227948208e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3638 Order of pole (three term test) = -5.05 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.149999999999935 y1[1] (analytic) = 1.423776817679369 y1[1] (numeric) = 1.423776817679427 absolute error = 5.795364188543317e-14 relative error = 4.070416175190471e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.09423335853126767 y2[1] (numeric) = 0.09423335853129659 absolute error = 2.892130979148533e-14 relative error = 3.069115888710357e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.37 Order of pole (three term test) = -5.234 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.159999999999934 y1[1] (analytic) = 1.432813144469393 y1[1] (numeric) = 1.432813144469451 absolute error = 5.795364188543317e-14 relative error = 4.044745269760551e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.09851634403361673 y2[1] (numeric) = 0.09851634403364631 absolute error = 2.958744360626042e-14 relative error = 3.003303045448408e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3761 Order of pole (three term test) = -5.421 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.169999999999934 y1[1] (analytic) = 1.441806190305646 y1[1] (numeric) = 1.441806190305704 absolute error = 5.773159728050814e-14 relative error = 4.004116341619376e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1028894771503285 y2[1] (numeric) = 0.1028894771503588 absolute error = 3.026745520884333e-14 relative error = 2.941744486136373e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3821 Order of pole (three term test) = -5.611 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.179999999999934 y1[1] (analytic) = 1.45075505589104 y1[1] (numeric) = 1.450755055891098 absolute error = 5.773159728050814e-14 relative error = 3.97941727282487e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1073523205717357 y2[1] (numeric) = 0.1073523205717666 absolute error = 3.093358902361842e-14 relative error = 2.881501662830639e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3879 Order of pole (three term test) = -5.804 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.189999999999934 y1[1] (analytic) = 1.459658846346473 y1[1] (numeric) = 1.45965884634653 absolute error = 5.750955267558311e-14 relative error = 3.939931088660173e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1119044280172151 y2[1] (numeric) = 0.1119044280172467 absolute error = 3.159972283839352e-14 relative error = 2.823813444945386e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3935 Order of pole (three term test) = -6 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.199999999999934 y1[1] (analytic) = 1.468516671300318 y1[1] (numeric) = 1.468516671300376 absolute error = 5.750955267558311e-14 relative error = 3.916166142306065e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1165453442798156 y2[1] (numeric) = 0.1165453442798479 absolute error = 3.226585665316861e-14 relative error = 2.768523861039099e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.399 Order of pole (three term test) = -6.198 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.209999999999933 y1[1] (analytic) = 1.477327644977463 y1[1] (numeric) = 1.47732764497752 absolute error = 5.728750807065808e-14 relative error = 3.877779466553746e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1212746052717784 y2[1] (numeric) = 0.1212746052718113 absolute error = 3.293199046794371e-14 relative error = 2.715489396493403e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4043 Order of pole (three term test) = -6.4 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.219999999999933 y1[1] (analytic) = 1.486090886287882 y1[1] (numeric) = 1.486090886287939 absolute error = 5.706546346573305e-14 relative error = 3.839971295986971e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1260917380709452 y2[1] (numeric) = 0.1260917380709788 absolute error = 3.361200207052661e-14 relative error = 2.665678385019556e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4095 Order of pole (three term test) = -6.604 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.229999999999933 y1[1] (analytic) = 1.494805518914746 y1[1] (numeric) = 1.494805518914803 absolute error = 5.684341886080801e-14 relative error = 3.802730063645823e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1309962609680505 y2[1] (numeric) = 0.1309962609680848 absolute error = 3.430589146091734e-14 relative error = 2.618845088203274e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4145 Order of pole (three term test) = -6.81 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.239999999999933 y1[1] (analytic) = 1.503470671402056 y1[1] (numeric) = 1.503470671402113 absolute error = 5.684341886080801e-14 relative error = 3.780813283693716e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1359876835148916 y2[1] (numeric) = 0.1359876835149266 absolute error = 3.497202527569243e-14 relative error = 2.57170534652594e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4193 Order of pole (three term test) = -7.019 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.249999999999932 y1[1] (analytic) = 1.512085477241783 y1[1] (numeric) = 1.512085477241839 absolute error = 5.662137425588298e-14 relative error = 3.744588193464226e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1410655065733734 y2[1] (numeric) = 0.141065506573409 absolute error = 3.563815909046752e-14 relative error = 2.526355305145471e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.424 Order of pole (three term test) = -7.231 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.259999999999932 y1[1] (analytic) = 1.520649074960522 y1[1] (numeric) = 1.520649074960578 absolute error = 5.639932965095795e-14 relative error = 3.708898428943717e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1462292223654215 y2[1] (numeric) = 0.1462292223654578 absolute error = 3.633204848085825e-14 relative error = 2.484595615920448e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4285 Order of pole (three term test) = -7.444 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.269999999999932 y1[1] (analytic) = 1.529160608205638 y1[1] (numeric) = 1.529160608205694 absolute error = 5.595524044110789e-14 relative error = 3.659212782545283e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1514783145237597 y2[1] (numeric) = 0.1514783145237967 absolute error = 3.699818229563334e-14 relative error = 2.442473855875264e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4328 Order of pole (three term test) = -7.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.279999999999932 y1[1] (analytic) = 1.537619225830899 y1[1] (numeric) = 1.537619225830954 absolute error = 5.573319583618286e-14 relative error = 3.624642232609036e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1568122581435465 y2[1] (numeric) = 0.1568122581435842 absolute error = 3.766431611040844e-14 relative error = 2.401873205341535e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.437 Order of pole (three term test) = -7.878 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.289999999999932 y1[1] (analytic) = 1.546024081981591 y1[1] (numeric) = 1.546024081981647 absolute error = 5.551115123125783e-14 relative error = 3.590574809165153e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1622305198348649 y2[1] (numeric) = 0.1622305198349032 absolute error = 3.833044992518353e-14 relative error = 2.3627151022015e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4409 Order of pole (three term test) = -8.098 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.299999999999931 y1[1] (analytic) = 1.554374336179104 y1[1] (numeric) = 1.554374336179159 absolute error = 5.551115123125783e-14 relative error = 3.571285882634485e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1677325577760608 y2[1] (numeric) = 0.1677325577760998 absolute error = 3.899658373995862e-14 relative error = 2.324926314664731e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4447 Order of pole (three term test) = -8.32 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.309999999999931 y1[1] (analytic) = 1.562669153404976 y1[1] (numeric) = 1.562669153405031 absolute error = 5.506706202140776e-14 relative error = 3.523910477238221e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1733178217679253 y2[1] (numeric) = 0.173317821767965 absolute error = 3.966271755473372e-14 relative error = 2.288438496985185e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4483 Order of pole (three term test) = -8.544 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.319999999999931 y1[1] (analytic) = 1.570907704184397 y1[1] (numeric) = 1.570907704184452 absolute error = 5.506706202140776e-14 relative error = 3.505429496254089e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1789857532887134 y2[1] (numeric) = 0.1789857532887538 absolute error = 4.035660694512444e-14 relative error = 2.254738503126956e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4518 Order of pole (three term test) = -8.77 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.329999999999931 y1[1] (analytic) = 1.579089164669154 y1[1] (numeric) = 1.579089164669209 absolute error = 5.46229728115577e-14 relative error = 3.459144298732627e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1847357855499964 y2[1] (numeric) = 0.1847357855500374 absolute error = 4.102274075989953e-14 relative error = 2.220616900930505e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.455 Order of pole (three term test) = -8.997 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.339999999999931 y1[1] (analytic) = 1.587212716720017 y1[1] (numeric) = 1.587212716720072 absolute error = 5.440092820663267e-14 relative error = 3.427450374707963e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1905673435533398 y2[1] (numeric) = 0.1905673435533815 absolute error = 4.168887457467463e-14 relative error = 2.187619022091574e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4581 Order of pole (three term test) = -9.226 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.34999999999993 y1[1] (analytic) = 1.59527754798855 y1[1] (numeric) = 1.595277547988605 absolute error = 5.440092820663267e-14 relative error = 3.410123102103805e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.196479844147803 y2[1] (numeric) = 0.1964798441478453 absolute error = 4.238276396506535e-14 relative error = 2.15710492589676e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.08 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.461 Order of pole (three term test) = -9.456 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.35999999999993 y1[1] (analytic) = 1.603282851998348 y1[1] (numeric) = 1.603282851998402 absolute error = 5.395683899678261e-14 relative error = 3.365397373865145e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2024726960882534 y2[1] (numeric) = 0.2024726960882964 absolute error = 4.304889777984044e-14 relative error = 2.126158173992822e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.37 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4637 Order of pole (three term test) = -9.688 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.36999999999993 y1[1] (analytic) = 1.61122782822568 y1[1] (numeric) = 1.611227828225733 absolute error = 5.373479439185758e-14 relative error = 3.335021494199957e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2085453000944911 y2[1] (numeric) = 0.2085453000945348 absolute error = 4.371503159461554e-14 relative error = 2.096188769289378e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4662 Order of pole (three term test) = -9.921 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.37999999999993 y1[1] (analytic) = 1.619111682179543 y1[1] (numeric) = 1.619111682179597 absolute error = 5.351274978693255e-14 relative error = 3.305068475257812e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.214697048911176 y2[1] (numeric) = 0.2146970489112204 absolute error = 4.438116540939063e-14 relative error = 2.067153024900305e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.98 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4686 Order of pole (three term test) = -10.16 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.38999999999993 y1[1] (analytic) = 1.626933625481114 y1[1] (numeric) = 1.626933625481167 absolute error = 5.329070518200751e-14 relative error = 3.275530381041112e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2209273273685529 y2[1] (numeric) = 0.2209273273685979 absolute error = 4.504729922416573e-14 relative error = 2.039009830097543e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.29 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4707 Order of pole (three term test) = -10.39 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.399999999999929 y1[1] (analytic) = 1.63469287594258 y1[1] (numeric) = 1.634692875942633 absolute error = 5.284661597215745e-14 relative error = 3.232816191340259e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2272355124439678 y2[1] (numeric) = 0.2272355124440135 absolute error = 4.574118861455645e-14 relative error = 2.0129419087096e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4727 Order of pole (three term test) = -10.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.409999999999929 y1[1] (analytic) = 1.64238865764536 y1[1] (numeric) = 1.642388657645413 absolute error = 5.262457136723242e-14 relative error = 3.20414848959555e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.23362097332417 y2[1] (numeric) = 0.2336209733242164 absolute error = 4.640732242933154e-14 relative error = 1.986436481665421e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.93 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4745 Order of pole (three term test) = -10.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.419999999999929 y1[1] (analytic) = 1.650020201017698 y1[1] (numeric) = 1.65002020101775 absolute error = 5.240252676230739e-14 relative error = 3.175871830537991e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2400830714683928 y2[1] (numeric) = 0.2400830714684399 absolute error = 4.707345624410664e-14 relative error = 1.960715345575871e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.25 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.476 Order of pole (three term test) = -11.1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.429999999999929 y1[1] (analytic) = 1.657586742911616 y1[1] (numeric) = 1.657586742911668 absolute error = 5.195843755245733e-14 relative error = 3.134583319675344e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2466211606722067 y2[1] (numeric) = 0.2466211606722545 absolute error = 4.773959005888173e-14 relative error = 1.935745899855454e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4774 Order of pole (three term test) = -11.34 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.439999999999928 y1[1] (analytic) = 1.665087526679229 y1[1] (numeric) = 1.665087526679281 absolute error = 5.173639294753229e-14 relative error = 3.107127530449578e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2532345871321398 y2[1] (numeric) = 0.2532345871321882 absolute error = 4.840572387365683e-14 relative error = 1.911497336199116e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.92 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4786 Order of pole (three term test) = -11.58 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.449999999999928 y1[1] (analytic) = 1.672521802248413 y1[1] (numeric) = 1.672521802248464 absolute error = 5.129230373768223e-14 relative error = 3.066764431335287e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2599226895110573 y2[1] (numeric) = 0.2599226895111063 absolute error = 4.901634653720066e-14 relative error = 1.885804837946457e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.27 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4796 Order of pole (three term test) = -11.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.459999999999928 y1[1] (analytic) = 1.679888826197804 y1[1] (numeric) = 1.679888826197855 absolute error = 5.10702591327572e-14 relative error = 3.040097555047596e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2666847990042946 y2[1] (numeric) = 0.2666847990043443 absolute error = 4.968248035197576e-14 relative error = 1.862966338444198e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4805 Order of pole (three term test) = -12.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.469999999999928 y1[1] (analytic) = 1.687187861831148 y1[1] (numeric) = 1.687187861831199 absolute error = 5.062616992290714e-14 relative error = 3.000624356552759e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2735202394065375 y2[1] (numeric) = 0.2735202394065878 absolute error = 5.034861416675085e-14 relative error = 1.840763750280172e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.97 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4811 Order of pole (three term test) = -12.3 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.479999999999928 y1[1] (analytic) = 1.694418179250964 y1[1] (numeric) = 1.694418179251014 absolute error = 5.018208071305708e-14 relative error = 2.961611326387009e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2804283271794419 y2[1] (numeric) = 0.280428327179493 absolute error = 5.101474798152594e-14 relative error = 1.819172424363619e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.34 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4815 Order of pole (three term test) = -12.54 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.489999999999927 y1[1] (analytic) = 1.701579055431534 y1[1] (numeric) = 1.701579055431584 absolute error = 4.973799150320701e-14 relative error = 2.92304911396509e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2874083715199874 y2[1] (numeric) = 0.2874083715200391 absolute error = 5.168088179630104e-14 relative error = 1.798168978968205e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.499999999999927 y1[1] (analytic) = 1.708669774291209 y1[1] (numeric) = 1.708669774291258 absolute error = 4.929390229335695e-14 relative error = 2.884928558755894e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2944596744295565 y2[1] (numeric) = 0.2944596744296088 absolute error = 5.229150445984487e-14 relative error = 1.775846032606905e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.08 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.509999999999927 y1[1] (analytic) = 1.71568962676401 y1[1] (numeric) = 1.715689626764059 absolute error = 4.907185768843192e-14 relative error = 2.86018268822824e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3015815307837343 y2[1] (numeric) = 0.3015815307837872 absolute error = 5.295763827461997e-14 relative error = 1.755997396027417e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.47 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4817 Order of pole (three term test) = -13.27 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.519999999999927 y1[1] (analytic) = 1.722637910870541 y1[1] (numeric) = 1.72263791087059 absolute error = 4.862776847858186e-14 relative error = 2.822866498625218e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3087732284028203 y2[1] (numeric) = 0.3087732284028739 absolute error = 5.35682609381638e-14 relative error = 1.734873881885886e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.13 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4813 Order of pole (three term test) = -13.51 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.529999999999927 y1[1] (analytic) = 1.729513931788182 y1[1] (numeric) = 1.72951393178823 absolute error = 4.818367926873179e-14 relative error = 2.785966529851174e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3160340481230456 y2[1] (numeric) = 0.3160340481230998 absolute error = 5.42343947529389e-14 relative error = 1.716093410663877e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4808 Order of pole (three term test) = -13.75 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.539999999999926 y1[1] (analytic) = 1.736317001920569 y1[1] (numeric) = 1.736317001920617 absolute error = 4.773959005888173e-14 relative error = 2.749474318691585e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3233632638684888 y2[1] (numeric) = 0.3233632638685437 absolute error = 5.490052856771399e-14 relative error = 1.697797328952058e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4801 Order of pole (three term test) = -13.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.549999999999926 y1[1] (analytic) = 1.743046440966361 y1[1] (numeric) = 1.743046440966408 absolute error = 4.729550084903167e-14 relative error = 2.713381567895037e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3307601427236832 y2[1] (numeric) = 0.3307601427237387 absolute error = 5.551115123125783e-14 relative error = 1.678290218831832e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.01 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4792 Order of pole (three term test) = -14.23 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.559999999999926 y1[1] (analytic) = 1.749701575987258 y1[1] (numeric) = 1.749701575987305 absolute error = 4.707345624410664e-14 relative error = 2.690370568909486e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3382239450069072 y2[1] (numeric) = 0.3382239450069633 absolute error = 5.612177389480166e-14 relative error = 1.659308121831988e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.478 Order of pole (three term test) = -14.47 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.569999999999926 y1[1] (analytic) = 1.756281741475307 y1[1] (numeric) = 1.756281741475353 absolute error = 4.662936703425657e-14 relative error = 2.655004942150518e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3457539243441522 y2[1] (numeric) = 0.345753924344209 absolute error = 5.678790770957676e-14 relative error = 1.64243711238551e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4767 Order of pole (three term test) = -14.71 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.579999999999925 y1[1] (analytic) = 1.76278627941944 y1[1] (numeric) = 1.762786279419486 absolute error = 4.618527782440651e-14 relative error = 2.62001573098341e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3533493277437596 y2[1] (numeric) = 0.353349327743817 absolute error = 5.739853037312059e-14 relative error = 1.624413176038207e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4753 Order of pole (three term test) = -14.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.589999999999925 y1[1] (analytic) = 1.769214539371285 y1[1] (numeric) = 1.769214539371331 absolute error = 4.551914400963142e-14 relative error = 2.572844784884442e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3610093956717189 y2[1] (numeric) = 0.3610093956717769 absolute error = 5.800915303666443e-14 relative error = 1.606859924759815e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4736 Order of pole (three term test) = -15.19 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.78 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.599999999999925 y1[1] (analytic) = 1.775565878510202 y1[1] (numeric) = 1.775565878510248 absolute error = 4.529709940470639e-14 relative error = 2.551135947865429e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3687333621276205 y2[1] (numeric) = 0.3687333621276792 absolute error = 5.861977570020827e-14 relative error = 1.589760561994378e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.28 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4717 Order of pole (three term test) = -15.42 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.609999999999925 y1[1] (analytic) = 1.781839661707572 y1[1] (numeric) = 1.781839661707616 absolute error = 4.463096558993129e-14 relative error = 2.504768894141719e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3765204547212557 y2[1] (numeric) = 0.3765204547213149 absolute error = 5.92303983637521e-14 relative error = 1.57309908720899e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4697 Order of pole (three term test) = -15.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.619999999999925 y1[1] (analytic) = 1.788035261590301 y1[1] (numeric) = 1.788035261590345 absolute error = 4.418687638008123e-14 relative error = 2.471253074773305e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3843698947498542 y2[1] (numeric) = 0.384369894749914 absolute error = 5.978550987606468e-14 relative error = 1.555416037850018e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4674 Order of pole (three term test) = -15.89 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.629999999999924 y1[1] (analytic) = 1.794152058603565 y1[1] (numeric) = 1.794152058603609 absolute error = 4.39648317751562e-14 relative error = 2.450451820085704e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3922808972759542 y2[1] (numeric) = 0.3922808972760147 absolute error = 6.045164369083977e-14 relative error = 1.541029504893643e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.465 Order of pole (three term test) = -16.13 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.639999999999924 y1[1] (analytic) = 1.80018944107276 y1[1] (numeric) = 1.800189441072804 absolute error = 4.352074256530614e-14 relative error = 2.417564594722401e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4002526712058958 y2[1] (numeric) = 0.4002526712059569 absolute error = 6.106226635438361e-14 relative error = 1.525592975317641e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.99 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4624 Order of pole (three term test) = -16.36 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.24 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.649999999999924 y1[1] (analytic) = 1.806146805264671 y1[1] (numeric) = 1.806146805264713 absolute error = 4.285460875053104e-14 relative error = 2.372709052531928e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4082844193689291 y2[1] (numeric) = 0.4082844193689907 absolute error = 6.161737786669619e-14 relative error = 1.509177792332512e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4596 Order of pole (three term test) = -16.59 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.659999999999924 y1[1] (analytic) = 1.812023555447841 y1[1] (numeric) = 1.812023555447883 absolute error = 4.218847493575595e-14 relative error = 2.328252014656017e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4163753385969307 y2[1] (numeric) = 0.4163753385969929 absolute error = 6.222800053024002e-14 relative error = 1.49451696010458e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4566 Order of pole (three term test) = -16.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.669999999999924 y1[1] (analytic) = 1.817819103952151 y1[1] (numeric) = 1.817819103952192 absolute error = 4.174438572590589e-14 relative error = 2.296399330117542e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4245246198047204 y2[1] (numeric) = 0.4245246198047832 absolute error = 6.283862319378386e-14 relative error = 1.480211518066711e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4534 Order of pole (three term test) = -17.05 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.679999999999923 y1[1] (analytic) = 1.823532871227579 y1[1] (numeric) = 1.82353287122762 absolute error = 4.107825191113079e-14 relative error = 2.252674057006576e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4327314480709684 y2[1] (numeric) = 0.4327314480710318 absolute error = 6.339373470609644e-14 relative error = 1.464967128890059e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4501 Order of pole (three term test) = -17.27 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.689999999999923 y1[1] (analytic) = 1.829164285902159 y1[1] (numeric) = 1.8291642859022 absolute error = 4.063416270128073e-14 relative error = 2.221460533340756e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4409950027196871 y2[1] (numeric) = 0.4409950027197511 absolute error = 6.394884621840902e-14 relative error = 1.450103647978462e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4465 Order of pole (three term test) = -17.5 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.699999999999923 y1[1] (analytic) = 1.834712784839117 y1[1] (numeric) = 1.834712784839157 absolute error = 4.019007349143067e-14 relative error = 2.190537604770376e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4493144574022979 y2[1] (numeric) = 0.4493144574023624 absolute error = 6.455946888195285e-14 relative error = 1.436843792100572e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4428 Order of pole (three term test) = -17.72 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.709999999999923 y1[1] (analytic) = 1.840177813193183 y1[1] (numeric) = 1.840177813193223 absolute error = 3.952393967665557e-14 relative error = 2.14783263841614e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4576889801802653 y2[1] (numeric) = 0.4576889801803304 absolute error = 6.511458039426543e-14 relative error = 1.422681847586092e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4389 Order of pole (three term test) = -17.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.719999999999922 y1[1] (analytic) = 1.845558824466076 y1[1] (numeric) = 1.845558824466115 absolute error = 3.885780586188048e-14 relative error = 2.10547641975715e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4661177336082904 y2[1] (numeric) = 0.4661177336083561 absolute error = 6.566969190657801e-14 relative error = 1.40886491054993e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4349 Order of pole (three term test) = -18.16 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.729999999999922 y1[1] (analytic) = 1.850855280561152 y1[1] (numeric) = 1.85085528056119 absolute error = 3.819167204710538e-14 relative error = 2.06346073883887e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4745998748180543 y2[1] (numeric) = 0.4745998748181205 absolute error = 6.622480341889059e-14 relative error = 1.39538181387593e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4306 Order of pole (three term test) = -18.38 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.739999999999922 y1[1] (analytic) = 1.856066651837215 y1[1] (numeric) = 1.856066651837253 absolute error = 3.774758283725532e-14 relative error = 2.033740695674432e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4831345556025043 y2[1] (numeric) = 0.4831345556025711 absolute error = 6.677991493120317e-14 relative error = 1.38222187083935e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4262 Order of pole (three term test) = -18.59 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.749999999999922 y1[1] (analytic) = 1.861192417161481 y1[1] (numeric) = 1.861192417161518 absolute error = 3.708144902248023e-14 relative error = 1.992349027460225e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4917209225006743 y2[1] (numeric) = 0.4917209225007417 absolute error = 6.7390537594747e-14 relative error = 1.370503765673192e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4217 Order of pole (three term test) = -18.81 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.759999999999922 y1[1] (analytic) = 1.866232063961689 y1[1] (numeric) = 1.866232063961726 absolute error = 3.641531520770513e-14 relative error = 1.951274758960131e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5003581168830299 y2[1] (numeric) = 0.5003581168830977 absolute error = 6.783462680459706e-14 relative error = 1.35572152256011e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4169 Order of pole (three term test) = -19.02 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.769999999999921 y1[1] (analytic) = 1.871185088277359 y1[1] (numeric) = 1.871185088277395 absolute error = 3.597122599785507e-14 relative error = 1.92237669181998e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5090452750373302 y2[1] (numeric) = 0.5090452750373986 absolute error = 6.838973831690964e-14 relative error = 1.343490288008161e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.412 Order of pole (three term test) = -19.22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.779999999999921 y1[1] (analytic) = 1.876050994810186 y1[1] (numeric) = 1.876050994810221 absolute error = 3.530509218307998e-14 relative error = 1.881883396599892e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5177815282549992 y2[1] (numeric) = 0.5177815282550682 absolute error = 6.894484982922222e-14 relative error = 1.331543248782486e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4069 Order of pole (three term test) = -19.43 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.789999999999921 y1[1] (analytic) = 1.880829296973572 y1[1] (numeric) = 1.880829296973606 absolute error = 3.463895836830488e-14 relative error = 1.841685389739631e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5265660029179953 y2[1] (numeric) = 0.5265660029180649 absolute error = 6.961098364399732e-14 relative error = 1.321980212513609e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4017 Order of pole (three term test) = -19.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.799999999999921 y1[1] (analytic) = 1.885519516941282 y1[1] (numeric) = 1.885519516941316 absolute error = 3.397282455352979e-14 relative error = 1.801775279878355e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5353978205861726 y2[1] (numeric) = 0.5353978205862427 absolute error = 7.016609515630989e-14 relative error = 1.310541292071185e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3963 Order of pole (three term test) = -19.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.809999999999921 y1[1] (analytic) = 1.890121185695229 y1[1] (numeric) = 1.890121185695262 absolute error = 3.33066907387547e-14 relative error = 1.762145781488807e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5442760980851241 y2[1] (numeric) = 0.5442760980851947 absolute error = 7.061018436615996e-14 relative error = 1.297322895761566e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3907 Order of pole (three term test) = -20.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.81999999999992 y1[1] (analytic) = 1.894633843072372 y1[1] (numeric) = 1.894633843072404 absolute error = 3.26405569239796e-14 relative error = 1.7227897117603e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5531999475944984 y2[1] (numeric) = 0.5531999475945696 absolute error = 7.116529587847253e-14 relative error = 1.286429909979628e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.385 Order of pole (three term test) = -20.22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.82999999999992 y1[1] (analytic) = 1.899057037810733 y1[1] (numeric) = 1.899057037810765 absolute error = 3.197442310920451e-14 relative error = 1.683699987550937e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5621684767367812 y2[1] (numeric) = 0.5621684767368529 absolute error = 7.172040739078511e-14 relative error = 1.275781377979436e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3792 Order of pole (three term test) = -20.41 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.83999999999992 y1[1] (analytic) = 1.903390327594525 y1[1] (numeric) = 1.903390327594556 absolute error = 3.130828929442941e-14 relative error = 1.644869622406685e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5711807886665319 y2[1] (numeric) = 0.571180788666604 absolute error = 7.216449660063518e-14 relative error = 1.263426537315953e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3731 Order of pole (three term test) = -20.6 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.84999999999992 y1[1] (analytic) = 1.90763327909838 y1[1] (numeric) = 1.90763327909841 absolute error = 3.064215547965432e-14 relative error = 1.606291723644965e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5802359821600678 y2[1] (numeric) = 0.5802359821601404 absolute error = 7.260858581048524e-14 relative error = 1.25136303233354e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.367 Order of pole (three term test) = -20.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.859999999999919 y1[1] (analytic) = 1.911785468030683 y1[1] (numeric) = 1.911785468030713 absolute error = 2.997602166487923e-14 relative error = 1.56795948950053e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5893331517055854 y2[1] (numeric) = 0.5893331517056586 absolute error = 7.316369732279782e-14 relative error = 1.241465834919607e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3607 Order of pole (three term test) = -20.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.869999999999919 y1[1] (analytic) = 1.915846479176003 y1[1] (numeric) = 1.915846479176032 absolute error = 2.930988785010413e-14 relative error = 1.529866206331427e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5984713875937113 y2[1] (numeric) = 0.5984713875937849 absolute error = 7.360778653264788e-14 relative error = 1.229929919099466e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3542 Order of pole (three term test) = -21.15 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.879999999999919 y1[1] (analytic) = 1.919815906436607 y1[1] (numeric) = 1.919815906436636 absolute error = 2.864375403532904e-14 relative error = 1.492005245882927e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6076497760084718 y2[1] (numeric) = 0.6076497760085459 absolute error = 7.405187574249794e-14 relative error = 1.218660463086643e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3476 Order of pole (three term test) = -21.32 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.889999999999919 y1[1] (analytic) = 1.923693352873079 y1[1] (numeric) = 1.923693352873107 absolute error = 2.797762022055394e-14 relative error = 1.454370062607366e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6168673991186739 y2[1] (numeric) = 0.6168673991187485 absolute error = 7.460698725481052e-14 relative error = 1.209449346186919e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3409 Order of pole (three term test) = -21.5 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.899999999999919 y1[1] (analytic) = 1.927478430744005 y1[1] (numeric) = 1.927478430744033 absolute error = 2.731148640577885e-14 relative error = 1.416954191037906e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6261233351696882 y2[1] (numeric) = 0.6261233351697633 absolute error = 7.505107646466058e-14 relative error = 1.198662823265015e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.334 Order of pole (three term test) = -21.67 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.909999999999918 y1[1] (analytic) = 1.931170761544753 y1[1] (numeric) = 1.93117076154478 absolute error = 2.664535259100376e-14 relative error = 1.379751243214246e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6354166585756226 y2[1] (numeric) = 0.6354166585756981 absolute error = 7.549516567451064e-14 relative error = 1.188120655252317e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.327 Order of pole (three term test) = -21.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.919999999999918 y1[1] (analytic) = 1.93476997604532 y1[1] (numeric) = 1.934769976045346 absolute error = 2.597921877622866e-14 relative error = 1.342754906158422e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.644746440011881 y2[1] (numeric) = 0.6447464400119569 absolute error = 7.593925488436071e-14 relative error = 1.177815807450776e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3198 Order of pole (three term test) = -21.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.929999999999918 y1[1] (analytic) = 1.938275714327254 y1[1] (numeric) = 1.93827571432728 absolute error = 2.531308496145357e-14 relative error = 1.305958939398844e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6541117465080944 y2[1] (numeric) = 0.6541117465081709 absolute error = 7.649436639667329e-14 relative error = 1.169438812328784e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3126 Order of pole (three term test) = -22.15 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.939999999999918 y1[1] (analytic) = 1.94168762581965 y1[1] (numeric) = 1.941687625819674 absolute error = 2.442490654175344e-14 relative error = 1.257921522337708e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.663511641541418 y2[1] (numeric) = 0.6635116415414949 absolute error = 7.693845560652335e-14 relative error = 1.159564516875484e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3052 Order of pole (three term test) = -22.31 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.949999999999918 y1[1] (analytic) = 1.9450053693342 y1[1] (numeric) = 1.945005369334224 absolute error = 2.375877272697835e-14 relative error = 1.221527359336354e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6729451851301813 y2[1] (numeric) = 0.6729451851302587 absolute error = 7.738254481637341e-14 relative error = 1.149908588786526e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2977 Order of pole (three term test) = -22.46 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.959999999999917 y1[1] (analytic) = 1.94822861309932 y1[1] (numeric) = 1.948228613099342 absolute error = 2.287059430727822e-14 relative error = 1.17391738081984e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6824114339278868 y2[1] (numeric) = 0.6824114339279647 absolute error = 7.782663402622347e-14 relative error = 1.140464976945971e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.29 Order of pole (three term test) = -22.6 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.969999999999917 y1[1] (analytic) = 1.951357034793316 y1[1] (numeric) = 1.951357034793339 absolute error = 2.242650509742816e-14 relative error = 1.149277384792042e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6919094413175433 y2[1] (numeric) = 0.6919094413176216 absolute error = 7.827072323607354e-14 relative error = 1.131227853850778e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2823 Order of pole (three term test) = -22.75 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.979999999999917 y1[1] (analytic) = 1.954390321576629 y1[1] (numeric) = 1.954390321576651 absolute error = 2.153832667772804e-14 relative error = 1.102048369762332e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7014382575063267 y2[1] (numeric) = 0.7014382575064054 absolute error = 7.87148124459236e-14 relative error = 1.122191605655522e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2744 Order of pole (three term test) = -22.89 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.989999999999917 y1[1] (analytic) = 1.957328170123107 y1[1] (numeric) = 1.957328170123128 absolute error = 2.087219286295294e-14 relative error = 1.066361440127855e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7109969296205589 y2[1] (numeric) = 0.710996929620638 absolute error = 7.904787935331115e-14 relative error = 1.111789320883523e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2665 Order of pole (three term test) = -23.02 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.999999999999917 y1[1] (analytic) = 1.960170286650343 y1[1] (numeric) = 1.960170286650363 absolute error = 1.998401444325282e-14 relative error = 1.019503998165522e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.720584501800994 y2[1] (numeric) = 0.7205845018010735 absolute error = 7.949196856316121e-14 relative error = 1.103159565109752e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2584 Order of pole (three term test) = -23.15 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.009999999999916 y1[1] (analytic) = 1.962916386949053 y1[1] (numeric) = 1.962916386949072 absolute error = 1.931788062847772e-14 relative error = 9.84141798240493e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.7302000152984034 y2[1] (numeric) = 0.7302000152984833 absolute error = 7.993605777301127e-14 relative error = 1.094714545306393e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2502 Order of pole (three term test) = -23.28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.019999999999916 y1[1] (analytic) = 1.965566196411496 y1[1] (numeric) = 1.965566196411515 absolute error = 1.865174681370263e-14 relative error = 9.489248872795452e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.7398425085694504 y2[1] (numeric) = 0.7398425085695308 absolute error = 8.038014698286133e-14 relative error = 1.086449427436703e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2419 Order of pole (three term test) = -23.41 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.029999999999916 y1[1] (analytic) = 1.968119450058934 y1[1] (numeric) = 1.968119450058951 absolute error = 1.77635683940025e-14 relative error = 9.025655629525225e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.7495110173728434 y2[1] (numeric) = 0.7495110173729241 absolute error = 8.071321389024888e-14 relative error = 1.07687828490049e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2335 Order of pole (three term test) = -23.52 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.039999999999916 y1[1] (analytic) = 1.970575892568129 y1[1] (numeric) = 1.970575892568146 absolute error = 1.709743457922741e-14 relative error = 8.676364429154458e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.7592045748657589 y2[1] (numeric) = 0.75920457486584 absolute error = 8.115730310009894e-14 relative error = 1.068978056598895e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2251 Order of pole (three term test) = -23.64 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.049999999999915 y1[1] (analytic) = 1.972935278296878 y1[1] (numeric) = 1.972935278296894 absolute error = 1.643130076445232e-14 relative error = 8.328352655661628e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.7689222117005257 y2[1] (numeric) = 0.7689222117006071 absolute error = 8.149037000748649e-14 relative error = 1.059799922117802e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2165 Order of pole (three term test) = -23.75 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.059999999999915 y1[1] (analytic) = 1.975197371308574 y1[1] (numeric) = 1.97519737130859 absolute error = 1.554312234475219e-14 relative error = 7.869148962290704e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.7786629561215582 y2[1] (numeric) = 0.77866295612164 absolute error = 8.182343691487404e-14 relative error = 1.050819693830413e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2079 Order of pole (three term test) = -23.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.069999999999915 y1[1] (analytic) = 1.977361945395801 y1[1] (numeric) = 1.977361945395816 absolute error = 1.48769885299771e-14 relative error = 7.523654718154914e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.7884258340625316 y2[1] (numeric) = 0.7884258340626138 absolute error = 8.215650382226158e-14 relative error = 1.042032113520846e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1991 Order of pole (three term test) = -23.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.079999999999915 y1[1] (analytic) = 1.979428784102954 y1[1] (numeric) = 1.979428784102968 absolute error = 1.398881011027697e-14 relative error = 7.067094417653667e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.7982098692437876 y2[1] (numeric) = 0.7982098692438702 absolute error = 8.260059303211165e-14 relative error = 1.034822998497453e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1903 Order of pole (three term test) = -24.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.089999999999915 y1[1] (analytic) = 1.981397680747885 y1[1] (numeric) = 1.981397680747898 absolute error = 1.310063169057685e-14 relative error = 6.611813376924906e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.8080140832699613 y2[1] (numeric) = 0.8080140832700442 absolute error = 8.293365993949919e-14 relative error = 1.026388792678885e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1814 Order of pole (three term test) = -24.15 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.099999999999914 y1[1] (analytic) = 1.983268438442569 y1[1] (numeric) = 1.983268438442581 absolute error = 1.243449787580175e-14 relative error = 6.269699872583249e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.8178374957278203 y2[1] (numeric) = 0.8178374957279035 absolute error = 8.326672684688674e-14 relative error = 1.018132908821758e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1725 Order of pole (three term test) = -24.24 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.109999999999914 y1[1] (analytic) = 1.985040870112797 y1[1] (numeric) = 1.985040870112808 absolute error = 1.154631945610163e-14 relative error = 5.81666585809164e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.8276791242843049 y2[1] (numeric) = 0.8276791242843885 absolute error = 8.359979375427429e-14 relative error = 1.010050770901865e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1635 Order of pole (three term test) = -24.32 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.119999999999914 y1[1] (analytic) = 1.986714798516878 y1[1] (numeric) = 1.986714798516889 absolute error = 1.088018564132653e-14 relative error = 5.476470829858825e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.8375379847847608 y2[1] (numeric) = 0.8375379847848448 absolute error = 8.393286066166183e-14 relative error = 1.002137958951578e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1544 Order of pole (three term test) = -24.4 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.129999999999914 y1[1] (analytic) = 1.988290056263367 y1[1] (numeric) = 1.988290056263377 absolute error = 9.992007221626409e-15 relative error = 5.025427346553543e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.8474130913513537 y2[1] (numeric) = 0.8474130913514379 absolute error = 8.426592756904938e-14 relative error = 9.94390202712966e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1452 Order of pole (three term test) = -24.48 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.139999999999914 y1[1] (analytic) = 1.989766485827802 y1[1] (numeric) = 1.989766485827811 absolute error = 9.103828801926284e-15 relative error = 4.575325228748548e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.8573034564816562 y2[1] (numeric) = 0.8573034564817407 absolute error = 8.448797217397441e-14 relative error = 9.855083580405722e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.136 Order of pole (three term test) = -24.55 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.149999999999913 y1[1] (analytic) = 1.991143939568457 y1[1] (numeric) = 1.991143939568466 absolute error = 8.215650382226158e-15 relative error = 4.126095667401496e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.8672080911473971 y2[1] (numeric) = 0.8672080911474819 absolute error = 8.482103908136196e-14 relative error = 9.780932621273842e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1267 Order of pole (three term test) = -24.61 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.159999999999913 y1[1] (analytic) = 1.992422279741106 y1[1] (numeric) = 1.992422279741114 absolute error = 7.327471962526033e-15 relative error = 3.67767015909808e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.8771260048933636 y2[1] (numeric) = 0.8771260048934487 absolute error = 8.515410598874951e-14 relative error = 9.708309355062629e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1174 Order of pole (three term test) = -24.67 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.169999999999913 y1[1] (analytic) = 1.993601378512797 y1[1] (numeric) = 1.993601378512803 absolute error = 6.439293542825908e-15 relative error = 3.229980482672793e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.8870562059364462 y2[1] (numeric) = 0.8870562059365316 absolute error = 8.537615059367454e-14 relative error = 9.624660762453578e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1081 Order of pole (three term test) = -24.73 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.179999999999913 y1[1] (analytic) = 1.994681117974634 y1[1] (numeric) = 1.99468111797464 absolute error = 5.773159728050814e-15 relative error = 2.894277023042552e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.8969977012648156 y2[1] (numeric) = 0.8969977012649013 absolute error = 8.570921750106208e-14 relative error = 9.555121198215717e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09866 Order of pole (three term test) = -24.78 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.189999999999912 y1[1] (analytic) = 1.995661390153572 y1[1] (numeric) = 1.995661390153577 absolute error = 4.884981308350689e-15 relative error = 2.44780068024204e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.9069494967372236 y2[1] (numeric) = 0.9069494967373095 absolute error = 8.593126210598712e-14 relative error = 9.474757129821149e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08922 Order of pole (three term test) = -24.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.199999999999912 y1[1] (analytic) = 1.99654209702321 y1[1] (numeric) = 1.996542097023214 absolute error = 3.996802888650564e-15 relative error = 2.00186256759108e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.916910597182416 y2[1] (numeric) = 0.9169105971825022 absolute error = 8.626432901337466e-14 relative error = 9.40815050872541e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07974 Order of pole (three term test) = -24.87 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.209999999999912 y1[1] (analytic) = 1.997323150513595 y1[1] (numeric) = 1.997323150513598 absolute error = 3.108624468950438e-15 relative error = 1.556395352525244e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.9268800064986492 y2[1] (numeric) = 0.9268800064987357 absolute error = 8.648637361829969e-14 relative error = 9.330913711798328e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07022 Order of pole (three term test) = -24.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.219999999999912 y1[1] (analytic) = 1.998004472520028 y1[1] (numeric) = 1.99800447252003 absolute error = 2.442490654175344e-15 relative error = 1.22246505839634e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.9368567277532994 y2[1] (numeric) = 0.9368567277533862 absolute error = 8.681944052568724e-14 relative error = 9.26709900817932e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06068 Order of pole (three term test) = -24.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.229999999999912 y1[1] (analytic) = 1.998585994910877 y1[1] (numeric) = 1.998585994910878 absolute error = 1.554312234475219e-15 relative error = 7.777059573283615e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 0.9468397632825551 y2[1] (numeric) = 0.9468397632826422 absolute error = 8.704148513061227e-14 relative error = 9.192842179425605e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05112 Order of pole (three term test) = -24.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.239999999999911 y1[1] (analytic) = 1.999067659534386 y1[1] (numeric) = 1.999067659534387 absolute error = 8.881784197001252e-16 relative error = 4.442963275725223e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 0.9568281147911826 y2[1] (numeric) = 0.9568281147912698 absolute error = 8.72635297355373e-14 relative error = 9.120084201808976e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04153 Order of pole (three term test) = -24.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.249999999999911 y1[1] (analytic) = 1.999449418224496 y1[1] (numeric) = 1.999449418224496 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 0.9668207834523544 y2[1] (numeric) = 0.9668207834524419 absolute error = 8.748557434046234e-14 relative error = 9.048789169391462e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03193 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.259999999999911 y1[1] (analytic) = 1.999731232805656 y1[1] (numeric) = 1.999731232805655 absolute error = 8.881784197001252e-16 relative error = 4.441488961764108e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 0.9768167700075318 y2[1] (numeric) = 0.9768167700076195 absolute error = 8.770761894538737e-14 relative error = 8.978922315667359e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02232 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.269999999999911 y1[1] (analytic) = 1.999913075096641 y1[1] (numeric) = 1.999913075096639 absolute error = 1.77635683940025e-15 relative error = 8.882170237896025e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 0.9868150748663891 y2[1] (numeric) = 0.9868150748664769 absolute error = 8.781864124784988e-14 relative error = 8.899199402658111e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0127 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.279999999999911 y1[1] (analytic) = 1.999994926913375 y1[1] (numeric) = 1.999994926913372 absolute error = 2.664535259100376e-15 relative error = 1.332271008913306e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.9968146982067723 y2[1] (numeric) = 0.9968146982068603 absolute error = 8.804068585277491e-14 relative error = 8.832201813552349e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.003067 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.28999999999991 y1[1] (analytic) = 1.999976780070744 y1[1] (numeric) = 1.99997678007074 absolute error = 3.552713678800501e-15 relative error = 1.776377463079763e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.00681464007468 y2[1] (numeric) = 1.006814640074769 absolute error = 8.815170815523743e-14 relative error = 8.755505198921102e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.006571 Order of pole (three term test) = -0.894 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.29999999999991 y1[1] (analytic) = 1.999858636383417 y1[1] (numeric) = 1.999858636383412 absolute error = 4.218847493575595e-15 relative error = 2.109572855211927e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.01681390048426 y2[1] (numeric) = 1.016813900484348 absolute error = 8.837375276016246e-14 relative error = 8.691241604591976e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.01621 Order of pole (three term test) = -0.8997 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.30999999999991 y1[1] (analytic) = 1.999640507665664 y1[1] (numeric) = 1.999640507665659 absolute error = 5.329070518200751e-15 relative error = 2.665014285203589e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.026811479517803 y2[1] (numeric) = 1.026811479517891 absolute error = 8.859579736508749e-14 relative error = 8.628243755776148e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02584 Order of pole (three term test) = -0.9102 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.31999999999991 y1[1] (analytic) = 1.999322415730176 y1[1] (numeric) = 1.99932241573017 absolute error = 5.995204332975845e-15 relative error = 2.998618074707239e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.036806377425736 y2[1] (numeric) = 1.036806377425825 absolute error = 8.881784197001252e-14 relative error = 8.566482990829627e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03547 Order of pole (three term test) = -0.9256 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.329999999999909 y1[1] (analytic) = 1.99890439238588 y1[1] (numeric) = 1.998904392385873 absolute error = 7.105427357601002e-15 relative error = 3.554660935593826e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.0467975947266 y2[1] (numeric) = 1.046797594726688 absolute error = 8.881784197001252e-14 relative error = 8.48471972207863e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04508 Order of pole (three term test) = -0.9458 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.339999999999909 y1[1] (analytic) = 1.998386479434764 y1[1] (numeric) = 1.998386479434756 absolute error = 7.993605777301127e-15 relative error = 4.00002995394669e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.056784132306988 y2[1] (numeric) = 1.056784132307077 absolute error = 8.903988657493755e-14 relative error = 8.425551051808579e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05467 Order of pole (three term test) = -0.9708 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.349999999999909 y1[1] (analytic) = 1.99776872866769 y1[1] (numeric) = 1.997768728667681 absolute error = 8.881784197001252e-15 relative error = 4.445852049613623e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.066764991521465 y2[1] (numeric) = 1.066764991521554 absolute error = 8.926193117986259e-14 relative error = 8.367534732514372e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06424 Order of pole (three term test) = -1.001 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.359999999999909 y1[1] (analytic) = 1.997051201859221 y1[1] (numeric) = 1.997051201859211 absolute error = 9.769962616701378e-15 relative error = 4.892194355160102e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.076739174292428 y2[1] (numeric) = 1.076739174292517 absolute error = 8.926193117986259e-14 relative error = 8.290023555474379e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07378 Order of pole (three term test) = -1.035 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.369999999999909 y1[1] (analytic) = 1.996233970761438 y1[1] (numeric) = 1.996233970761428 absolute error = 1.06581410364015e-14 relative error = 5.339124167061484e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.08670568320991 y2[1] (numeric) = 1.086705683209999 absolute error = 8.926193117986259e-14 relative error = 8.213993223648263e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08329 Order of pole (three term test) = -1.075 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.379999999999908 y1[1] (analytic) = 1.995317117096773 y1[1] (numeric) = 1.995317117096761 absolute error = 1.176836406102666e-14 relative error = 5.897991833072565e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.096663521631326 y2[1] (numeric) = 1.096663521631416 absolute error = 8.948397578478762e-14 relative error = 8.159656450656534e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09277 Order of pole (three term test) = -1.119 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.389999999999908 y1[1] (analytic) = 1.994300732549825 y1[1] (numeric) = 1.994300732549812 absolute error = 1.265654248072678e-14 relative error = 6.34635603053943e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.106611693781132 y2[1] (numeric) = 1.106611693781221 absolute error = 8.948397578478762e-14 relative error = 8.086303107735455e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1022 Order of pole (three term test) = -1.168 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.399999999999908 y1[1] (analytic) = 1.993184918758203 y1[1] (numeric) = 1.99318491875819 absolute error = 1.354472090042691e-14 relative error = 6.795516448551878e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.116549204850402 y2[1] (numeric) = 1.116549204850491 absolute error = 8.948397578478762e-14 relative error = 8.014333394001825e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1116 Order of pole (three term test) = -1.221 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.409999999999908 y1[1] (analytic) = 1.991969787302357 y1[1] (numeric) = 1.991969787302343 absolute error = 1.443289932012704e-14 relative error = 7.245541278852886e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.126475061096311 y2[1] (numeric) = 1.126475061096401 absolute error = 8.970602038971265e-14 relative error = 7.963427108844178e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.121 Order of pole (three term test) = -1.28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.419999999999908 y1[1] (analytic) = 1.99065545969442 y1[1] (numeric) = 1.990655459694405 absolute error = 1.554312234475219e-14 relative error = 7.808042456095427e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.136388269941506 y2[1] (numeric) = 1.136388269941596 absolute error = 8.970602038971265e-14 relative error = 7.893958672622529e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1303 Order of pole (three term test) = -1.343 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.429999999999907 y1[1] (analytic) = 1.989242067366057 y1[1] (numeric) = 1.98924206736604 absolute error = 1.643130076445232e-14 relative error = 8.260081080131641e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.146287840073364 y2[1] (numeric) = 1.146287840073453 absolute error = 8.970602038971265e-14 relative error = 7.825784873018575e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1395 Order of pole (three term test) = -1.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.439999999999907 y1[1] (analytic) = 1.987729751655323 y1[1] (numeric) = 1.987729751655305 absolute error = 1.754152378907747e-14 relative error = 8.824903775007347e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.15617278154312 y2[1] (numeric) = 1.156172781543209 absolute error = 8.970602038971265e-14 relative error = 7.75887668536738e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1487 Order of pole (three term test) = -1.483 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.449999999999907 y1[1] (analytic) = 1.986118663792528 y1[1] (numeric) = 1.98611866379251 absolute error = 1.84297022087776e-14 relative error = 9.279255335925277e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.166042105864865 y2[1] (numeric) = 1.166042105864955 absolute error = 8.970602038971265e-14 relative error = 7.693205926142503e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1579 Order of pole (three term test) = -1.559 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.459999999999907 y1[1] (analytic) = 1.984408964885117 y1[1] (numeric) = 1.984408964885098 absolute error = 1.931788062847772e-14 relative error = 9.734828339477941e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 1.175894826114392 y2[1] (numeric) = 1.175894826114482 absolute error = 8.970602038971265e-14 relative error = 7.628745224276201e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.167 Order of pole (three term test) = -1.641 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.469999999999906 y1[1] (analytic) = 1.982600825901556 y1[1] (numeric) = 1.982600825901536 absolute error = 2.020605904817785e-14 relative error = 1.019169304491209e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.185729957027886 y2[1] (numeric) = 1.185729957027976 absolute error = 8.970602038971265e-14 relative error = 7.565467993620315e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.176 Order of pole (three term test) = -1.727 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.479999999999906 y1[1] (analytic) = 1.980694427654236 y1[1] (numeric) = 1.980694427654214 absolute error = 2.109423746787797e-14 relative error = 1.064992013576783e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.195546515100452 y2[1] (numeric) = 1.195546515100542 absolute error = 8.992806499463768e-14 relative error = 7.521921051066907e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1849 Order of pole (three term test) = -1.817 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.489999999999906 y1[1] (analytic) = 1.978689960781393 y1[1] (numeric) = 1.978689960781371 absolute error = 2.19824158875781e-14 relative error = 1.110958074447255e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.205343518684463 y2[1] (numeric) = 1.205343518684552 absolute error = 8.970602038971265e-14 relative error = 7.442361368286088e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1938 Order of pole (three term test) = -1.912 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.499999999999906 y1[1] (analytic) = 1.976587625728044 y1[1] (numeric) = 1.976587625728021 absolute error = 2.287059430727822e-14 relative error = 1.157074647720422e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.215119988087723 y2[1] (numeric) = 1.215119988087813 absolute error = 8.992806499463768e-14 relative error = 7.400755964533231e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2026 Order of pole (three term test) = -2.012 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.509999999999906 y1[1] (analytic) = 1.974387632725942 y1[1] (numeric) = 1.974387632725918 absolute error = 2.398081733190338e-14 relative error = 1.214595195716163e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.224874945671442 y2[1] (numeric) = 1.224874945671532 absolute error = 8.970602038971265e-14 relative error = 7.323688079891154e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2113 Order of pole (three term test) = -2.115 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.519999999999905 y1[1] (analytic) = 1.972090201772555 y1[1] (numeric) = 1.972090201772531 absolute error = 2.486899575160351e-14 relative error = 1.261047579327291e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.234607415947989 y2[1] (numeric) = 1.234607415948078 absolute error = 8.970602038971265e-14 relative error = 7.265955090738883e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2199 Order of pole (three term test) = -2.223 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.529999999999905 y1[1] (analytic) = 1.969695562609064 y1[1] (numeric) = 1.969695562609038 absolute error = 2.575717417130363e-14 relative error = 1.307672853625441e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.244316425678446 y2[1] (numeric) = 1.244316425678535 absolute error = 8.970602038971265e-14 relative error = 7.209261128318043e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2284 Order of pole (three term test) = -2.336 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.539999999999905 y1[1] (analytic) = 1.967203954697388 y1[1] (numeric) = 1.967203954697361 absolute error = 2.664535259100376e-14 relative error = 1.354478396984647e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.254001003969931 y2[1] (numeric) = 1.254001003970021 absolute error = 8.970602038971265e-14 relative error = 7.153584415460615e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2369 Order of pole (three term test) = -2.453 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.549999999999905 y1[1] (analytic) = 1.964615627196243 y1[1] (numeric) = 1.964615627196216 absolute error = 2.753353101070388e-14 relative error = 1.401471648171594e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.263660182372687 y2[1] (numeric) = 1.263660182372776 absolute error = 8.948397578478762e-14 relative error = 7.081332231009272e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2452 Order of pole (three term test) = -2.573 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.559999999999905 y1[1] (analytic) = 1.961930838936222 y1[1] (numeric) = 1.961930838936194 absolute error = 2.864375403532904e-14 relative error = 1.459977766130633e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.273292994976921 y2[1] (numeric) = 1.27329299497701 absolute error = 8.948397578478762e-14 relative error = 7.027760000078345e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2535 Order of pole (three term test) = -2.698 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.569999999999904 y1[1] (analytic) = 1.959149858393914 y1[1] (numeric) = 1.959149858393885 absolute error = 2.953193245502916e-14 relative error = 1.507385069523934e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.282898478509401 y2[1] (numeric) = 1.28289847850949 absolute error = 8.948397578478762e-14 relative error = 6.975140845810263e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2616 Order of pole (three term test) = -2.828 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.579999999999904 y1[1] (analytic) = 1.956272963665056 y1[1] (numeric) = 1.956272963665025 absolute error = 3.042011087472929e-14 relative error = 1.555003388573011e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.292475672429778 y2[1] (numeric) = 1.292475672429867 absolute error = 8.926193117986259e-14 relative error = 6.906275536471447e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2697 Order of pole (three term test) = -2.961 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.589999999999904 y1[1] (analytic) = 1.953300442436722 y1[1] (numeric) = 1.953300442436691 absolute error = 3.130828929442941e-14 relative error = 1.602840434284274e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.302023619026641 y2[1] (numeric) = 1.30202361902673 absolute error = 8.903988657493755e-14 relative error = 6.838576910110238e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2776 Order of pole (three term test) = -3.098 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.599999999999904 y1[1] (analytic) = 1.950232591958559 y1[1] (numeric) = 1.950232591958527 absolute error = 3.241851231905457e-14 relative error = 1.662289536782771e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.311541363513287 y2[1] (numeric) = 1.311541363513376 absolute error = 8.903988657493755e-14 relative error = 6.788949937226706e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2854 Order of pole (three term test) = -3.239 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.609999999999904 y1[1] (analytic) = 1.947069719013059 y1[1] (numeric) = 1.947069719013025 absolute error = 3.33066907387547e-14 relative error = 1.71060596410679e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.321027954123198 y2[1] (numeric) = 1.321027954123287 absolute error = 8.881784197001252e-14 relative error = 6.723388531847028e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2931 Order of pole (three term test) = -3.384 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.619999999999903 y1[1] (analytic) = 1.943812139884879 y1[1] (numeric) = 1.943812139884844 absolute error = 3.441691376337985e-14 relative error = 1.770588477002627e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.330482442205219 y2[1] (numeric) = 1.330482442205308 absolute error = 8.881784197001252e-14 relative error = 6.675611729441587e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3007 Order of pole (three term test) = -3.533 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.629999999999903 y1[1] (analytic) = 1.940460180329218 y1[1] (numeric) = 1.940460180329182 absolute error = 3.530509218307998e-14 relative error = 1.819418534890529e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.339903882318422 y2[1] (numeric) = 1.33990388231851 absolute error = 8.859579736508749e-14 relative error = 6.612100952479599e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3082 Order of pole (three term test) = -3.686 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.639999999999903 y1[1] (analytic) = 1.937014175539238 y1[1] (numeric) = 1.937014175539202 absolute error = 3.641531520770513e-14 relative error = 1.879971539060503e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.349291332326644 y2[1] (numeric) = 1.349291332326733 absolute error = 8.837375276016246e-14 relative error = 6.549642070832516e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3155 Order of pole (three term test) = -3.842 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.649999999999903 y1[1] (analytic) = 1.933474470112547 y1[1] (numeric) = 1.93347447011251 absolute error = 3.730349362740526e-14 relative error = 1.929350203689725e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.358643853492709 y2[1] (numeric) = 1.358643853492797 absolute error = 8.815170815523743e-14 relative error = 6.488213075753665e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3228 Order of pole (three term test) = -4.002 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.659999999999902 y1[1] (analytic) = 1.929841418016737 y1[1] (numeric) = 1.929841418016699 absolute error = 3.841371665203042e-14 relative error = 1.990511567085522e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.367960510572294 y2[1] (numeric) = 1.367960510572382 absolute error = 8.79296635503124e-14 relative error = 6.427792532806853e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3299 Order of pole (three term test) = -4.166 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.669999999999902 y1[1] (analytic) = 1.926115382553991 y1[1] (numeric) = 1.926115382553952 absolute error = 3.930189507173054e-14 relative error = 2.040474596055455e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.377240371907454 y2[1] (numeric) = 1.377240371907542 absolute error = 8.770761894538737e-14 relative error = 6.368359564127055e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3368 Order of pole (three term test) = -4.333 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.679999999999902 y1[1] (analytic) = 1.92229673632475 y1[1] (numeric) = 1.92229673632471 absolute error = 4.019007349143067e-14 relative error = 2.090732025497286e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.386482509519789 y2[1] (numeric) = 1.386482509519877 absolute error = 8.748557434046234e-14 relative error = 6.309893831315848e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3437 Order of pole (three term test) = -4.503 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.689999999999902 y1[1] (analytic) = 1.918385861190455 y1[1] (numeric) = 1.918385861190414 absolute error = 4.107825191113079e-14 relative error = 2.141292465825393e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.39568599920324 y2[1] (numeric) = 1.395685999203327 absolute error = 8.72635297355373e-14 relative error = 6.252375518945788e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3503 Order of pole (three term test) = -4.677 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.699999999999902 y1[1] (analytic) = 1.914383148235359 y1[1] (numeric) = 1.914383148235317 absolute error = 4.218847493575595e-14 relative error = 2.203763388465076e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.404849920616508 y2[1] (numeric) = 1.404849920616595 absolute error = 8.704148513061227e-14 relative error = 6.19578531864918e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3569 Order of pole (three term test) = -4.855 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.709999999999901 y1[1] (analytic) = 1.910288997727424 y1[1] (numeric) = 1.91028899772738 absolute error = 4.307665335545607e-14 relative error = 2.254980969199019e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.413973357375088 y2[1] (numeric) = 1.413973357375175 absolute error = 8.681944052568724e-14 relative error = 6.140104413767708e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3633 Order of pole (three term test) = -5.035 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.719999999999901 y1[1] (analytic) = 1.906103819078287 y1[1] (numeric) = 1.906103819078243 absolute error = 4.418687638008123e-14 relative error = 2.318177842036337e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.423055397142907 y2[1] (numeric) = 1.423055397142994 absolute error = 8.681944052568724e-14 relative error = 6.100917834962441e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3696 Order of pole (three term test) = -5.219 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.729999999999901 y1[1] (analytic) = 1.901828030802326 y1[1] (numeric) = 1.901828030802281 absolute error = 4.529709940470639e-14 relative error = 2.381766314885834e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.432095131723558 y2[1] (numeric) = 1.432095131723644 absolute error = 8.637535131583718e-14 relative error = 6.031397593809468e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3757 Order of pole (three term test) = -5.406 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.739999999999901 y1[1] (analytic) = 1.897462060474806 y1[1] (numeric) = 1.89746206047476 absolute error = 4.618527782440651e-14 relative error = 2.434055404135431e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.441091657151113 y2[1] (numeric) = 1.441091657151199 absolute error = 8.637535131583718e-14 relative error = 5.993744456656712e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3816 Order of pole (three term test) = -5.596 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.749999999999901 y1[1] (analytic) = 1.893006344689121 y1[1] (numeric) = 1.893006344689074 absolute error = 4.729550084903167e-14 relative error = 2.498433298003487e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.450044073780529 y2[1] (numeric) = 1.450044073780615 absolute error = 8.615330671091215e-14 relative error = 5.941426765484087e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3874 Order of pole (three term test) = -5.788 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.7599999999999 y1[1] (analytic) = 1.888461329013137 y1[1] (numeric) = 1.888461329013089 absolute error = 4.818367926873179e-14 relative error = 2.551478207600438e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.458951486377602 y2[1] (numeric) = 1.458951486377688 absolute error = 8.593126210598712e-14 relative error = 5.889932798200435e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3931 Order of pole (three term test) = -5.984 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.7699999999999 y1[1] (analytic) = 1.883827467944633 y1[1] (numeric) = 1.883827467944584 absolute error = 4.907185768843192e-14 relative error = 2.604901909725958e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.467813004208496 y2[1] (numeric) = 1.467813004208581 absolute error = 8.548717289613705e-14 relative error = 5.824118784274923e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3986 Order of pole (three term test) = -6.182 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.7799999999999 y1[1] (analytic) = 1.879105224865856 y1[1] (numeric) = 1.879105224865806 absolute error = 4.996003610813204e-14 relative error = 2.658714128778954e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.476627741128811 y2[1] (numeric) = 1.476627741128896 absolute error = 8.504308368628699e-14 relative error = 5.759277122971807e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4039 Order of pole (three term test) = -6.384 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.7899999999999 y1[1] (analytic) = 1.874295071997177 y1[1] (numeric) = 1.874295071997126 absolute error = 5.084821452783217e-14 relative error = 2.712924730344101e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.485394815672203 y2[1] (numeric) = 1.485394815672287 absolute error = 8.482103908136196e-14 relative error = 5.710336281399833e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4091 Order of pole (three term test) = -6.587 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.799999999999899 y1[1] (analytic) = 1.869397490349875 y1[1] (numeric) = 1.869397490349823 absolute error = 5.195843755245733e-14 relative error = 2.779421595496677e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.494113351138521 y2[1] (numeric) = 1.494113351138605 absolute error = 8.43769498715119e-14 relative error = 5.647292409723552e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4141 Order of pole (three term test) = -6.794 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.809999999999899 y1[1] (analytic) = 1.864412969678033 y1[1] (numeric) = 1.864412969677981 absolute error = 5.284661597215745e-14 relative error = 2.834490900440559e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.502782475681485 y2[1] (numeric) = 1.502782475681569 absolute error = 8.415490526658687e-14 relative error = 5.599939221305074e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4189 Order of pole (three term test) = -7.003 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.819999999999899 y1[1] (analytic) = 1.859342008429566 y1[1] (numeric) = 1.859342008429512 absolute error = 5.395683899678261e-14 relative error = 2.901931906672487e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.511401322395865 y2[1] (numeric) = 1.511401322395949 absolute error = 8.37108160567368e-14 relative error = 5.538622655433361e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4236 Order of pole (three term test) = -7.214 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.829999999999899 y1[1] (analytic) = 1.854185113696371 y1[1] (numeric) = 1.854185113696317 absolute error = 5.484501741648273e-14 relative error = 2.957904095516526e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.519969029404172 y2[1] (numeric) = 1.519969029404256 absolute error = 8.326672684688674e-14 relative error = 5.478185754845761e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4281 Order of pole (three term test) = -7.427 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.839999999999899 y1[1] (analytic) = 1.848942801163626 y1[1] (numeric) = 1.84894280116357 absolute error = 5.595524044110789e-14 relative error = 3.026337018424402e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.528484739942845 y2[1] (numeric) = 1.528484739942928 absolute error = 8.304468224196171e-14 relative error = 5.433137804507425e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4325 Order of pole (three term test) = -7.643 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.849999999999898 y1[1] (analytic) = 1.843615595058214 y1[1] (numeric) = 1.843615595058157 absolute error = 5.684341886080801e-14 relative error = 3.083257649434948e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.536947602447926 y2[1] (numeric) = 1.536947602448008 absolute error = 8.260059303211165e-14 relative error = 5.374327198959295e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4366 Order of pole (three term test) = -7.861 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.859999999999898 y1[1] (analytic) = 1.838204028096307 y1[1] (numeric) = 1.838204028096249 absolute error = 5.773159728050814e-14 relative error = 3.14065231052162e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.545356770640216 y2[1] (numeric) = 1.545356770640299 absolute error = 8.215650382226158e-14 relative error = 5.316345415060722e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4406 Order of pole (three term test) = -8.081 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.869999999999898 y1[1] (analytic) = 1.832708641430091 y1[1] (numeric) = 1.832708641430032 absolute error = 5.88418203051333e-14 relative error = 3.210647834301589e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.553711403609906 y2[1] (numeric) = 1.553711403609987 absolute error = 8.193445921733655e-14 relative error = 5.273467069043155e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4444 Order of pole (three term test) = -8.302 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.879999999999898 y1[1] (analytic) = 1.827129984593654 y1[1] (numeric) = 1.827129984593594 absolute error = 5.950795411990839e-14 relative error = 3.256908628377784e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.562010665900659 y2[1] (numeric) = 1.56201066590074 absolute error = 8.149037000748649e-14 relative error = 5.217017513801609e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4481 Order of pole (three term test) = -8.526 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.889999999999898 y1[1] (analytic) = 1.82146861544803 y1[1] (numeric) = 1.82146861544797 absolute error = 6.039613253960852e-14 relative error = 3.315793202659864e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.570253727593162 y2[1] (numeric) = 1.570253727593243 absolute error = 8.104628079763643e-14 relative error = 5.161349364975668e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4515 Order of pole (three term test) = -8.752 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.899999999999897 y1[1] (analytic) = 1.815725100125416 y1[1] (numeric) = 1.815725100125355 absolute error = 6.128431095930864e-14 relative error = 3.375197652721526e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.578439764388116 y2[1] (numeric) = 1.578439764388197 absolute error = 8.060219158778636e-14 relative error = 5.106447100883314e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4548 Order of pole (three term test) = -8.979 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.909999999999897 y1[1] (analytic) = 1.809900012972559 y1[1] (numeric) = 1.809900012972497 absolute error = 6.217248937900877e-14 relative error = 3.435133926370738e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.586567957688663 y2[1] (numeric) = 1.586567957688743 absolute error = 8.01581023779363e-14 relative error = 5.052295553397655e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4579 Order of pole (three term test) = -9.207 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.919999999999897 y1[1] (analytic) = 1.803993936493318 y1[1] (numeric) = 1.803993936493255 absolute error = 6.306066779870889e-14 relative error = 3.495614177134594e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.594637494682246 y2[1] (numeric) = 1.594637494682325 absolute error = 7.971401316808624e-14 relative error = 4.998879898027884e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.05 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4608 Order of pole (three term test) = -9.438 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.929999999999897 y1[1] (analytic) = 1.798007461290421 y1[1] (numeric) = 1.798007461290357 absolute error = 6.394884621840902e-14 relative error = 3.556650770098208e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.60264756842189 y2[1] (numeric) = 1.602647568421969 absolute error = 7.904787935331115e-14 relative error = 4.932330782565548e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.35 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4635 Order of pole (three term test) = -9.669 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.939999999999896 y1[1] (analytic) = 1.791941186006399 y1[1] (numeric) = 1.791941186006334 absolute error = 6.483702463810914e-14 relative error = 3.618256287897922e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.610597377906897 y2[1] (numeric) = 1.610597377906976 absolute error = 7.882583474838611e-14 relative error = 4.894198626526187e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.466 Order of pole (three term test) = -9.902 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.949999999999896 y1[1] (analytic) = 1.785795717263725 y1[1] (numeric) = 1.785795717263659 absolute error = 6.59472476627343e-14 relative error = 3.692877467742031e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.618486128162942 y2[1] (numeric) = 1.618486128163021 absolute error = 7.815970093361102e-14 relative error = 4.829185717045715e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4684 Order of pole (three term test) = -10.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.959999999999896 y1[1] (analytic) = 1.779571669604153 y1[1] (numeric) = 1.779571669604086 absolute error = 6.683542608243442e-14 relative error = 3.75570297190117e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.626313030321575 y2[1] (numeric) = 1.626313030321653 absolute error = 7.771561172376096e-14 relative error = 4.778637954366882e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.07 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.26 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4706 Order of pole (three term test) = -10.37 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.969999999999896 y1[1] (analytic) = 1.77326966542726 y1[1] (numeric) = 1.773269665427193 absolute error = 6.772360450213455e-14 relative error = 3.819137372195271e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.634077301699101 y2[1] (numeric) = 1.634077301699178 absolute error = 7.72715225139109e-14 relative error = 4.728755636808893e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4725 Order of pole (three term test) = -10.61 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.979999999999896 y1[1] (analytic) = 1.766890334928215 y1[1] (numeric) = 1.766890334928146 absolute error = 6.861178292183467e-14 relative error = 3.883194195219945e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.641778165874853 y2[1] (numeric) = 1.64177816587493 absolute error = 7.682743330406083e-14 relative error = 4.679525827603015e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4743 Order of pole (three term test) = -10.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.989999999999895 y1[1] (analytic) = 1.760434316034749 y1[1] (numeric) = 1.76043431603468 absolute error = 6.972200594645983e-14 relative error = 3.960500276062761e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.649414852768831 y2[1] (numeric) = 1.649414852768908 absolute error = 7.638334409421077e-14 relative error = 4.630935871954103e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.23 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4759 Order of pole (three term test) = -11.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.999999999999895 y1[1] (analytic) = 1.753902254343374 y1[1] (numeric) = 1.753902254343303 absolute error = 7.061018436615996e-14 relative error = 4.025890507370094e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.65698659871871 y2[1] (numeric) = 1.656986598718786 absolute error = 7.593925488436071e-14 relative error = 4.582973389349189e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4773 Order of pole (three term test) = -11.32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.009999999999895 y1[1] (analytic) = 1.747294803054813 y1[1] (numeric) = 1.747294803054742 absolute error = 7.149836278586008e-14 relative error = 4.091946170781185e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.664492646556204 y2[1] (numeric) = 1.664492646556279 absolute error = 7.527312106958561e-14 relative error = 4.52228618884703e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.78 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.89 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4785 Order of pole (three term test) = -11.56 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.019999999999895 y1[1] (analytic) = 1.740612622908691 y1[1] (numeric) = 1.740612622908619 absolute error = 7.238654120556021e-14 relative error = 4.158681848727317e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.671932245682784 y2[1] (numeric) = 1.671932245682858 absolute error = 7.460698725481052e-14 relative error = 4.462321212325354e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.24 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4796 Order of pole (three term test) = -11.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.029999999999895 y1[1] (analytic) = 1.733856382117453 y1[1] (numeric) = 1.73385638211738 absolute error = 7.30526750203353e-14 relative error = 4.213306002376074e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.679304652144737 y2[1] (numeric) = 1.679304652144811 absolute error = 7.416289804496046e-14 relative error = 4.416286106886128e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.59 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4804 Order of pole (three term test) = -12.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.039999999999894 y1[1] (analytic) = 1.727026756299548 y1[1] (numeric) = 1.727026756299475 absolute error = 7.394085344003543e-14 relative error = 4.281395940759274e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.686609128707562 y2[1] (numeric) = 1.686609128707635 absolute error = 7.371880883511039e-14 relative error = 4.370829469635367e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.94 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.481 Order of pole (three term test) = -12.28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.049999999999894 y1[1] (analytic) = 1.720124428411868 y1[1] (numeric) = 1.720124428411793 absolute error = 7.482903185973555e-14 relative error = 4.350210404768372e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.693844944929688 y2[1] (numeric) = 1.693844944929761 absolute error = 7.30526750203353e-14 relative error = 4.312831303656768e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.31 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4815 Order of pole (three term test) = -12.52 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.059999999999894 y1[1] (analytic) = 1.713150088681447 y1[1] (numeric) = 1.713150088681371 absolute error = 7.571721027943568e-14 relative error = 4.419765132062224e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.701011377235523 y2[1] (numeric) = 1.701011377235595 absolute error = 7.238654120556021e-14 relative error = 4.255500120357957e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4817 Order of pole (three term test) = -12.77 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.069999999999894 y1[1] (analytic) = 1.706104434536448 y1[1] (numeric) = 1.706104434536372 absolute error = 7.638334409421077e-14 relative error = 4.477061459310038e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.708107708987809 y2[1] (numeric) = 1.70810770898788 absolute error = 7.172040739078511e-14 relative error = 4.198822299870378e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4818 Order of pole (three term test) = -13.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.079999999999893 y1[1] (analytic) = 1.698988170536414 y1[1] (numeric) = 1.698988170536337 absolute error = 7.72715225139109e-14 relative error = 4.548090672668681e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.715133230559283 y2[1] (numeric) = 1.715133230559355 absolute error = 7.105427357601002e-14 relative error = 4.142784496854516e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4817 Order of pole (three term test) = -13.25 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.089999999999893 y1[1] (analytic) = 1.691802008301814 y1[1] (numeric) = 1.691802008301736 absolute error = 7.815970093361102e-14 relative error = 4.619908272367264e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.722087239403645 y2[1] (numeric) = 1.722087239403715 absolute error = 7.061018436615996e-14 relative error = 4.100267556167022e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4814 Order of pole (three term test) = -13.49 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.099999999999893 y1[1] (analytic) = 1.684546666442884 y1[1] (numeric) = 1.684546666442805 absolute error = 7.904787935331115e-14 relative error = 4.692531286190481e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.728969040125803 y2[1] (numeric) = 1.728969040125873 absolute error = 6.994405055138486e-14 relative error = 4.045419491507819e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4808 Order of pole (three term test) = -13.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.109999999999893 y1[1] (analytic) = 1.677222870487764 y1[1] (numeric) = 1.677222870487684 absolute error = 7.993605777301127e-14 relative error = 4.765977091032903e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.735777944551421 y2[1] (numeric) = 1.73577794455149 absolute error = 6.927791673660977e-14 relative error = 3.991173926023893e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4801 Order of pole (three term test) = -13.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.119999999999893 y1[1] (analytic) = 1.669831352809945 y1[1] (numeric) = 1.669831352809864 absolute error = 8.060219158778636e-14 relative error = 4.826965995826542e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.74251327179573 y2[1] (numeric) = 1.742513271795798 absolute error = 6.838973831690964e-14 relative error = 3.924775749135688e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4792 Order of pole (three term test) = -14.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.129999999999892 y1[1] (analytic) = 1.662372852555036 y1[1] (numeric) = 1.662372852554954 absolute error = 8.171241461241152e-14 relative error = 4.915408386681789e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.749174348331618 y2[1] (numeric) = 1.749174348331686 absolute error = 6.772360450213455e-14 relative error = 3.871746951167565e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4781 Order of pole (three term test) = -14.45 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.139999999999892 y1[1] (analytic) = 1.654848115566847 y1[1] (numeric) = 1.654848115566764 absolute error = 8.237854842718662e-14 relative error = 4.978012643714369e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.755760508056983 y2[1] (numeric) = 1.75576050805705 absolute error = 6.705747068735946e-14 relative error = 3.819283460337582e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4769 Order of pole (three term test) = -14.69 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.149999999999892 y1[1] (analytic) = 1.647257894312806 y1[1] (numeric) = 1.647257894312723 absolute error = 8.326672684688674e-14 relative error = 5.054868890558481e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.762271092361341 y2[1] (numeric) = 1.762271092361408 absolute error = 6.639133687258436e-14 relative error = 3.767373655526733e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4754 Order of pole (three term test) = -14.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.159999999999892 y1[1] (analytic) = 1.639602947808714 y1[1] (numeric) = 1.63960294780863 absolute error = 8.393286066166183e-14 relative error = 5.119096716301705e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.768705450191687 y2[1] (numeric) = 1.768705450191752 absolute error = 6.572520305780927e-14 relative error = 3.716006136052002e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4737 Order of pole (three term test) = -15.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.169999999999892 y1[1] (analytic) = 1.631884041542842 y1[1] (numeric) = 1.631884041542757 absolute error = 8.482103908136196e-14 relative error = 5.197736905446364e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.775062938117598 y2[1] (numeric) = 1.775062938117663 absolute error = 6.505906924303417e-14 relative error = 3.665169715730045e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4719 Order of pole (three term test) = -15.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.179999999999891 y1[1] (analytic) = 1.624101947399383 y1[1] (numeric) = 1.624101947399298 absolute error = 8.570921750106208e-14 relative error = 5.277329889192313e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.781342920395582 y2[1] (numeric) = 1.781342920395647 absolute error = 6.417089082333405e-14 relative error = 3.602388405320837e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4698 Order of pole (three term test) = -15.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.189999999999891 y1[1] (analytic) = 1.616257443581268 y1[1] (numeric) = 1.616257443581182 absolute error = 8.637535131583718e-14 relative error = 5.344157990353848e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.787544769032644 y2[1] (numeric) = 1.787544769032707 absolute error = 6.350475700855895e-14 relative error = 3.552624701138282e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.87 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4676 Order of pole (three term test) = -15.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.199999999999891 y1[1] (analytic) = 1.608351314532341 y1[1] (numeric) = 1.608351314532254 absolute error = 8.704148513061227e-14 relative error = 5.411845306690426e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.793667863849087 y2[1] (numeric) = 1.793667863849149 absolute error = 6.283862319378386e-14 relative error = 3.503358925042931e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4652 Order of pole (three term test) = -16.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.209999999999891 y1[1] (analytic) = 1.600384350858919 y1[1] (numeric) = 1.600384350858831 absolute error = 8.79296635503124e-14 relative error = 5.494284138877075e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.799711592540532 y2[1] (numeric) = 1.799711592540595 absolute error = 6.217248937900877e-14 relative error = 3.454580702636028e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4626 Order of pole (three term test) = -16.34 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.219999999999891 y1[1] (analytic) = 1.592357349250729 y1[1] (numeric) = 1.59235734925064 absolute error = 8.881784197001252e-14 relative error = 5.577758159109515e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.805675350739149 y2[1] (numeric) = 1.80567535073921 absolute error = 6.128431095930864e-14 relative error = 3.393982807276073e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.97 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4598 Order of pole (three term test) = -16.57 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.22999999999989 y1[1] (analytic) = 1.584271112401244 y1[1] (numeric) = 1.584271112401154 absolute error = 8.948397578478762e-14 relative error = 5.648274154867268e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.811558542074085 y2[1] (numeric) = 1.811558542074145 absolute error = 6.039613253960852e-14 relative error = 3.333932143890859e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4568 Order of pole (three term test) = -16.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.23999999999989 y1[1] (analytic) = 1.576126448927409 y1[1] (numeric) = 1.576126448927319 absolute error = 9.015010959956271e-14 relative error = 5.719725702269128e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.81736057823111 y2[1] (numeric) = 1.817360578231169 absolute error = 5.972999872483342e-14 relative error = 3.286634443395398e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4537 Order of pole (three term test) = -17.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.24999999999989 y1[1] (analytic) = 1.567924173288785 y1[1] (numeric) = 1.567924173288695 absolute error = 9.081624341433781e-14 relative error = 5.792132359554544e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.823080879011443 y2[1] (numeric) = 1.823080879011502 absolute error = 5.88418203051333e-14 relative error = 3.227603392836855e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4503 Order of pole (three term test) = -17.26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.25999999999989 y1[1] (analytic) = 1.559665105706102 y1[1] (numeric) = 1.55966510570601 absolute error = 9.170442183403793e-14 relative error = 5.879750819488964e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.828718872389774 y2[1] (numeric) = 1.828718872389832 absolute error = 5.81756864903582e-14 relative error = 3.181226342042071e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4468 Order of pole (three term test) = -17.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.269999999999889 y1[1] (analytic) = 1.551350072079233 y1[1] (numeric) = 1.551350072079141 absolute error = 9.237055564881302e-14 relative error = 5.954204490093666e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.834273994571462 y2[1] (numeric) = 1.83427399457152 absolute error = 5.728750807065808e-14 relative error = 3.123170706241302e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4431 Order of pole (three term test) = -17.7 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.279999999999889 y1[1] (analytic) = 1.542979903904614 y1[1] (numeric) = 1.542979903904521 absolute error = 9.325873406851315e-14 relative error = 6.044066668173427e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.83974569004892 y2[1] (numeric) = 1.839745690048976 absolute error = 5.639932965095795e-14 relative error = 3.065604662428005e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4393 Order of pole (three term test) = -17.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.289999999999889 y1[1] (analytic) = 1.534555438192086 y1[1] (numeric) = 1.534555438191992 absolute error = 9.414691248821327e-14 relative error = 6.13512618345878e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.845133411657158 y2[1] (numeric) = 1.845133411657214 absolute error = 5.551115123125783e-14 relative error = 3.008516938696695e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4352 Order of pole (three term test) = -18.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.299999999999889 y1[1] (analytic) = 1.5260775173812 y1[1] (numeric) = 1.526077517381105 absolute error = 9.481304630298837e-14 relative error = 6.212859125641975e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.850436620628506 y2[1] (numeric) = 1.850436620628561 absolute error = 5.46229728115577e-14 relative error = 2.951896444472918e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.431 Order of pole (three term test) = -18.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.309999999999889 y1[1] (analytic) = 1.517546989256972 y1[1] (numeric) = 1.517546989256877 absolute error = 9.547918011776346e-14 relative error = 6.291678662583778e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.855654786646486 y2[1] (numeric) = 1.85565478664654 absolute error = 5.395683899678261e-14 relative error = 2.907698101234264e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4266 Order of pole (three term test) = -18.58 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.319999999999888 y1[1] (analytic) = 1.508964706865106 y1[1] (numeric) = 1.50896470686501 absolute error = 9.614531393253856e-14 relative error = 6.37160786432717e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.860787387898845 y2[1] (numeric) = 1.860787387898898 absolute error = 5.306866057708248e-14 relative error = 2.851946489007877e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.422 Order of pole (three term test) = -18.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.329999999999888 y1[1] (analytic) = 1.50033152842669 y1[1] (numeric) = 1.500331528426593 absolute error = 9.703349235223868e-14 relative error = 6.46747005670087e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.865833911129734 y2[1] (numeric) = 1.865833911129786 absolute error = 5.218048215738236e-14 relative error = 2.796630602870106e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4173 Order of pole (three term test) = -19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.339999999999888 y1[1] (analytic) = 1.491648317252373 y1[1] (numeric) = 1.491648317252275 absolute error = 9.769962616701378e-14 relative error = 6.549776179614321e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.870793851691036 y2[1] (numeric) = 1.870793851691087 absolute error = 5.129230373768223e-14 relative error = 2.741740020757414e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4124 Order of pole (three term test) = -19.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.349999999999888 y1[1] (analytic) = 1.482915941656036 y1[1] (numeric) = 1.482915941655937 absolute error = 9.836575998178887e-14 relative error = 6.633266068469101e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.875666713592828 y2[1] (numeric) = 1.875666713592879 absolute error = 5.040412531798211e-14 relative error = 2.687264477889748e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4073 Order of pole (three term test) = -19.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.359999999999888 y1[1] (analytic) = 1.474135274867962 y1[1] (numeric) = 1.474135274867863 absolute error = 9.903189379656396e-14 relative error = 6.717965134199387e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.880452009552981 y2[1] (numeric) = 1.88045200955303 absolute error = 4.951594689828198e-14 relative error = 2.633193862259365e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4021 Order of pole (three term test) = -19.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.369999999999887 y1[1] (analytic) = 1.465307194947512 y1[1] (numeric) = 1.465307194947413 absolute error = 9.969802761133906e-14 relative error = 6.803899411338813e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.885149261045886 y2[1] (numeric) = 1.885149261045934 absolute error = 4.862776847858186e-14 relative error = 2.579518210224003e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3967 Order of pole (three term test) = -19.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.379999999999887 y1[1] (analytic) = 1.456432584695323 y1[1] (numeric) = 1.456432584695222 absolute error = 1.003641614261142e-13 relative error = 6.891095577012908e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.889757998350308 y2[1] (numeric) = 1.889757998350356 absolute error = 4.773959005888173e-14 relative error = 2.526227702200848e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3912 Order of pole (three term test) = -20.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.389999999999887 y1[1] (analytic) = 1.447512331565023 y1[1] (numeric) = 1.447512331564922 absolute error = 1.012523398458143e-13 relative error = 6.994920708989205e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.894277760596358 y2[1] (numeric) = 1.894277760596405 absolute error = 4.685141163918161e-14 relative error = 2.47331265845785e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3855 Order of pole (three term test) = -20.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.399999999999887 y1[1] (analytic) = 1.438547327574492 y1[1] (numeric) = 1.438547327574391 absolute error = 1.019184736605894e-13 relative error = 7.084818949435066e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.898708095811577 y2[1] (numeric) = 1.898708095811623 absolute error = 4.596323321948148e-14 relative error = 2.42076353499905e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3796 Order of pole (three term test) = -20.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.409999999999886 y1[1] (analytic) = 1.429538469216659 y1[1] (numeric) = 1.429538469216557 absolute error = 1.025846074753645e-13 relative error = 7.176064840813798e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.903048560966136 y2[1] (numeric) = 1.903048560966181 absolute error = 4.485301019485632e-14 relative error = 2.356903082498611e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3736 Order of pole (three term test) = -20.59 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.419999999999886 y1[1] (analytic) = 1.420486657369852 y1[1] (numeric) = 1.420486657369749 absolute error = 1.032507412901396e-13 relative error = 7.268687865137488e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.907298722017136 y2[1] (numeric) = 1.90729872201718 absolute error = 4.39648317751562e-14 relative error = 2.305083690752937e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3675 Order of pole (three term test) = -20.77 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.429999999999886 y1[1] (analytic) = 1.411392797207712 y1[1] (numeric) = 1.411392797207608 absolute error = 1.039168751049147e-13 relative error = 7.362718253239136e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.911458153952015 y2[1] (numeric) = 1.911458153952058 absolute error = 4.307665335545607e-14 relative error = 2.253601694936057e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3612 Order of pole (three term test) = -20.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.439999999999886 y1[1] (analytic) = 1.402257798108678 y1[1] (numeric) = 1.402257798108573 absolute error = 1.043609643147647e-13 relative error = 7.442352216227543e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.915526440831044 y2[1] (numeric) = 1.915526440831086 absolute error = 4.218847493575595e-14 relative error = 2.202448060046232e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3547 Order of pole (three term test) = -21.13 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.449999999999886 y1[1] (analytic) = 1.393082573565046 y1[1] (numeric) = 1.393082573564941 absolute error = 1.050270981295398e-13 relative error = 7.539186845239498e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.919503175828926 y2[1] (numeric) = 1.919503175828967 absolute error = 4.130029651605582e-14 relative error = 2.151613867386312e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3481 Order of pole (three term test) = -21.31 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.459999999999885 y1[1] (analytic) = 1.383868041091626 y1[1] (numeric) = 1.38386804109152 absolute error = 1.056932319443149e-13 relative error = 7.637522423087517e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.923387961275475 y2[1] (numeric) = 1.923387961275515 absolute error = 4.019007349143067e-14 relative error = 2.089545858692962e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3414 Order of pole (three term test) = -21.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.469999999999885 y1[1] (analytic) = 1.374615122133985 y1[1] (numeric) = 1.374615122133879 absolute error = 1.06137321154165e-13 relative error = 7.721239163249919e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.927180408695384 y2[1] (numeric) = 1.927180408695423 absolute error = 3.930189507173054e-14 relative error = 2.039346959651597e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3345 Order of pole (three term test) = -21.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.479999999999885 y1[1] (analytic) = 1.365324741976309 y1[1] (numeric) = 1.365324741976203 absolute error = 1.06581410364015e-13 relative error = 7.806304763051339e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.930880138847071 y2[1] (numeric) = 1.93088013884711 absolute error = 3.841371665203042e-14 relative error = 1.98944076740917e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3275 Order of pole (three term test) = -21.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.489999999999885 y1[1] (analytic) = 1.355997829648872 y1[1] (numeric) = 1.355997829648765 absolute error = 1.072475441787901e-13 relative error = 7.909123586618222e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.934486781760605 y2[1] (numeric) = 1.934486781760642 absolute error = 3.730349362740526e-14 relative error = 1.928340579998939e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3204 Order of pole (three term test) = -21.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.499999999999885 y1[1] (analytic) = 1.346635317835134 y1[1] (numeric) = 1.346635317835026 absolute error = 1.076916333886402e-13 relative error = 7.997089632385884e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.937999976774699 y2[1] (numeric) = 1.937999976774735 absolute error = 3.641531520770513e-14 relative error = 1.879015255114143e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3132 Order of pole (three term test) = -22.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.509999999999884 y1[1] (analytic) = 1.337238142778474 y1[1] (numeric) = 1.337238142778366 absolute error = 1.083577672034153e-13 relative error = 8.103101739101808e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.941419372572779 y2[1] (numeric) = 1.941419372572815 absolute error = 3.552713678800501e-14 relative error = 1.829956849607628e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3058 Order of pole (three term test) = -22.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.519999999999884 y1[1] (analytic) = 1.327807244188567 y1[1] (numeric) = 1.327807244188459 absolute error = 1.088018564132653e-13 relative error = 8.194100227232527e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.944744627218116 y2[1] (numeric) = 1.944744627218151 absolute error = 3.463895836830488e-14 relative error = 1.781157170124419e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2983 Order of pole (three term test) = -22.45 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.529999999999884 y1[1] (analytic) = 1.318343565147414 y1[1] (numeric) = 1.318343565147304 absolute error = 1.094679902280404e-13 relative error = 8.303449352809639e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.947975408188015 y2[1] (numeric) = 1.947975408188049 absolute error = 3.352873534367973e-14 relative error = 1.721209374756316e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2906 Order of pole (three term test) = -22.59 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.539999999999884 y1[1] (analytic) = 1.30884805201503 y1[1] (numeric) = 1.30884805201492 absolute error = 1.099120794378905e-13 relative error = 8.397619515013673e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.951111392407073 y2[1] (numeric) = 1.951111392407106 absolute error = 3.26405569239796e-14 relative error = 1.672921241247593e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2829 Order of pole (three term test) = -22.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.549999999999883 y1[1] (analytic) = 1.299321654334818 y1[1] (numeric) = 1.299321654334708 absolute error = 1.103561686477406e-13 relative error = 8.493367926222773e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.95415226627948 y2[1] (numeric) = 1.954152266279511 absolute error = 3.153033389935445e-14 relative error = 1.613504456302436e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2751 Order of pole (three term test) = -22.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.559999999999883 y1[1] (analytic) = 1.289765324738606 y1[1] (numeric) = 1.289765324738495 absolute error = 1.108002578575906e-13 relative error = 8.590730091154083e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.957097725720383 y2[1] (numeric) = 1.957097725720414 absolute error = 3.042011087472929e-14 relative error = 1.554348077510132e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2671 Order of pole (three term test) = -23.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.569999999999883 y1[1] (analytic) = 1.280180018851391 y1[1] (numeric) = 1.28018001885128 absolute error = 1.114663916723657e-13 relative error = 8.707087287018908e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.959947476186293 y2[1] (numeric) = 1.959947476186323 absolute error = 2.930988785010413e-14 relative error = 1.49544251599721e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.259 Order of pole (three term test) = -23.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.579999999999883 y1[1] (analytic) = 1.270566695195773 y1[1] (numeric) = 1.270566695195661 absolute error = 1.119104808822158e-13 relative error = 8.807918648062175e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.962701232704538 y2[1] (numeric) = 1.962701232704567 absolute error = 2.819966482547898e-14 relative error = 1.436778270456414e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2509 Order of pole (three term test) = -23.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.589999999999883 y1[1] (analytic) = 1.260926315096107 y1[1] (numeric) = 1.260926315095995 absolute error = 1.123545700920658e-13 relative error = 8.910478649460357e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.965358719901761 y2[1] (numeric) = 1.965358719901788 absolute error = 2.708944180085382e-14 relative error = 1.378345923649393e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2426 Order of pole (three term test) = -23.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.599999999999882 y1[1] (analytic) = 1.251259842582369 y1[1] (numeric) = 1.251259842582256 absolute error = 1.127986593019159e-13 relative error = 9.014806954015268e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.967919672031457 y2[1] (numeric) = 1.967919672031483 absolute error = 2.597921877622866e-14 relative error = 1.320136138961946e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2342 Order of pole (three term test) = -23.51 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.609999999999882 y1[1] (analytic) = 1.241568244293756 y1[1] (numeric) = 1.241568244293642 absolute error = 1.13242748511766e-13 relative error = 9.120944340532978e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.970383833000546 y2[1] (numeric) = 1.970383833000571 absolute error = 2.509104035652854e-14 relative error = 1.27340876108993e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2257 Order of pole (three term test) = -23.63 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.619999999999882 y1[1] (analytic) = 1.231852489382019 y1[1] (numeric) = 1.231852489381905 absolute error = 1.13686837721616e-13 relative error = 9.228932741666908e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.972750956394986 y2[1] (numeric) = 1.97275095639501 absolute error = 2.398081733190338e-14 relative error = 1.215602874461459e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2172 Order of pole (three term test) = -23.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.629999999999882 y1[1] (analytic) = 1.222113549414554 y1[1] (numeric) = 1.22211354941444 absolute error = 1.139088823265411e-13 relative error = 9.320646381926493e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.97502080550441 y2[1] (numeric) = 1.975020805504433 absolute error = 2.264854970235319e-14 relative error = 1.146749929885871e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2086 Order of pole (three term test) = -23.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.639999999999882 y1[1] (analytic) = 1.212352398277242 y1[1] (numeric) = 1.212352398277127 absolute error = 1.145750161413162e-13 relative error = 9.450636325224232e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.977193153345798 y2[1] (numeric) = 1.977193153345819 absolute error = 2.153832667772804e-14 relative error = 1.089338522201585e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1998 Order of pole (three term test) = -23.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.649999999999881 y1[1] (analytic) = 1.202570012077061 y1[1] (numeric) = 1.202570012076946 absolute error = 1.147970607462412e-13 relative error = 9.545977331329378e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.979267782686176 y2[1] (numeric) = 1.979267782686196 absolute error = 2.042810365310288e-14 relative error = 1.032104085753306e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.191 Order of pole (three term test) = -24.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.659999999999881 y1[1] (analytic) = 1.19276736904448 y1[1] (numeric) = 1.192767369044365 absolute error = 1.152411499560912e-13 relative error = 9.661661858540808e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.981244486064339 y2[1] (numeric) = 1.981244486064359 absolute error = 1.931788062847772e-14 relative error = 9.750376979901102e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1822 Order of pole (three term test) = -24.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.669999999999881 y1[1] (analytic) = 1.182945449435634 y1[1] (numeric) = 1.182945449435519 absolute error = 1.154631945610163e-13 relative error = 9.760652498059149e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.983123065811597 y2[1] (numeric) = 1.983123065811615 absolute error = 1.820765760385257e-14 relative error = 9.181304941557445e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1732 Order of pole (three term test) = -24.23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.679999999999881 y1[1] (analytic) = 1.173105235434299 y1[1] (numeric) = 1.173105235434183 absolute error = 1.159072837708663e-13 relative error = 9.880382447356135e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.98490333407154 y2[1] (numeric) = 1.984903334071557 absolute error = 1.709743457922741e-14 relative error = 8.613736641852596e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1642 Order of pole (three term test) = -24.31 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.68999999999988 y1[1] (analytic) = 1.163247711053674 y1[1] (numeric) = 1.163247711053558 absolute error = 1.161293283757914e-13 relative error = 9.983198528764009e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 1.986585112818826 y2[1] (numeric) = 1.986585112818842 absolute error = 1.598721155460225e-14 relative error = 8.047584496350882e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1551 Order of pole (three term test) = -24.39 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.69999999999988 y1[1] (analytic) = 1.153373862037983 y1[1] (numeric) = 1.153373862037866 absolute error = 1.165734175856414e-13 relative error = 1.010716658513998e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.988168233876982 y2[1] (numeric) = 1.988168233876997 absolute error = 1.48769885299771e-14 relative error = 7.482761406446258e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.146 Order of pole (three term test) = -24.47 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.70999999999988 y1[1] (analytic) = 1.143484675763899 y1[1] (numeric) = 1.143484675763782 absolute error = 1.170175067954915e-13 relative error = 1.02334127667534e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.989652538935221 y2[1] (numeric) = 1.989652538935234 absolute error = 1.354472090042691e-14 relative error = 6.807581040092297e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1367 Order of pole (three term test) = -24.54 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.71999999999988 y1[1] (analytic) = 1.133581141141809 y1[1] (numeric) = 1.133581141141692 absolute error = 1.174615960053416e-13 relative error = 1.036199278042217e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.991037879564274 y2[1] (numeric) = 1.991037879564286 absolute error = 1.243449787580175e-14 relative error = 6.245234208463661e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1275 Order of pole (three term test) = -24.61 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.72999999999988 y1[1] (analytic) = 1.123664248516922 y1[1] (numeric) = 1.123664248516804 absolute error = 1.176836406102666e-13 relative error = 1.047320325137979e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.992324117231232 y2[1] (numeric) = 1.992324117231244 absolute error = 1.13242748511766e-14 relative error = 5.683952100581977e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1182 Order of pole (three term test) = -24.67 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.739999999999879 y1[1] (analytic) = 1.113734989570237 y1[1] (numeric) = 1.113734989570119 absolute error = 1.179056852151916e-13 relative error = 1.05865117213107e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.993511123313402 y2[1] (numeric) = 1.993511123313412 absolute error = 9.992007221626409e-15 relative error = 5.012265597504546e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1088 Order of pole (three term test) = -24.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.749999999999879 y1[1] (analytic) = 1.103794357219373 y1[1] (numeric) = 1.103794357219255 absolute error = 1.183497744250417e-13 relative error = 1.072208547280336e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.994598779111164 y2[1] (numeric) = 1.994598779111173 absolute error = 8.881784197001252e-15 relative error = 4.452917694534621e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09941 Order of pole (three term test) = -24.78 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.759999999999879 y1[1] (analytic) = 1.093843345519283 y1[1] (numeric) = 1.093843345519164 absolute error = 1.187938636348917e-13 relative error = 1.086022638630182e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.995586975859843 y2[1] (numeric) = 1.995586975859851 absolute error = 7.771561172376096e-15 relative error = 3.894373568472276e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08997 Order of pole (three term test) = -24.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.769999999999879 y1[1] (analytic) = 1.083882949562843 y1[1] (numeric) = 1.083882949562724 absolute error = 1.190159082398168e-13 relative error = 1.098051300537746e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.99647561474059 y2[1] (numeric) = 1.996475614740597 absolute error = 6.661338147750939e-15 relative error = 3.336548715430452e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08049 Order of pole (three term test) = -24.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.779999999999879 y1[1] (analytic) = 1.073914165381349 y1[1] (numeric) = 1.073914165381229 absolute error = 1.192379528447418e-13 relative error = 1.110311761297982e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.997264606890257 y2[1] (numeric) = 1.997264606890262 absolute error = 5.551115123125783e-15 relative error = 2.779358881129364e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07098 Order of pole (three term test) = -24.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.789999999999878 y1[1] (analytic) = 1.063937989844912 y1[1] (numeric) = 1.063937989844792 absolute error = 1.194599974496668e-13 relative error = 1.122809774534701e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.997953873410286 y2[1] (numeric) = 1.99795387341029 absolute error = 4.218847493575595e-15 relative error = 2.111584030903822e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06144 Order of pole (three term test) = -24.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.799999999999878 y1[1] (analytic) = 1.053955420562771 y1[1] (numeric) = 1.053955420562652 absolute error = 1.196820420545919e-13 relative error = 1.135551273987341e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.998543345374598 y2[1] (numeric) = 1.998543345374602 absolute error = 3.108624468950438e-15 relative error = 1.555445107630513e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05188 Order of pole (three term test) = -24.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.809999999999878 y1[1] (analytic) = 1.043967455783537 y1[1] (numeric) = 1.043967455783418 absolute error = 1.199040866595169e-13 relative error = 1.148542380274913e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.999032963836491 y2[1] (numeric) = 1.999032963836493 absolute error = 1.998401444325282e-15 relative error = 9.996840874949871e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0423 Order of pole (three term test) = -24.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.819999999999878 y1[1] (analytic) = 1.033975094295365 y1[1] (numeric) = 1.033975094295245 absolute error = 1.201261312644419e-13 relative error = 1.161789407957701e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.999422679834524 y2[1] (numeric) = 1.999422679834524 absolute error = 6.661338147750939e-16 relative error = 3.331630782692854e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0327 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.829999999999878 y1[1] (analytic) = 1.023979335326075 y1[1] (numeric) = 1.023979335325955 absolute error = 1.20570220474292e-13 relative error = 1.177467321016764e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.999712454397423 y2[1] (numeric) = 1.999712454397423 absolute error = 4.440892098500626e-16 relative error = 2.220765334903517e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02308 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.839999999999877 y1[1] (analytic) = 1.013981178443235 y1[1] (numeric) = 1.013981178443115 absolute error = 1.20570220474292e-13 relative error = 1.189077500032135e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.999902258547974 y2[1] (numeric) = 1.999902258547972 absolute error = 1.77635683940025e-15 relative error = 8.88221827745708e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.01346 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.849999999999877 y1[1] (analytic) = 1.003981623454202 y1[1] (numeric) = 1.003981623454081 absolute error = 1.20792265079217e-13 relative error = 1.203132231281593e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.999992073305918 y2[1] (numeric) = 1.999992073305915 absolute error = 2.886579864025407e-15 relative error = 1.443295652294256e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.003834 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.859999999999877 y1[1] (analytic) = 0.9939816703061418 y1[1] (numeric) = 0.9939816703060208 absolute error = 1.210143096841421e-13 relative error = 1.217470234102709e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.999981889689856 y2[1] (numeric) = 1.999981889689852 absolute error = 3.996802888650564e-15 relative error = 1.998419540324118e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.005803 Order of pole (three term test) = -0.8937 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.869999999999877 y1[1] (analytic) = 0.9839823189860355 y1[1] (numeric) = 0.9839823189859143 absolute error = 1.212363542890671e-13 relative error = 1.232098910212102e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.999871708718141 y2[1] (numeric) = 1.999871708718136 absolute error = 5.329070518200751e-15 relative error = 2.664706188386718e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01544 Order of pole (three term test) = -0.8991 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.879999999999876 y1[1] (analytic) = 0.9739845694206826 y1[1] (numeric) = 0.9739845694205611 absolute error = 1.214583988939921e-13 relative error = 1.247025904796772e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.999661541408777 y2[1] (numeric) = 1.999661541408771 absolute error = 6.439293542825908e-15 relative error = 3.220191722189834e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02508 Order of pole (three term test) = -0.9092 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.889999999999876 y1[1] (analytic) = 0.9639894213767081 y1[1] (numeric) = 0.9639894213765865 absolute error = 1.215694211964546e-13 relative error = 1.261107419859826e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.999351408778322 y2[1] (numeric) = 1.999351408778314 absolute error = 7.771561172376096e-15 relative error = 3.887041136567788e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0347 Order of pole (three term test) = -0.9242 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.899999999999876 y1[1] (analytic) = 0.9539978743605873 y1[1] (numeric) = 0.9539978743604655 absolute error = 1.217914658013797e-13 relative error = 1.276642947270819e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.998941341839778 y2[1] (numeric) = 1.998941341839769 absolute error = 8.881784197001252e-15 relative error = 4.443244036779324e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04431 Order of pole (three term test) = -0.944 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.909999999999876 y1[1] (analytic) = 0.9440109275186954 y1[1] (numeric) = 0.9440109275185734 absolute error = 1.220135104063047e-13 relative error = 1.292501038383248e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.998431381599499 y2[1] (numeric) = 1.998431381599488 absolute error = 1.021405182655144e-14 relative error = 5.111034544691921e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0539 Order of pole (three term test) = -0.9686 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.919999999999876 y1[1] (analytic) = 0.9340295795373942 y1[1] (numeric) = 0.9340295795372722 absolute error = 1.220135104063047e-13 relative error = 1.306313130540636e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.997821579053082 y2[1] (numeric) = 1.997821579053071 absolute error = 1.13242748511766e-14 relative error = 5.668311409742616e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06348 Order of pole (three term test) = -0.9981 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.929999999999875 y1[1] (analytic) = 0.9240548285431641 y1[1] (numeric) = 0.924054828543042 absolute error = 1.221245327087672e-13 relative error = 1.32161565457436e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.997111995180276 y2[1] (numeric) = 1.997111995180264 absolute error = 1.265654248072678e-14 relative error = 6.337422493716631e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07302 Order of pole (three term test) = -1.032 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.939999999999875 y1[1] (analytic) = 0.9140876720027923 y1[1] (numeric) = 0.91408767200267 absolute error = 1.222355550112297e-13 relative error = 1.33724104104159e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.996302700938877 y2[1] (numeric) = 1.996302700938863 absolute error = 1.398881011027697e-14 relative error = 7.00735920644596e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08254 Order of pole (three term test) = -1.071 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.949999999999875 y1[1] (analytic) = 0.9041291066236269 y1[1] (numeric) = 0.9041291066235045 absolute error = 1.223465773136923e-13 relative error = 1.35319808219185e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.995393777257632 y2[1] (numeric) = 1.995393777257617 absolute error = 1.509903313490213e-14 relative error = 7.566944082412383e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09202 Order of pole (three term test) = -1.115 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.959999999999875 y1[1] (analytic) = 0.8941801282539069 y1[1] (numeric) = 0.8941801282537845 absolute error = 1.224575996161548e-13 relative error = 1.369495873893792e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.994385315028154 y2[1] (numeric) = 1.994385315028137 absolute error = 1.643130076445232e-14 relative error = 8.238779457830276e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1015 Order of pole (three term test) = -1.164 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.969999999999875 y1[1] (analytic) = 0.8842417317831786 y1[1] (numeric) = 0.8842417317830561 absolute error = 1.224575996161548e-13 relative error = 1.384888263181206e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.993277415095824 y2[1] (numeric) = 1.993277415095807 absolute error = 1.77635683940025e-14 relative error = 8.911739158569929e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1109 Order of pole (three term test) = -1.217 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.979999999999874 y1[1] (analytic) = 0.874314911042807 y1[1] (numeric) = 0.8743149110426846 absolute error = 1.224575996161548e-13 relative error = 1.400612045722724e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.992070188249714 y2[1] (numeric) = 1.992070188249695 absolute error = 1.909583602355269e-14 relative error = 9.585925303330203e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1202 Order of pole (three term test) = -1.275 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.989999999999874 y1[1] (analytic) = 0.864400658706594 y1[1] (numeric) = 0.8644006587064715 absolute error = 1.224575996161548e-13 relative error = 1.416676380133589e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.990763755211501 y2[1] (numeric) = 1.99076375521148 absolute error = 2.042810365310288e-14 relative error = 1.02614404143261e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1295 Order of pole (three term test) = -1.337 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.999999999999874 y1[1] (analytic) = 0.8544999661915113 y1[1] (numeric) = 0.8544999661913888 absolute error = 1.224575996161548e-13 relative error = 1.433090748522153e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.9893582466234 y2[1] (numeric) = 1.989358246623379 absolute error = 2.153832667772804e-14 relative error = 1.082677125363705e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1388 Order of pole (three term test) = -1.405 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.009999999999874 y1[1] (analytic) = 0.8446138235585597 y1[1] (numeric) = 0.8446138235584373 absolute error = 1.224575996161548e-13 relative error = 1.449864970244172e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.9878538030351 y2[1] (numeric) = 1.987853803035077 absolute error = 2.264854970235319e-14 relative error = 1.139346850747921e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.148 Order of pole (three term test) = -1.477 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.019999999999873 y1[1] (analytic) = 0.8347432194137643 y1[1] (numeric) = 0.8347432194136418 absolute error = 1.224575996161548e-13 relative error = 1.467009216345071e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.986250574889705 y2[1] (numeric) = 1.986250574889681 absolute error = 2.398081733190338e-14 relative error = 1.207340988849558e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1572 Order of pole (three term test) = -1.553 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.029999999999873 y1[1] (analytic) = 0.824889140809314 y1[1] (numeric) = 0.8248891408091915 absolute error = 1.224575996161548e-13 relative error = 1.484534024729788e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.984548722508693 y2[1] (numeric) = 1.984548722508668 absolute error = 2.509104035652854e-14 relative error = 1.264319695049393e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1662 Order of pole (three term test) = -1.634 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.039999999999873 y1[1] (analytic) = 0.8150525731448575 y1[1] (numeric) = 0.815052573144735 absolute error = 1.224575996161548e-13 relative error = 1.502450316102378e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.982748416075885 y2[1] (numeric) = 1.982748416075859 absolute error = 2.642330798607873e-14 relative error = 1.332660652851452e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1753 Order of pole (three term test) = -1.72 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.049999999999873 y1[1] (analytic) = 0.8052345000689641 y1[1] (numeric) = 0.8052345000688417 absolute error = 1.224575996161548e-13 relative error = 1.520769410720317e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.980849835620424 y2[1] (numeric) = 1.980849835620397 absolute error = 2.775557561562891e-14 relative error = 1.401195341338712e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1842 Order of pole (three term test) = -1.81 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.059999999999873 y1[1] (analytic) = 0.7954359033807598 y1[1] (numeric) = 0.7954359033806375 absolute error = 1.222355550112297e-13 relative error = 1.536711562700457e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.978853170998774 y2[1] (numeric) = 1.978853170998744 absolute error = 2.90878432451791e-14 relative error = 1.469934387830189e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1931 Order of pole (three term test) = -1.905 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.069999999999872 y1[1] (analytic) = 0.7856577629317479 y1[1] (numeric) = 0.7856577629316257 absolute error = 1.222355550112297e-13 relative error = 1.555837169546922e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.976758621875731 y2[1] (numeric) = 1.976758621875701 absolute error = 3.019806626980426e-14 relative error = 1.527655725672239e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2019 Order of pole (three term test) = -2.004 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.079999999999872 y1[1] (analytic) = 0.7759010565278249 y1[1] (numeric) = 0.7759010565277028 absolute error = 1.221245327087672e-13 relative error = 1.573970439675354e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.974566397704464 y2[1] (numeric) = 1.974566397704432 absolute error = 3.153033389935445e-14 relative error = 1.596823177787797e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2106 Order of pole (three term test) = -2.107 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.089999999999872 y1[1] (analytic) = 0.7661667598315007 y1[1] (numeric) = 0.7661667598313786 absolute error = 1.221245327087672e-13 relative error = 1.593968038180428e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.972276717705562 y2[1] (numeric) = 1.972276717705529 absolute error = 3.286260152890463e-14 relative error = 1.66622671321371e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2192 Order of pole (three term test) = -2.215 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.099999999999872 y1[1] (analytic) = 0.7564558462643329 y1[1] (numeric) = 0.7564558462642109 absolute error = 1.220135104063047e-13 relative error = 1.612962752668961e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.969889810845117 y2[1] (numeric) = 1.969889810845084 absolute error = 3.397282455352979e-14 relative error = 1.724605323937122e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2278 Order of pole (three term test) = -2.327 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.109999999999872 y1[1] (analytic) = 0.7467692869095859 y1[1] (numeric) = 0.7467692869094641 absolute error = 1.217914658013797e-13 relative error = 1.630911553759781e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.967405915811827 y2[1] (numeric) = 1.967405915811792 absolute error = 3.530509218307998e-14 relative error = 1.79449964541312e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2362 Order of pole (three term test) = -2.443 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.119999999999871 y1[1] (analytic) = 0.7371080504151231 y1[1] (numeric) = 0.7371080504150014 absolute error = 1.216804434989172e-13 relative error = 1.65078163819252e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.964825280993125 y2[1] (numeric) = 1.964825280993088 absolute error = 3.663735981263017e-14 relative error = 1.864662480020195e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2446 Order of pole (three term test) = -2.564 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.129999999999871 y1[1] (analytic) = 0.7274731028965428 y1[1] (numeric) = 0.7274731028964213 absolute error = 1.214583988939921e-13 relative error = 1.66959298440571e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.962148164450342 y2[1] (numeric) = 1.962148164450304 absolute error = 3.774758283725532e-14 relative error = 1.923788606852204e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2528 Order of pole (three term test) = -2.688 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.139999999999871 y1[1] (analytic) = 0.7178654078405678 y1[1] (numeric) = 0.7178654078404466 absolute error = 1.212363542890671e-13 relative error = 1.688845192495927e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.959374833892901 y2[1] (numeric) = 1.959374833892862 absolute error = 3.907985046680551e-14 relative error = 1.994506094025989e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.261 Order of pole (three term test) = -2.817 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.149999999999871 y1[1] (analytic) = 0.7082859260086976 y1[1] (numeric) = 0.7082859260085764 absolute error = 1.211253319866046e-13 relative error = 1.710119141702629e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.956505566651547 y2[1] (numeric) = 1.956505566651507 absolute error = 4.04121180963557e-14 relative error = 2.065525331753533e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.269 Order of pole (three term test) = -2.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.15999999999987 y1[1] (analytic) = 0.698735615341132 y1[1] (numeric) = 0.6987356153410111 absolute error = 1.209032873816795e-13 relative error = 1.730315225489872e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.953540649650613 y2[1] (numeric) = 1.953540649650572 absolute error = 4.174438572590589e-14 relative error = 2.136857798857259e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.277 Order of pole (three term test) = -3.087 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.16999999999987 y1[1] (analytic) = 0.6892154308609797 y1[1] (numeric) = 0.6892154308608589 absolute error = 1.20792265079217e-13 relative error = 1.752605349075271e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.950480379379329 y2[1] (numeric) = 1.950480379379286 absolute error = 4.285460875053104e-14 relative error = 2.197130983915255e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2848 Order of pole (three term test) = -3.228 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.17999999999987 y1[1] (analytic) = 0.6797263245787549 y1[1] (numeric) = 0.6797263245786344 absolute error = 1.20570220474292e-13 relative error = 1.773805370109988e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.947325061862171 y2[1] (numeric) = 1.947325061862127 absolute error = 4.418687638008123e-14 relative error = 2.269106336968035e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2925 Order of pole (three term test) = -3.373 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.18999999999987 y1[1] (analytic) = 0.6702692453971784 y1[1] (numeric) = 0.6702692453970581 absolute error = 1.202371535669045e-13 relative error = 1.793863501758254e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.944075012628262 y2[1] (numeric) = 1.944075012628217 absolute error = 4.551914400963142e-14 relative error = 2.341429405447299e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3001 Order of pole (three term test) = -3.521 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.19999999999987 y1[1] (analytic) = 0.6608451390162875 y1[1] (numeric) = 0.6608451390161675 absolute error = 1.200151089619794e-13 relative error = 1.816085219914457e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.940730556679817 y2[1] (numeric) = 1.94073055667977 absolute error = 4.685141163918161e-14 relative error = 2.414112122773732e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3076 Order of pole (three term test) = -3.673 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.209999999999869 y1[1] (analytic) = 0.6514549478388668 y1[1] (numeric) = 0.6514549478387471 absolute error = 1.196820420545919e-13 relative error = 1.837149943394005e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.937292028459643 y2[1] (numeric) = 1.937292028459595 absolute error = 4.796163466380676e-14 relative error = 2.475704950994995e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.315 Order of pole (three term test) = -3.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.219999999999869 y1[1] (analytic) = 0.642099610876209 y1[1] (numeric) = 0.6420996108760896 absolute error = 1.194599974496668e-13 relative error = 1.86045896035744e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.933759771817698 y2[1] (numeric) = 1.933759771817648 absolute error = 4.929390229335695e-14 relative error = 2.54912233731192e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3222 Order of pole (three term test) = -3.989 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.229999999999869 y1[1] (analytic) = 0.6327800636542142 y1[1] (numeric) = 0.6327800636540951 absolute error = 1.191269305422793e-13 relative error = 1.882596140187134e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.930134139976701 y2[1] (numeric) = 1.93013413997665 absolute error = 5.062616992290714e-14 relative error = 2.622935311818186e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3293 Order of pole (three term test) = -4.153 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.239999999999869 y1[1] (analytic) = 0.6234972381198385 y1[1] (numeric) = 0.6234972381197197 absolute error = 1.187938636348917e-13 relative error = 1.905282916619097e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.926415495496816 y2[1] (numeric) = 1.926415495496764 absolute error = 5.195843755245733e-14 relative error = 2.697156333818704e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3363 Order of pole (three term test) = -4.319 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.249999999999869 y1[1] (analytic) = 0.6142520625478994 y1[1] (numeric) = 0.614252062547781 absolute error = 1.184607967275042e-13 relative error = 1.928537223564742e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.922604210239391 y2[1] (numeric) = 1.922604210239338 absolute error = 5.329070518200751e-14 relative error = 2.771798007004889e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3431 Order of pole (three term test) = -4.49 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.259999999999868 y1[1] (analytic) = 0.6050454614482501 y1[1] (numeric) = 0.605045461448132 absolute error = 1.181277298201167e-13 relative error = 1.952377752530587e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.918700665329777 y2[1] (numeric) = 1.918700665329722 absolute error = 5.46229728115577e-14 relative error = 2.846873084404199e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3498 Order of pole (three term test) = -4.663 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.269999999999868 y1[1] (analytic) = 0.5958783554733282 y1[1] (numeric) = 0.5958783554732104 absolute error = 1.177946629127291e-13 relative error = 1.976823991520223e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.914705251119211 y2[1] (numeric) = 1.914705251119155 absolute error = 5.573319583618286e-14 relative error = 2.910797669960162e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3564 Order of pole (three term test) = -4.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.279999999999868 y1[1] (analytic) = 0.5867516613260921 y1[1] (numeric) = 0.5867516613259747 absolute error = 1.174615960053416e-13 relative error = 2.00189626629896e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.910618367145785 y2[1] (numeric) = 1.910618367145728 absolute error = 5.728750807065808e-14 relative error = 2.998375241008395e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3628 Order of pole (three term test) = -5.021 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.289999999999868 y1[1] (analytic) = 0.5776662916683509 y1[1] (numeric) = 0.5776662916682339 absolute error = 1.170175067954915e-13 relative error = 2.025693873491124e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.90644042209449 y2[1] (numeric) = 1.906440422094432 absolute error = 5.839773109528323e-14 relative error = 3.063181540765129e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3691 Order of pole (three term test) = -5.204 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.299999999999867 y1[1] (analytic) = 0.5686231550294993 y1[1] (numeric) = 0.5686231550293827 absolute error = 1.16684439888104e-13 relative error = 2.052052204628398e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.902171833756351 y2[1] (numeric) = 1.902171833756291 absolute error = 5.972999872483342e-14 relative error = 3.140094794006094e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3752 Order of pole (three term test) = -5.391 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.309999999999867 y1[1] (analytic) = 0.5596231557156653 y1[1] (numeric) = 0.559623155715549 absolute error = 1.163513729807164e-13 relative error = 2.079102192115733e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.897813028986643 y2[1] (numeric) = 1.897813028986582 absolute error = 6.084022174945858e-14 relative error = 3.205806937785902e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3812 Order of pole (three term test) = -5.58 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.319999999999867 y1[1] (analytic) = 0.5506671937192802 y1[1] (numeric) = 0.5506671937191643 absolute error = 1.159072837708663e-13 relative error = 2.104851806914681e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.893364443662212 y2[1] (numeric) = 1.89336444366215 absolute error = 6.195044477408373e-14 relative error = 3.271976770317764e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.387 Order of pole (three term test) = -5.773 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.329999999999867 y1[1] (analytic) = 0.5417561646290804 y1[1] (numeric) = 0.5417561646289649 absolute error = 1.154631945610163e-13 relative error = 2.131276062914199e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.888826522637882 y2[1] (numeric) = 1.888826522637819 absolute error = 6.328271240363392e-14 relative error = 3.350371865556772e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3926 Order of pole (three term test) = -5.968 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.339999999999867 y1[1] (analytic) = 0.5328909595405491 y1[1] (numeric) = 0.5328909595404341 absolute error = 1.150191053511662e-13 relative error = 2.158398510838578e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.884199719701975 y2[1] (numeric) = 1.88419971970191 absolute error = 6.439293542825908e-14 relative error = 3.417521760296417e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3981 Order of pole (three term test) = -6.167 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.349999999999866 y1[1] (analytic) = 0.5240724649668075 y1[1] (numeric) = 0.5240724649666929 absolute error = 1.145750161413162e-13 relative error = 2.186243769715565e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.879484497530928 y2[1] (numeric) = 1.879484497530862 absolute error = 6.572520305780927e-14 relative error = 3.496980323282912e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4035 Order of pole (three term test) = -6.367 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.359999999999866 y1[1] (analytic) = 0.5153015627499643 y1[1] (numeric) = 0.5153015627498502 absolute error = 1.141309269314661e-13 relative error = 2.214837586022322e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.87468132764303 y2[1] (numeric) = 1.874681327642963 absolute error = 6.705747068735946e-14 relative error = 3.577006379621246e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4087 Order of pole (three term test) = -6.571 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.369999999999866 y1[1] (analytic) = 0.5065791299729321 y1[1] (numeric) = 0.5065791299728184 absolute error = 1.13686837721616e-13 relative error = 2.244206896713069e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.869790690351266 y2[1] (numeric) = 1.869790690351197 absolute error = 6.838973831690964e-14 relative error = 3.657614655470431e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4137 Order of pole (three term test) = -6.777 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.379999999999866 y1[1] (analytic) = 0.4979060388717198 y1[1] (numeric) = 0.4979060388716067 absolute error = 1.131317262093035e-13 relative error = 2.272150112211245e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.86481307471529 y2[1] (numeric) = 1.86481307471522 absolute error = 6.94999613415348e-14 relative error = 3.72691302328764e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4186 Order of pole (three term test) = -6.986 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.389999999999866 y1[1] (analytic) = 0.4892831567482102 y1[1] (numeric) = 0.4892831567480975 absolute error = 1.126876369994534e-13 relative error = 2.303117028355904e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.859748978492517 y2[1] (numeric) = 1.859748978492446 absolute error = 7.083222897108499e-14 relative error = 3.808698366835532e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4233 Order of pole (three term test) = -7.197 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.399999999999865 y1[1] (analytic) = 0.4807113458834298 y1[1] (numeric) = 0.4807113458833177 absolute error = 1.121325254871408e-13 relative error = 2.332637380985229e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.85459890808835 y2[1] (numeric) = 1.854598908088279 absolute error = 7.194245199571014e-14 relative error = 3.87913805416103e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4278 Order of pole (three term test) = -7.41 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.409999999999865 y1[1] (analytic) = 0.4721914634513219 y1[1] (numeric) = 0.4721914634512103 absolute error = 1.115774139748282e-13 relative error = 2.362969740267884e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.849363378505539 y2[1] (numeric) = 1.849363378505465 absolute error = 7.327471962526033e-14 relative error = 3.962159112530566e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4321 Order of pole (three term test) = -7.626 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.419999999999865 y1[1] (analytic) = 0.4637243614330299 y1[1] (numeric) = 0.4637243614329189 absolute error = 1.110223024625157e-13 relative error = 2.394144273969727e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.844042913292676 y2[1] (numeric) = 1.844042913292602 absolute error = 7.438494264988549e-14 relative error = 4.033796725319457e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4363 Order of pole (three term test) = -7.843 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.429999999999865 y1[1] (analytic) = 0.4553108865316998 y1[1] (numeric) = 0.4553108865315893 absolute error = 1.104671909502031e-13 relative error = 2.42619261295682e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.838638044491852 y2[1] (numeric) = 1.838638044491776 absolute error = 7.571721027943568e-14 relative error = 4.118113976063288e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4403 Order of pole (three term test) = -8.063 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.439999999999864 y1[1] (analytic) = 0.4469518800878103 y1[1] (numeric) = 0.4469518800877005 absolute error = 1.098565682866592e-13 relative error = 2.457905944261299e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.833149312585441 y2[1] (numeric) = 1.833149312585364 absolute error = 7.682743330406083e-14 relative error = 4.191007943357588e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4441 Order of pole (three term test) = -8.285 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.449999999999864 y1[1] (analytic) = 0.4386481779950402 y1[1] (numeric) = 0.438648177994931 absolute error = 1.092459456231154e-13 relative error = 2.490514063513348e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.82757726644206 y2[1] (numeric) = 1.827577266441982 absolute error = 7.815970093361102e-14 relative error = 4.276683802582688e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4478 Order of pole (three term test) = -8.508 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.459999999999864 y1[1] (analytic) = 0.4304006106166791 y1[1] (numeric) = 0.4304006106165704 absolute error = 1.086908341108028e-13 relative error = 2.525341075958752e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.82192246326168 y2[1] (numeric) = 1.821922463261601 absolute error = 7.949196856316121e-14 relative error = 4.363081863585536e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4512 Order of pole (three term test) = -8.734 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.469999999999864 y1[1] (analytic) = 0.4222100027025916 y1[1] (numeric) = 0.4222100027024835 absolute error = 1.080247002960277e-13 relative error = 2.558553790875516e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.816185468519907 y2[1] (numeric) = 1.816185468519827 absolute error = 8.08242361927114e-14 relative error = 4.450219297183275e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4545 Order of pole (three term test) = -8.961 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.479999999999864 y1[1] (analytic) = 0.4140771733067438 y1[1] (numeric) = 0.4140771733066364 absolute error = 1.073585664812526e-13 relative error = 2.592718782924134e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.810366855911435 y2[1] (numeric) = 1.810366855911353 absolute error = 8.193445921733655e-14 relative error = 4.525848390882432e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4576 Order of pole (three term test) = -9.189 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.489999999999863 y1[1] (analytic) = 0.4060029357052979 y1[1] (numeric) = 0.4060029357051912 absolute error = 1.066924326664775e-13 relative error = 2.627873428578397e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.804467207292675 y2[1] (numeric) = 1.804467207292592 absolute error = 8.304468224196171e-14 relative error = 4.602171871361268e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4606 Order of pole (three term test) = -9.419 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.499999999999863 y1[1] (analytic) = 0.3979880973152856 y1[1] (numeric) = 0.3979880973151795 absolute error = 1.060818100029337e-13 relative error = 2.665451824276439e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.798487112623573 y2[1] (numeric) = 1.798487112623488 absolute error = 8.43769498715119e-14 relative error = 4.691551542364162e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.32 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4633 Order of pole (three term test) = -9.651 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.509999999999863 y1[1] (analytic) = 0.3900334596138669 y1[1] (numeric) = 0.3900334596137615 absolute error = 1.054156761881586e-13 relative error = 2.702734178050266e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.792427169908612 y2[1] (numeric) = 1.792427169908526 absolute error = 8.570921750106208e-14 relative error = 4.781740588401816e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4659 Order of pole (three term test) = -9.884 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.519999999999863 y1[1] (analytic) = 0.382139818058183 y1[1] (numeric) = 0.3821398180580783 absolute error = 1.046940312221523e-13 relative error = 2.739678679760401e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.786287985137014 y2[1] (numeric) = 1.786287985136927 absolute error = 8.681944052568724e-14 relative error = 4.860327183974645e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.93 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4682 Order of pole (three term test) = -10.12 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.529999999999863 y1[1] (analytic) = 0.3743079620058115 y1[1] (numeric) = 0.3743079620057075 absolute error = 1.040278974073772e-13 relative error = 2.779206107450154e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.78007017222214 y2[1] (numeric) = 1.780070172222052 absolute error = 8.815170815523743e-14 relative error = 4.952147928258006e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.24 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4704 Order of pole (three term test) = -10.35 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.539999999999862 y1[1] (analytic) = 0.3665386746358311 y1[1] (numeric) = 0.3665386746357279 absolute error = 1.032507412901396e-13 relative error = 2.816912605272084e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.7737743529401 y2[1] (numeric) = 1.773774352940011 absolute error = 8.926193117986259e-14 relative error = 5.032316034556902e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4724 Order of pole (three term test) = -10.59 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.549999999999862 y1[1] (analytic) = 0.3588327328705045 y1[1] (numeric) = 0.358832732870402 absolute error = 1.025290963241332e-13 relative error = 2.857294971502332e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.767401156867576 y2[1] (numeric) = 1.767401156867486 absolute error = 9.037215420448774e-14 relative error = 5.113279113421954e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.87 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4742 Order of pole (three term test) = -10.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.559999999999862 y1[1] (analytic) = 0.3511909072975866 y1[1] (numeric) = 0.3511909072974848 absolute error = 1.018074513581269e-13 relative error = 2.898920480075496e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.760951221318864 y2[1] (numeric) = 1.760951221318773 absolute error = 9.170442183403793e-14 relative error = 5.207663944567181e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4758 Order of pole (three term test) = -11.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.569999999999862 y1[1] (analytic) = 0.3436139620932664 y1[1] (numeric) = 0.3436139620931654 absolute error = 1.010302952408892e-13 relative error = 2.940226719118788e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.754425191282144 y2[1] (numeric) = 1.754425191282052 absolute error = 9.259260025373806e-14 relative error = 5.27766021109574e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4772 Order of pole (three term test) = -11.3 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.579999999999862 y1[1] (analytic) = 0.3361026549457504 y1[1] (numeric) = 0.3361026549456501 absolute error = 1.002531391236516e-13 relative error = 2.982813067627606e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.747823719354982 y2[1] (numeric) = 1.747823719354888 absolute error = 9.392486788328824e-14 relative error = 5.373818128406585e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.87 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4785 Order of pole (three term test) = -11.54 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.589999999999861 y1[1] (analytic) = 0.3286577369794939 y1[1] (numeric) = 0.3286577369793944 absolute error = 9.947598300641403e-14 relative error = 3.026734861641815e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.741147465679068 y2[1] (numeric) = 1.741147465678973 absolute error = 9.50350909079134e-14 relative error = 5.458187360991195e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.21 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4795 Order of pole (three term test) = -11.78 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.599999999999861 y1[1] (analytic) = 0.3212799526800893 y1[1] (numeric) = 0.3212799526799907 absolute error = 9.864331573794516e-14 relative error = 3.07032277971505e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.734397097874207 y2[1] (numeric) = 1.734397097874111 absolute error = 9.614531393253856e-14 relative error = 5.543442966456797e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4803 Order of pole (three term test) = -12.02 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.609999999999861 y1[1] (analytic) = 0.3139700398198186 y1[1] (numeric) = 0.3139700398197208 absolute error = 9.786615962070755e-14 relative error = 3.117054088245842e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.727573290971555 y2[1] (numeric) = 1.727573290971457 absolute error = 9.747758156208874e-14 relative error = 5.642457085410783e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.92 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.481 Order of pole (three term test) = -12.26 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.619999999999861 y1[1] (analytic) = 0.3067287293838762 y1[1] (numeric) = 0.3067287293837792 absolute error = 9.703349235223868e-14 relative error = 3.163495396963602e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.720676727346114 y2[1] (numeric) = 1.720676727346016 absolute error = 9.85878045867139e-14 relative error = 5.729594816963138e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.28 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4815 Order of pole (three term test) = -12.51 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.62999999999986 y1[1] (analytic) = 0.2995567454972713 y1[1] (numeric) = 0.2995567454971751 absolute error = 9.614531393253856e-14 relative error = 3.20958600925294e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.713708096648501 y2[1] (numeric) = 1.713708096648401 absolute error = 9.969802761133906e-14 relative error = 5.817678506994191e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4817 Order of pole (three term test) = -12.75 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.63999999999986 y1[1] (analytic) = 0.2924548053524159 y1[1] (numeric) = 0.2924548053523206 absolute error = 9.531264666406969e-14 relative error = 3.259055584647186e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.706668095735977 y2[1] (numeric) = 1.706668095735876 absolute error = 1.008082506359642e-13 relative error = 5.906728489729694e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.02 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.64999999999986 y1[1] (analytic) = 0.2854236191374062 y1[1] (numeric) = 0.2854236191373118 absolute error = 9.442446824436956e-14 relative error = 3.308221951979123e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.699557428602768 y2[1] (numeric) = 1.699557428602666 absolute error = 1.019184736605894e-13 relative error = 5.996765507616773e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.41 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4817 Order of pole (three term test) = -13.23 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.65999999999986 y1[1] (analytic) = 0.2784638899650044 y1[1] (numeric) = 0.2784638899649109 absolute error = 9.353628982466944e-14 relative error = 3.359009666798251e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.692376806309662 y2[1] (numeric) = 1.692376806309559 absolute error = 1.028066520802895e-13 relative error = 6.074690441100178e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.19 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4814 Order of pole (three term test) = -13.47 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.66999999999986 y1[1] (analytic) = 0.2715763138023281 y1[1] (numeric) = 0.2715763138022354 absolute error = 9.264811140496931e-14 relative error = 3.411494548541703e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.685126946912903 y2[1] (numeric) = 1.685126946912799 absolute error = 1.041389197098397e-13 relative error = 6.17988572912081e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.81 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4809 Order of pole (three term test) = -13.71 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.87 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.679999999999859 y1[1] (analytic) = 0.2647615794012538 y1[1] (numeric) = 0.264761579401162 absolute error = 9.175993298526919e-14 relative error = 3.465757123551691e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.67780857539239 y2[1] (numeric) = 1.677808575392285 absolute error = 1.052491427344648e-13 relative error = 6.273012564013757e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.44 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4802 Order of pole (three term test) = -13.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.689999999999859 y1[1] (analytic) = 0.2580203682295427 y1[1] (numeric) = 0.2580203682294518 absolute error = 9.081624341433781e-14 relative error = 3.5197315637324e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.670422423579176 y2[1] (numeric) = 1.67042242357907 absolute error = 1.0635936575909e-13 relative error = 6.367213721376907e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.07 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4793 Order of pole (three term test) = -14.19 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.699999999999859 y1[1] (analytic) = 0.2513533544026944 y1[1] (numeric) = 0.2513533544026044 absolute error = 8.992806499463768e-14 relative error = 3.577754719380571e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.662969230082288 y2[1] (numeric) = 1.662969230082181 absolute error = 1.074695887837152e-13 relative error = 6.462512164365017e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4782 Order of pole (three term test) = -14.43 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.709999999999859 y1[1] (analytic) = 0.2447612046165356 y1[1] (numeric) = 0.2447612046164466 absolute error = 8.89843754237063e-14 relative error = 3.635558811827104e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.655449740214865 y2[1] (numeric) = 1.655449740214756 absolute error = 1.083577672034153e-13 relative error = 6.545518391234956e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.477 Order of pole (three term test) = -14.67 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.719999999999859 y1[1] (analytic) = 0.2382445780805517 y1[1] (numeric) = 0.2382445780804636 absolute error = 8.804068585277491e-14 relative error = 3.69539095336759e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.647864705919626 y2[1] (numeric) = 1.647864705919516 absolute error = 1.094679902280404e-13 relative error = 6.643020500093149e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.01 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4755 Order of pole (three term test) = -14.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.16 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.729999999999858 y1[1] (analytic) = 0.2318041264519656 y1[1] (numeric) = 0.2318041264518785 absolute error = 8.70692407062279e-14 relative error = 3.75615576991337e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.64021488569368 y2[1] (numeric) = 1.64021488569357 absolute error = 1.105782132526656e-13 relative error = 6.74169062951162e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4739 Order of pole (three term test) = -15.15 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.739999999999858 y1[1] (analytic) = 0.2254404937705732 y1[1] (numeric) = 0.2254404937704871 absolute error = 8.609779555968089e-14 relative error = 3.819091864095236e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.632501044512676 y2[1] (numeric) = 1.632501044512565 absolute error = 1.116884362772907e-13 relative error = 6.841553740667361e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.33 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.472 Order of pole (three term test) = -15.39 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.749999999999858 y1[1] (analytic) = 0.2191543163943397 y1[1] (numeric) = 0.2191543163942546 absolute error = 8.509859483751825e-14 relative error = 3.883044433603325e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.624723953754303 y2[1] (numeric) = 1.624723953754191 absolute error = 1.125766146969909e-13 relative error = 6.928968729540569e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.47 Order of pole (three term test) = -15.62 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.759999999999858 y1[1] (analytic) = 0.2129462229357641 y1[1] (numeric) = 0.21294622293568 absolute error = 8.409939411535561e-14 relative error = 3.9493254661166e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.616884391121157 y2[1] (numeric) = 1.616884391121043 absolute error = 1.13464793116691e-13 relative error = 7.017495730663458e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4678 Order of pole (three term test) = -15.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.769999999999857 y1[1] (analytic) = 0.206816834199019 y1[1] (numeric) = 0.206816834198936 absolute error = 8.307243781757734e-14 relative error = 4.016715473830194e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.608983140562966 y2[1] (numeric) = 1.608983140562852 absolute error = 1.143529715363911e-13 relative error = 7.10715784730847e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4654 Order of pole (three term test) = -16.09 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.59 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.779999999999857 y1[1] (analytic) = 0.2007667631178703 y1[1] (numeric) = 0.2007667631177882 absolute error = 8.204548151979907e-14 relative error = 4.086606779212261e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.601020992198204 y2[1] (numeric) = 1.601020992198088 absolute error = 1.154631945610163e-13 relative error = 7.211847634957313e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.04 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4628 Order of pole (three term test) = -16.32 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.789999999999857 y1[1] (analytic) = 0.1947966146943842 y1[1] (numeric) = 0.1947966146943032 absolute error = 8.10185252220208e-14 relative error = 4.159134148667342e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.592998742235071 y2[1] (numeric) = 1.592998742234955 absolute error = 1.163513729807164e-13 relative error = 7.303921208215682e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.46 Order of pole (three term test) = -16.55 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.99 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.799999999999857 y1[1] (analytic) = 0.1889069859384282 y1[1] (numeric) = 0.1889069859383482 absolute error = 7.999156892424253e-14 relative error = 4.234442073535319e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.584917192891878 y2[1] (numeric) = 1.584917192891761 absolute error = 1.174615960053416e-13 relative error = 7.411213439550005e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4571 Order of pole (three term test) = -16.78 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.809999999999857 y1[1] (analytic) = 0.1830984658079697 y1[1] (numeric) = 0.1830984658078908 absolute error = 7.8909101475233e-14 relative error = 4.309653886340665e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.576777152316826 y2[1] (numeric) = 1.576777152316708 absolute error = 1.185718190299667e-13 relative error = 7.519884395568775e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4539 Order of pole (three term test) = -17.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.819999999999856 y1[1] (analytic) = 0.1773716351501814 y1[1] (numeric) = 0.1773716351501035 absolute error = 7.78543896018391e-14 relative error = 4.389337085150026e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.568579434507188 y2[1] (numeric) = 1.568579434507068 absolute error = 1.194599974496668e-13 relative error = 7.615807961118555e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4506 Order of pole (three term test) = -17.24 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.829999999999856 y1[1] (analytic) = 0.1717270666433567 y1[1] (numeric) = 0.1717270666432799 absolute error = 7.677192215282957e-14 relative error = 4.470577856679386e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.560324859227914 y2[1] (numeric) = 1.560324859227793 absolute error = 1.20570220474292e-13 relative error = 7.727251140121745e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4471 Order of pole (three term test) = -17.46 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.839999999999856 y1[1] (analytic) = 0.1661653247396425 y1[1] (numeric) = 0.1661653247395669 absolute error = 7.566169912820442e-14 relative error = 4.553398806083974e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.552014251929653 y2[1] (numeric) = 1.552014251929531 absolute error = 1.214583988939921e-13 relative error = 7.825855899388827e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4434 Order of pole (three term test) = -17.69 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.849999999999856 y1[1] (analytic) = 0.1606869656085945 y1[1] (numeric) = 0.1606869656085199 absolute error = 7.457923167919489e-14 relative error = 4.641274505167825e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.543648443666209 y2[1] (numeric) = 1.543648443666087 absolute error = 1.223465773136923e-13 relative error = 7.925805763332721e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4396 Order of pole (three term test) = -17.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.859999999999856 y1[1] (analytic) = 0.1552925370815604 y1[1] (numeric) = 0.155292537081487 absolute error = 7.344125307895411e-14 relative error = 4.729219733230477e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.535228271011438 y2[1] (numeric) = 1.535228271011315 absolute error = 1.232347557333924e-13 relative error = 8.027129128634594e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4355 Order of pole (three term test) = -18.13 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.869999999999855 y1[1] (analytic) = 0.1499825785968976 y1[1] (numeric) = 0.1499825785968253 absolute error = 7.233103005432895e-14 relative error = 4.822628783355583e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.526754575975587 y2[1] (numeric) = 1.526754575975463 absolute error = 1.241229341530925e-13 relative error = 8.129855060285552e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4313 Order of pole (three term test) = -18.34 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.879999999999855 y1[1] (analytic) = 0.1447576211460296 y1[1] (numeric) = 0.1447576211459584 absolute error = 7.119305145408816e-14 relative error = 4.918086584351198e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.5182282059211 y2[1] (numeric) = 1.518228205920975 absolute error = 1.250111125727926e-13 relative error = 8.234013311388135e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.427 Order of pole (three term test) = -18.56 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.889999999999855 y1[1] (analytic) = 0.1396181872203474 y1[1] (numeric) = 0.1396181872202774 absolute error = 7.005507285384738e-14 relative error = 5.017617994372427e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.509650013477876 y2[1] (numeric) = 1.50965001347775 absolute error = 1.256772463875677e-13 relative error = 8.324925993809463e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4224 Order of pole (three term test) = -18.77 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.899999999999855 y1[1] (analytic) = 0.1345647907589607 y1[1] (numeric) = 0.1345647907588919 absolute error = 6.888933867799096e-14 relative error = 5.119417812746354e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.501020856458011 y2[1] (numeric) = 1.501020856457884 absolute error = 1.265654248072678e-13 relative error = 8.431956442359291e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4177 Order of pole (three term test) = -18.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.909999999999854 y1[1] (analytic) = 0.1295979370973045 y1[1] (numeric) = 0.1295979370972368 absolute error = 6.772360450213455e-14 relative error = 5.225669946527498e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.492341597770016 y2[1] (numeric) = 1.492341597769889 absolute error = 1.27453603226968e-13 relative error = 8.540511329136707e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4128 Order of pole (three term test) = -19.19 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.919999999999854 y1[1] (analytic) = 0.124718122916606 y1[1] (numeric) = 0.1247181229165394 absolute error = 6.654399253847032e-14 relative error = 5.335551159871579e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.483613105332527 y2[1] (numeric) = 1.483613105332399 absolute error = 1.281197370417431e-13 relative error = 8.63565686911529e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4078 Order of pole (three term test) = -19.4 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.929999999999854 y1[1] (analytic) = 0.1199258361942166 y1[1] (numeric) = 0.1199258361941513 absolute error = 6.535050278699828e-14 relative error = 5.449243037268877e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.474836251987515 y2[1] (numeric) = 1.474836251987386 absolute error = 1.290079154614432e-13 relative error = 8.747270436808822e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4025 Order of pole (three term test) = -19.6 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.939999999999854 y1[1] (analytic) = 0.1152215561548151 y1[1] (numeric) = 0.115221556154751 absolute error = 6.415701303552623e-14 relative error = 5.568143251712635e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.466011915413 y2[1] (numeric) = 1.46601191541287 absolute error = 1.298960938811433e-13 relative error = 8.860507374835996e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3972 Order of pole (three term test) = -19.8 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.949999999999854 y1[1] (analytic) = 0.1106057532224853 y1[1] (numeric) = 0.1106057532224223 absolute error = 6.294964549624638e-14 relative error = 5.691353628741367e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.457140978035285 y2[1] (numeric) = 1.457140978035155 absolute error = 1.305622276959184e-13 relative error = 8.960164435973799e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3916 Order of pole (three term test) = -20 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.959999999999853 y1[1] (analytic) = 0.1060788889736737 y1[1] (numeric) = 0.106078888973612 absolute error = 6.17284001691587e-14 relative error = 5.819103194461079e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.448224326940717 y2[1] (numeric) = 1.448224326940585 absolute error = 1.314504061156185e-13 relative error = 9.076660547009268e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3859 Order of pole (three term test) = -20.19 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.969999999999853 y1[1] (analytic) = 0.1016414160910331 y1[1] (numeric) = 0.1016414160909726 absolute error = 6.050715484207103e-14 relative error = 5.953001952263142e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.439262853786973 y2[1] (numeric) = 1.439262853786841 absolute error = 1.321165399303936e-13 relative error = 9.179458747425462e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3801 Order of pole (three term test) = -20.38 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.979999999999853 y1[1] (analytic) = 0.09729377831815364 y1[1] (numeric) = 0.09729377831809437 absolute error = 5.927203172717554e-14 relative error = 6.092068038857961e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.430257454713902 y2[1] (numeric) = 1.430257454713769 absolute error = 1.330047183500938e-13 relative error = 9.299355015541524e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3741 Order of pole (three term test) = -20.57 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.989999999999853 y1[1] (analytic) = 0.0930364104151897 y1[1] (numeric) = 0.09303641041513168 absolute error = 5.802303082447224e-14 relative error = 6.236593884645301e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.421209030253906 y2[1] (numeric) = 1.421209030253772 absolute error = 1.336708521648688e-13 relative error = 9.40543222843074e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.368 Order of pole (three term test) = -20.76 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.999999999999853 y1[1] (analytic) = 0.08886973811538378 y1[1] (numeric) = 0.088869738115327 absolute error = 5.677402992176894e-14 relative error = 6.388454734507774e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.412118485241891 y2[1] (numeric) = 1.412118485241756 absolute error = 1.34559030584569e-13 relative error = 9.528876789791439e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3617 Order of pole (three term test) = -20.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.009999999999852 y1[1] (analytic) = 0.08479417808249361 y1[1] (numeric) = 0.08479417808243811 absolute error = 5.549727344345001e-14 relative error = 6.544939133611089e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.402986728724783 y2[1] (numeric) = 1.402986728724647 absolute error = 1.352251643993441e-13 relative error = 9.638378013899984e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3552 Order of pole (three term test) = -21.12 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.019999999999852 y1[1] (analytic) = 0.08081013786912622 y1[1] (numeric) = 0.08081013786907199 absolute error = 5.42343947529389e-14 relative error = 6.711335506044141e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.393814673870623 y2[1] (numeric) = 1.393814673870487 absolute error = 1.361133428190442e-13 relative error = 9.765526606278112e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3487 Order of pole (three term test) = -21.3 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.029999999999852 y1[1] (analytic) = 0.07691801587598292 y1[1] (numeric) = 0.07691801587592996 absolute error = 5.295763827461997e-14 relative error = 6.884945961165334e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.384603237877254 y2[1] (numeric) = 1.384603237877118 absolute error = 1.367794766338193e-13 relative error = 9.878604418368755e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3419 Order of pole (three term test) = -21.47 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.039999999999852 y1[1] (analytic) = 0.07311820131201958 y1[1] (numeric) = 0.07311820131196792 absolute error = 5.166700400849322e-14 relative error = 7.066230169969991e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.375353341880599 y2[1] (numeric) = 1.375353341880462 absolute error = 1.374456104485944e-13 relative error = 9.993476313560057e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3351 Order of pole (three term test) = -21.64 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.049999999999851 y1[1] (analytic) = 0.06941107415552614 y1[1] (numeric) = 0.06941107415547576 absolute error = 5.037636974236648e-14 relative error = 7.257684793854437e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.36606591086255 y2[1] (numeric) = 1.366065910862412 absolute error = 1.381117442633695e-13 relative error = 1.011018159264102e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3281 Order of pole (three term test) = -21.81 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.059999999999851 y1[1] (analytic) = 0.06579700511612893 y1[1] (numeric) = 0.06579700511607986 absolute error = 4.907185768843192e-14 relative error = 7.458068585617562e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.356741873558468 y2[1] (numeric) = 1.356741873558329 absolute error = 1.387778780781446e-13 relative error = 1.022876059055783e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.321 Order of pole (three term test) = -21.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.069999999999851 y1[1] (analytic) = 0.06227635559772021 y1[1] (numeric) = 0.06227635559767246 absolute error = 4.774652895278564e-14 relative error = 7.666879105965785e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.347382162364314 y2[1] (numeric) = 1.347382162364175 absolute error = 1.394440118929197e-13 relative error = 1.034925470946051e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3137 Order of pole (three term test) = -22.13 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.079999999999851 y1[1] (analytic) = 0.05884947766231795 y1[1] (numeric) = 0.05884947766227152 absolute error = 4.642813911104327e-14 relative error = 7.889303517263294e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.337987713243408 y2[1] (numeric) = 1.337987713243268 absolute error = 1.403321903126198e-13 relative error = 1.048830186731994e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3064 Order of pole (three term test) = -22.28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.089999999999851 y1[1] (analytic) = 0.05551671399485996 y1[1] (numeric) = 0.05551671399481487 absolute error = 4.508893258758917e-14 relative error = 8.121686127129885e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.328559465632833 y2[1] (numeric) = 1.328559465632692 absolute error = 1.407762795224698e-13 relative error = 1.059615946173805e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2989 Order of pole (three term test) = -22.43 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.09999999999985 y1[1] (analytic) = 0.05227839786893571 y1[1] (numeric) = 0.05227839786889196 absolute error = 4.374972606413507e-14 relative error = 8.368604977875872e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.319098362349494 y2[1] (numeric) = 1.319098362349352 absolute error = 1.4166445794217e-13 relative error = 1.073949160924181e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2913 Order of pole (three term test) = -22.58 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.10999999999985 y1[1] (analytic) = 0.04913485311345918 y1[1] (numeric) = 0.04913485311341678 absolute error = 4.239664175287317e-14 relative error = 8.62862898052701e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.309605349495833 y2[1] (numeric) = 1.309605349495691 absolute error = 1.4210854715202e-13 relative error = 1.085124974533194e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2835 Order of pole (three term test) = -22.73 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.11999999999985 y1[1] (analytic) = 0.04608639408028632 y1[1] (numeric) = 0.04608639408024529 absolute error = 4.103661854770735e-14 relative error = 8.904280616144138e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.300081376365227 y2[1] (numeric) = 1.300081376365084 absolute error = 1.427746809667951e-13 relative error = 1.098198032541357e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2757 Order of pole (three term test) = -22.87 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.12999999999985 y1[1] (analytic) = 0.04313332561278008 y1[1] (numeric) = 0.04313332561274041 absolute error = 3.966965644863762e-14 relative error = 9.196985366897794e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.290527395347052 y2[1] (numeric) = 1.290527395346908 absolute error = 1.434408147815702e-13 relative error = 1.111489886218152e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2677 Order of pole (three term test) = -23 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.13999999999985 y1[1] (analytic) = 0.04027594301532632 y1[1] (numeric) = 0.04027594301528803 absolute error = 3.828881656176009e-14 relative error = 9.506621991989097e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.280944361831447 y2[1] (numeric) = 1.280944361831303 absolute error = 1.438849039914203e-13 relative error = 1.123272081745213e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2597 Order of pole (three term test) = -23.13 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.149999999999849 y1[1] (analytic) = 0.03751453202380364 y1[1] (numeric) = 0.03751453202376673 absolute error = 3.690103778097864e-14 relative error = 9.836464908469144e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.271333234113778 y2[1] (numeric) = 1.271333234113634 absolute error = 1.443289932012704e-13 relative error = 1.135256983208492e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2515 Order of pole (three term test) = -23.26 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.159999999999849 y1[1] (analytic) = 0.03484936877701002 y1[1] (numeric) = 0.03484936877697451 absolute error = 3.551325900019719e-14 relative error = 1.019050279717696e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.261694973298808 y2[1] (numeric) = 1.261694973298663 absolute error = 1.449951270160454e-13 relative error = 1.149209040889997e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2432 Order of pole (three term test) = -23.39 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.169999999999849 y1[1] (analytic) = 0.03228071978904919 y1[1] (numeric) = 0.03228071978901507 absolute error = 3.411854132551184e-14 relative error = 1.056932483181063e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.252030543204587 y2[1] (numeric) = 1.252030543204442 absolute error = 1.454392162258955e-13 relative error = 1.161626743175467e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2349 Order of pole (three term test) = -23.51 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.179999999999849 y1[1] (analytic) = 0.02980884192267941 y1[1] (numeric) = 0.02980884192264669 absolute error = 3.271341530997063e-14 relative error = 1.097439994308579e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.24234091026607 y2[1] (numeric) = 1.242340910265924 absolute error = 1.461053500406706e-13 relative error = 1.176048770778863e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2264 Order of pole (three term test) = -23.62 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.189999999999849 y1[1] (analytic) = 0.02743398236362741 y1[1] (numeric) = 0.02743398236359611 absolute error = 3.129788095357355e-14 relative error = 1.140843518040202e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.232627043438477 y2[1] (numeric) = 1.23262704343833 absolute error = 1.467714838554457e-13 relative error = 1.190720945453371e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2179 Order of pole (three term test) = -23.73 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.199999999999848 y1[1] (analytic) = 0.02515637859587007 y1[1] (numeric) = 0.02515637859584019 absolute error = 2.987887715022453e-14 relative error = 1.187725690975638e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.222889914100395 y2[1] (numeric) = 1.222889914100248 absolute error = 1.472155730652958e-13 relative error = 1.203833406162265e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2092 Order of pole (three term test) = -23.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.209999999999848 y1[1] (analytic) = 0.02297625837788616 y1[1] (numeric) = 0.02297625837785771 absolute error = 2.844946500601964e-14 relative error = 1.238211397962048e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.213130495956644 y2[1] (numeric) = 1.213130495956496 absolute error = 1.478817068800709e-13 relative error = 1.219009062693252e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2005 Order of pole (three term test) = -23.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.219999999999848 y1[1] (analytic) = 0.02089383971988072 y1[1] (numeric) = 0.02089383971985371 absolute error = 2.701311396791084e-14 relative error = 1.29287456638272e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.203349764940905 y2[1] (numeric) = 1.203349764940757 absolute error = 1.483257960899209e-13 relative error = 1.232607512888865e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1917 Order of pole (three term test) = -24.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.229999999999848 y1[1] (analytic) = 0.01890933086198421 y1[1] (numeric) = 0.01890933086195864 absolute error = 2.556635458894618e-14 relative error = 1.352049671960917e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.19354869911813 y2[1] (numeric) = 1.193548699117981 absolute error = 1.48991929904696e-13 relative error = 1.24831043772894e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1829 Order of pole (three term test) = -24.13 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.239999999999847 y1[1] (analytic) = 0.01702293025342866 y1[1] (numeric) = 0.01702293025340455 absolute error = 2.411612576302957e-14 relative error = 1.416684754269744e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.183728278586733 y2[1] (numeric) = 1.183728278586584 absolute error = 1.494360191145461e-13 relative error = 1.26241825778598e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1739 Order of pole (three term test) = -24.22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.249999999999847 y1[1] (analytic) = 0.01523482653270294 y1[1] (numeric) = 0.01523482653268028 absolute error = 2.265722331973308e-14 relative error = 1.487199297681354e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.173889485380584 y2[1] (numeric) = 1.173889485380434 absolute error = 1.498801083243961e-13 relative error = 1.276782100793789e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1649 Order of pole (three term test) = -24.31 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.259999999999847 y1[1] (analytic) = 0.01354519850868903 y1[1] (numeric) = 0.01354519850866784 absolute error = 2.119138198253268e-14 relative error = 1.564494013796751e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.164033303370804 y2[1] (numeric) = 1.164033303370654 absolute error = 1.503241975342462e-13 relative error = 1.291408047337974e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1558 Order of pole (three term test) = -24.39 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.269999999999847 y1[1] (analytic) = 0.01195421514278133 y1[1] (numeric) = 0.01195421514276161 absolute error = 1.972033647490434e-14 relative error = 1.649655476278814e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.154160718167381 y2[1] (numeric) = 1.15416071816723 absolute error = 1.507682867440963e-13 relative error = 1.306302357816264e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1467 Order of pole (three term test) = -24.46 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.279999999999847 y1[1] (analytic) = 0.0104620355319906 y1[1] (numeric) = 0.01046203553197236 absolute error = 1.824061734989613e-14 relative error = 1.743505582075337e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.144272717020608 y2[1] (numeric) = 1.144272717020457 absolute error = 1.512123759539463e-13 relative error = 1.321471478824248e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1375 Order of pole (three term test) = -24.54 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.289999999999846 y1[1] (analytic) = 0.009068808893034441 y1[1] (numeric) = 0.009068808893017685 absolute error = 1.675569405445998e-14 relative error = 1.847617945431585e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.13437028872236 y2[1] (numeric) = 1.134370288722209 absolute error = 1.516564651637964e-13 relative error = 1.336922049806213e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1282 Order of pole (three term test) = -24.6 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.299999999999846 y1[1] (analytic) = 0.007774674547415737 y1[1] (numeric) = 0.007774674547400473 absolute error = 1.526469922685791e-14 relative error = 1.963387551949917e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.124454423507215 y2[1] (numeric) = 1.124454423507063 absolute error = 1.521005543736464e-13 relative error = 1.352660909983698e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1189 Order of pole (three term test) = -24.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.309999999999846 y1[1] (analytic) = 0.006579761907490606 y1[1] (numeric) = 0.006579761907476838 absolute error = 1.376850022882792e-14 relative error = 2.092552955928911e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.114526112953431 y2[1] (numeric) = 1.114526112953278 absolute error = 1.523225989785715e-13 relative error = 1.366702827401013e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1096 Order of pole (three term test) = -24.72 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.319999999999846 y1[1] (analytic) = 0.005484190463527282 y1[1] (numeric) = 0.005484190463515016 absolute error = 1.2266229698632e-14 relative error = 2.236652753074279e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.104586349883789 y2[1] (numeric) = 1.104586349883636 absolute error = 1.527666881884215e-13 relative error = 1.383021691373371e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1002 Order of pole (three term test) = -24.77 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.329999999999846 y1[1] (analytic) = 0.004488069771757189 y1[1] (numeric) = 0.004488069771746432 absolute error = 1.075702027453218e-14 relative error = 2.396803263225684e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.094636128266314 y2[1] (numeric) = 1.094636128266161 absolute error = 1.532107773982716e-13 relative error = 1.399650289643984e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09072 Order of pole (three term test) = -24.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.339999999999845 y1[1] (analytic) = 0.003591499443419406 y1[1] (numeric) = 0.003591499443410164 absolute error = 9.242606680004428e-15 relative error = 2.57346738475468e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.084676443114875 y2[1] (numeric) = 1.084676443114722 absolute error = 1.534328220031966e-13 relative error = 1.414549223200443e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08125 Order of pole (three term test) = -24.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.349999999999845 y1[1] (analytic) = 0.002794569134799628 y1[1] (numeric) = 0.002794569134791904 absolute error = 7.723856276786734e-15 relative error = 2.763880907652169e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.074708290389689 y2[1] (numeric) = 1.074708290389535 absolute error = 1.538769112130467e-13 relative error = 1.431801658078314e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07174 Order of pole (three term test) = -24.9 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.359999999999845 y1[1] (analytic) = 0.00209735853826461 y1[1] (numeric) = 0.002097358538258411 absolute error = 6.19903434140312e-15 relative error = 2.955638832515639e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.06473266689772 y2[1] (numeric) = 1.064732666897566 absolute error = 1.540989558179717e-13 relative error = 1.447301849646121e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0622 Order of pole (three term test) = -24.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.369999999999845 y1[1] (analytic) = 0.001499937374292999 y1[1] (numeric) = 0.001499937374288329 absolute error = 4.670092437764062e-15 relative error = 3.113524949643533e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.054750570193005 y2[1] (numeric) = 1.054750570192851 absolute error = 1.543210004228968e-13 relative error = 1.463104214247147e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05264 Order of pole (three term test) = -24.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.379999999999844 y1[1] (analytic) = 0.001002365384503342 y1[1] (numeric) = 0.001002365384500205 absolute error = 3.136813725435061e-15 relative error = 3.129411464053409e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.044762998476896 y2[1] (numeric) = 1.044762998476742 absolute error = 1.545430450278218e-13 relative error = 1.479216293581623e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04306 Order of pole (three term test) = -24.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.389999999999844 y1[1] (analytic) = 0.0006046923256799765 y1[1] (numeric) = 0.0006046923256783775 absolute error = 1.598981363981622e-15 relative error = 2.644289163391594e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 1.034770950498242 y2[1] (numeric) = 1.034770950498088 absolute error = 1.547650896327468e-13 relative error = 1.495645867892092e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03346 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.399999999999844 y1[1] (analytic) = 0.0003069579647973919 y1[1] (numeric) = 0.0003069579647973353 absolute error = 5.659535340374333e-17 relative error = 1.843749304276864e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 1.024775425453514 y2[1] (numeric) = 1.024775425453359 absolute error = 1.549871342376719e-13 relative error = 1.512400965012235e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02385 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.409999999999844 y1[1] (analytic) = 0.0001091920750435652 y1[1] (numeric) = 0.000109192075045056 absolute error = 1.490832197276193e-15 relative error = 1.3653300357937e-09 % Correct digits = 11 h = 0.01 y2[1] (analytic) = 1.014777422886886 y2[1] (numeric) = 1.014777422886731 absolute error = 1.552091788425969e-13 relative error = 1.529489869818453e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01423 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.419999999999844 y1[1] (analytic) = 1.141443284266743e-05 y1[1] (numeric) = 1.141443284571023e-05 absolute error = 3.042799844553412e-15 relative error = 2.665747730521794e-08 % Correct digits = 10 h = 0.01 y2[1] (analytic) = 1.004777942590285 y2[1] (numeric) = 1.004777942590129 absolute error = 1.554312234475219e-13 relative error = 1.546921134104768e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.004601 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.429999999999843 y1[1] (analytic) = 1.363481587743755e-05 y1[1] (numeric) = 1.363481588203644e-05 absolute error = 4.598887460086076e-15 relative error = 3.372900302743484e-08 % Correct digits = 10 h = 0.01 y2[1] (analytic) = 0.9947779845034057 y2[1] (numeric) = 0.9947779845032501 absolute error = 1.556532680524469e-13 relative error = 1.564703586902853e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.005035 Order of pole (three term test) = -0.8935 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.439999999999843 y1[1] (analytic) = 0.0001158530021114224 y1[1] (numeric) = 0.0001158530021175807 absolute error = 6.158295444771977e-15 relative error = 5.315611449454884e-09 % Correct digits = 11 h = 0.01 y2[1] (analytic) = 0.9847785486137246 y2[1] (numeric) = 0.9847785486135687 absolute error = 1.55875312657372e-13 relative error = 1.582846345270194e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.01468 Order of pole (three term test) = -0.8985 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.449999999999843 y1[1] (analytic) = 0.0003180587698111801 y1[1] (numeric) = 0.0003180587698189018 absolute error = 7.721687872441763e-15 relative error = 2.427755058294996e-09 % Correct digits = 11 h = 0.01 y2[1] (analytic) = 0.9747806348564976 y2[1] (numeric) = 0.9747806348563416 absolute error = 1.559863349598345e-13 relative error = 1.600219879037688e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02431 Order of pole (three term test) = -0.9082 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.459999999999843 y1[1] (analytic) = 0.0006202318985684451 y1[1] (numeric) = 0.0006202318985777334 absolute error = 9.288360011683316e-15 relative error = 1.497562449322866e-09 % Correct digits = 11 h = 0.01 y2[1] (analytic) = 0.9647852430147689 y2[1] (numeric) = 0.9647852430146128 absolute error = 1.56097357262297e-13 relative error = 1.617949262724238e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03394 Order of pole (three term test) = -0.9228 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.469999999999843 y1[1] (analytic) = 0.001022342171322151 y1[1] (numeric) = 0.001022342171333009 absolute error = 1.085806791700783e-14 relative error = 1.062077670430591e-09 % Correct digits = 11 h = 0.01 y2[1] (analytic) = 0.9547933726193931 y2[1] (numeric) = 0.9547933726192369 absolute error = 1.562083795647595e-13 relative error = 1.636043818949176e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04355 Order of pole (three term test) = -0.9423 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.479999999999842 y1[1] (analytic) = 0.001524349377380115 y1[1] (numeric) = 0.001524349377392546 absolute error = 1.24310284288498e-14 relative error = 8.154973271426065e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9448060228490833 y2[1] (numeric) = 0.9448060228489271 absolute error = 1.562083795647595e-13 relative error = 1.653338101017918e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05314 Order of pole (three term test) = -0.9665 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.489999999999842 y1[1] (analytic) = 0.002126203316440067 y1[1] (numeric) = 0.002126203316454074 absolute error = 1.400615734503674e-14 relative error = 6.587402642418718e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9348241924304939 y2[1] (numeric) = 0.9348241924303375 absolute error = 1.56319401867222e-13 relative error = 1.672179679697846e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06271 Order of pole (three term test) = -0.9956 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.499999999999842 y1[1] (analytic) = 0.002827843803609646 y1[1] (numeric) = 0.002827843803625231 absolute error = 1.558518938904463e-14 relative error = 5.511333182246723e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9248488795383484 y2[1] (numeric) = 0.9248488795381919 absolute error = 1.564304241696846e-13 relative error = 1.69141605326666e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07226 Order of pole (three term test) = -1.029 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.509999999999842 y1[1] (analytic) = 0.003629200675424833 y1[1] (numeric) = 0.003629200675441999 absolute error = 1.716638983739749e-14 relative error = 4.730074573621641e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9148810816956232 y2[1] (numeric) = 0.9148810816954668 absolute error = 1.564304241696846e-13 relative error = 1.709844342608543e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08178 Order of pole (three term test) = -1.068 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.519999999999841 y1[1] (analytic) = 0.004530193796866241 y1[1] (numeric) = 0.004530193796884991 absolute error = 1.875062605183331e-14 relative error = 4.139033977929166e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9049217956737964 y2[1] (numeric) = 0.90492179567364 absolute error = 1.564304241696846e-13 relative error = 1.728662354222642e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09127 Order of pole (three term test) = -1.111 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.529999999999841 y1[1] (analytic) = 0.005530733069372551 y1[1] (numeric) = 0.005530733069392888 absolute error = 2.03370306706141e-14 relative error = 3.67709495568212e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.8949720173931707 y2[1] (numeric) = 0.8949720173930141 absolute error = 1.565414464721471e-13 relative error = 1.749121128145583e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1007 Order of pole (three term test) = -1.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.539999999999841 y1[1] (analytic) = 0.006630718439850294 y1[1] (numeric) = 0.006630718439872219 absolute error = 2.192517001287086e-14 relative error = 3.306605492566486e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.8850327418232825 y2[1] (numeric) = 0.885032741823126 absolute error = 1.565414464721471e-13 relative error = 1.768764465703849e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1101 Order of pole (three term test) = -1.212 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.549999999999841 y1[1] (analytic) = 0.007830039910679073 y1[1] (numeric) = 0.007830039910702588 absolute error = 2.35159114403416e-14 relative error = 3.003293943402409e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.8751049628834063 y2[1] (numeric) = 0.8751049628832498 absolute error = 1.565414464721471e-13 relative error = 1.788830518756911e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1195 Order of pole (three term test) = -1.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.559999999999841 y1[1] (analytic) = 0.009128577550711234 y1[1] (numeric) = 0.009128577550736343 absolute error = 2.510838759128831e-14 relative error = 2.75052574750072e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.8651896733431629 y2[1] (numeric) = 0.8651896733430064 absolute error = 1.564304241696846e-13 relative error = 1.808047749405338e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1288 Order of pole (three term test) = -1.332 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.56999999999984 y1[1] (analytic) = 0.01052620150726489 y1[1] (numeric) = 0.01052620150729159 absolute error = 2.670259846571099e-14 relative error = 2.536774395519753e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.8552878647232437 y2[1] (numeric) = 0.8552878647230873 absolute error = 1.564304241696846e-13 relative error = 1.828979816290305e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1381 Order of pole (three term test) = -1.399 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.57999999999984 y1[1] (analytic) = 0.01202277201910906 y1[1] (numeric) = 0.01202277201913736 absolute error = 2.829854406360965e-14 relative error = 2.353745377408122e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.845400527196259 y2[1] (numeric) = 0.8454005271961027 absolute error = 1.56319401867222e-13 relative error = 1.849057302881627e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1473 Order of pole (three term test) = -1.471 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.58999999999984 y1[1] (analytic) = 0.0136181394304397 y1[1] (numeric) = 0.0136181394304696 absolute error = 2.989448966150832e-14 relative error = 2.195196327237419e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.8355286494877223 y2[1] (numeric) = 0.8355286494875661 absolute error = 1.562083795647595e-13 relative error = 1.869575383926496e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1564 Order of pole (three term test) = -1.547 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.59999999999984 y1[1] (analytic) = 0.01531214420584516 y1[1] (numeric) = 0.01531214420587665 absolute error = 3.149043525940698e-14 relative error = 2.056566006437297e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.8256732187771778 y2[1] (numeric) = 0.8256732187770217 absolute error = 1.56097357262297e-13 relative error = 1.890546450004485e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1655 Order of pole (three term test) = -1.628 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.60999999999984 y1[1] (analytic) = 0.01710461694625955 y1[1] (numeric) = 0.01710461694629263 absolute error = 3.308811558078162e-14 relative error = 1.93445522251332e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.8158352205994838 y2[1] (numeric) = 0.8158352205993278 absolute error = 1.559863349598345e-13 relative error = 1.911983339542686e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1745 Order of pole (three term test) = -1.713 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.619999999999839 y1[1] (analytic) = 0.01899537840590254 y1[1] (numeric) = 0.01899537840593724 absolute error = 3.469100007258419e-14 relative error = 1.826286338249753e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.8060156387462596 y2[1] (numeric) = 0.8060156387461038 absolute error = 1.557642903549095e-13 relative error = 1.932521937132604e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1835 Order of pole (three term test) = -1.803 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.629999999999839 y1[1] (analytic) = 0.02098423951020383 y1[1] (numeric) = 0.02098423951024012 absolute error = 3.62904151174348e-14 relative error = 1.729412929155149e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.7962154551675077 y2[1] (numeric) = 0.7962154551673521 absolute error = 1.555422457499844e-13 relative error = 1.95351954977138e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1924 Order of pole (three term test) = -1.897 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.639999999999839 y1[1] (analytic) = 0.02307100137471033 y1[1] (numeric) = 0.02307100137474822 absolute error = 3.788983016228542e-14 relative error = 1.642314069809687e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.7864356498734192 y2[1] (numeric) = 0.7864356498732638 absolute error = 1.554312234475219e-13 relative error = 1.976401037675992e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2012 Order of pole (three term test) = -1.996 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.649999999999839 y1[1] (analytic) = 0.02525545532497458 y1[1] (numeric) = 0.02525545532501407 absolute error = 3.948924520713604e-14 relative error = 1.563592685184573e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.7766772008363737 y2[1] (numeric) = 0.7766772008362184 absolute error = 1.553202011450594e-13 relative error = 1.999803792074765e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2099 Order of pole (three term test) = -2.099 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.659999999999838 y1[1] (analytic) = 0.02753738291742191 y1[1] (numeric) = 0.027537382917463 absolute error = 4.109212969893861e-14 relative error = 1.492230754903767e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.7669410838931427 y2[1] (numeric) = 0.7669410838929877 absolute error = 1.550981565401344e-13 relative error = 2.022295581726119e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2185 Order of pole (three term test) = -2.206 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.669999999999838 y1[1] (analytic) = 0.02991655596119469 y1[1] (numeric) = 0.02991655596123738 absolute error = 4.269154474378922e-14 relative error = 1.427020703825842e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.7572282726473075 y2[1] (numeric) = 0.7572282726471525 absolute error = 1.549871342376719e-13 relative error = 2.046768984150963e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2271 Order of pole (three term test) = -2.318 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.679999999999838 y1[1] (analytic) = 0.03239273654097116 y1[1] (numeric) = 0.03239273654101545 absolute error = 4.429095978863984e-14 relative error = 1.367311456771165e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.7475397383718984 y2[1] (numeric) = 0.7475397383717436 absolute error = 1.547650896327468e-13 relative error = 2.070325919660364e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2355 Order of pole (three term test) = -2.434 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.689999999999838 y1[1] (analytic) = 0.03496567704075684 y1[1] (numeric) = 0.03496567704080273 absolute error = 4.589384428044241e-14 relative error = 1.312539843771577e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.7378764499122691 y2[1] (numeric) = 0.7378764499121147 absolute error = 1.544320227253593e-13 relative error = 2.092925214562963e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2439 Order of pole (three term test) = -2.554 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.699999999999838 y1[1] (analytic) = 0.03763512016864584 y1[1] (numeric) = 0.03763512016869334 absolute error = 4.749672877224498e-14 relative error = 1.262032074280845e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.7282393735892131 y2[1] (numeric) = 0.7282393735890589 absolute error = 1.542099781204342e-13 relative error = 2.117572651426306e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2522 Order of pole (three term test) = -2.678 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.709999999999837 y1[1] (analytic) = 0.04040079898254992 y1[1] (numeric) = 0.04040079898259902 absolute error = 4.909961326404755e-14 relative error = 1.215312926985797e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.7186294731023318 y2[1] (numeric) = 0.7186294731021778 absolute error = 1.539879335155092e-13 relative error = 2.142800139420131e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2603 Order of pole (three term test) = -2.807 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.719999999999837 y1[1] (analytic) = 0.0432624369168924 y1[1] (numeric) = 0.0432624369169431 absolute error = 5.069555886194621e-14 relative error = 1.171814684395447e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.7090477094336656 y2[1] (numeric) = 0.7090477094335119 absolute error = 1.536548666081217e-13 relative error = 2.167059628904939e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2684 Order of pole (three term test) = -2.939 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.729999999999837 y1[1] (analytic) = 0.04621974781026455 y1[1] (numeric) = 0.04621974781031684 absolute error = 5.229150445984487e-14 relative error = 1.131367152293979e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.6994950407515965 y2[1] (numeric) = 0.6994950407514432 absolute error = 1.533217997007341e-13 relative error = 2.191892590632126e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2763 Order of pole (three term test) = -3.076 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.739999999999837 y1[1] (analytic) = 0.04927243593404144 y1[1] (numeric) = 0.04927243593409533 absolute error = 5.388745005774354e-14 relative error = 1.093663202076715e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.6899724223150323 y2[1] (numeric) = 0.6899724223148793 absolute error = 1.529887327933466e-13 relative error = 2.217316632453665e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2842 Order of pole (three term test) = -3.216 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.749999999999837 y1[1] (analytic) = 0.05242019602195459 y1[1] (numeric) = 0.05242019602201007 absolute error = 5.54833956556422e-14 relative error = 1.058435486055884e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.6804808063778812 y2[1] (numeric) = 0.6804808063777286 absolute error = 1.52655665885959e-13 relative error = 2.243350061532625e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2919 Order of pole (three term test) = -3.361 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.759999999999836 y1[1] (analytic) = 0.05566271330061833 y1[1] (numeric) = 0.05566271330067541 absolute error = 5.707934125354086e-14 relative error = 1.02545021377725e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.6710211420938272 y2[1] (numeric) = 0.6710211420936749 absolute error = 1.523225989785715e-13 relative error = 2.270011918004106e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2995 Order of pole (three term test) = -3.509 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.769999999999836 y1[1] (analytic) = 0.0589996635210069 y1[1] (numeric) = 0.05899966352106557 absolute error = 5.866834795753562e-14 relative error = 9.943844499493914e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.6615943754214156 y2[1] (numeric) = 0.6615943754212638 absolute error = 1.518785097687214e-13 relative error = 2.29564390827808e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.307 Order of pole (three term test) = -3.661 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.779999999999836 y1[1] (analytic) = 0.06243071299087902 y1[1] (numeric) = 0.06243071299093928 absolute error = 6.025735466153037e-14 relative error = 9.65187674059302e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.6522014490294582 y2[1] (numeric) = 0.6522014490293068 absolute error = 1.514344205588714e-13 relative error = 2.321896413818477e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3144 Order of pole (three term test) = -3.817 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.789999999999836 y1[1] (analytic) = 0.06595551860814693 y1[1] (numeric) = 0.06595551860820877 absolute error = 6.183942247162122e-14 relative error = 9.375928470674283e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.6428433022027668 y2[1] (numeric) = 0.6428433022026157 absolute error = 1.511013536514838e-13 relative error = 2.35051610763805e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3216 Order of pole (three term test) = -3.976 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.799999999999836 y1[1] (analytic) = 0.0695737278951862 y1[1] (numeric) = 0.06957372789524963 absolute error = 6.342149028171207e-14 relative error = 9.115724024053653e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.6335208707482253 y2[1] (numeric) = 0.6335208707480747 absolute error = 1.505462421391712e-13 relative error = 2.376342265746783e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3287 Order of pole (three term test) = -4.139 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.809999999999835 y1[1] (analytic) = 0.07328497903408331 y1[1] (numeric) = 0.07328497903414832 absolute error = 6.501743587961073e-14 relative error = 8.871863884872299e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.6242350869012108 y2[1] (numeric) = 0.6242350869010607 absolute error = 1.501021529293212e-13 relative error = 2.404577315165813e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3357 Order of pole (three term test) = -4.306 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.819999999999835 y1[1] (analytic) = 0.07708890090281706 y1[1] (numeric) = 0.07708890090288366 absolute error = 6.659950368970158e-14 relative error = 8.639311614218103e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.6149868792323698 y2[1] (numeric) = 0.6149868792322202 absolute error = 1.496580637194711e-13 relative error = 2.433516368776439e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3426 Order of pole (three term test) = -4.476 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.829999999999835 y1[1] (analytic) = 0.08098511311237051 y1[1] (numeric) = 0.08098511311243868 absolute error = 6.816769371198461e-14 relative error = 8.417311662873008e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.6057771725547624 y2[1] (numeric) = 0.6057771725546133 absolute error = 1.491029522071585e-13 relative error = 2.461349799272596e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3493 Order of pole (three term test) = -4.649 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.839999999999835 y1[1] (analytic) = 0.08497322604476953 y1[1] (numeric) = 0.08497322604483928 absolute error = 6.974976152207546e-14 relative error = 8.208439854375619e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5966068878313816 y2[1] (numeric) = 0.5966068878312329 absolute error = 1.486588629973085e-13 relative error = 2.491738966301102e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3559 Order of pole (three term test) = -4.826 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.849999999999834 y1[1] (analytic) = 0.08905284089204431 y1[1] (numeric) = 0.08905284089211563 absolute error = 7.131795154435849e-14 relative error = 8.008498193877362e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5874769420830578 y2[1] (numeric) = 0.5874769420829097 absolute error = 1.481037514849959e-13 relative error = 2.521013862430994e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3623 Order of pole (three term test) = -5.006 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.859999999999834 y1[1] (analytic) = 0.09322354969610977 y1[1] (numeric) = 0.09322354969618266 absolute error = 7.288614156664153e-14 relative error = 7.818425902493078e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5783882482967576 y2[1] (numeric) = 0.5783882482966101 absolute error = 1.475486399726833e-13 relative error = 2.551031083483901e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3686 Order of pole (three term test) = -5.189 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.869999999999834 y1[1] (analytic) = 0.09748493538956109 y1[1] (numeric) = 0.09748493538963554 absolute error = 7.445433158892456e-14 relative error = 7.637521765942238e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5693417153342859 y2[1] (numeric) = 0.5693417153341388 absolute error = 1.471045507628332e-13 relative error = 2.583765545380099e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3747 Order of pole (three term test) = -5.376 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.879999999999834 y1[1] (analytic) = 0.1018365718373801 y1[1] (numeric) = 0.1018365718374561 absolute error = 7.602252161120759e-14 relative error = 7.465149330891245e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5603382478414 y2[1] (numeric) = 0.5603382478412534 absolute error = 1.465494392505207e-13 relative error = 2.615374549481058e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3807 Order of pole (three term test) = -5.565 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.889999999999834 y1[1] (analytic) = 0.1062780238795483 y1[1] (numeric) = 0.1062780238796259 absolute error = 7.757683384568281e-14 relative error = 7.299423814428995e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5513787461573463 y2[1] (numeric) = 0.5513787461572004 absolute error = 1.458833054357456e-13 relative error = 2.645791236104611e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3865 Order of pole (three term test) = -5.757 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.899999999999833 y1[1] (analytic) = 0.1108088473745627 y1[1] (numeric) = 0.1108088473746418 absolute error = 7.911726829235022e-14 relative error = 7.139977552957778e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5424641062248271 y2[1] (numeric) = 0.5424641062246818 absolute error = 1.45328193923433e-13 relative error = 2.679037972388923e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3922 Order of pole (three term test) = -5.953 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.909999999999833 y1[1] (analytic) = 0.1154285892438495 y1[1] (numeric) = 0.1154285892439302 absolute error = 8.067158052682544e-14 relative error = 6.98887347192662e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5335952195004068 y2[1] (numeric) = 0.5335952195002621 absolute error = 1.446620601086579e-13 relative error = 2.711082386459566e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3977 Order of pole (three term test) = -6.151 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.919999999999833 y1[1] (analytic) = 0.1201367875170715 y1[1] (numeric) = 0.1201367875171538 absolute error = 8.222589276130066e-14 relative error = 6.844355876389343e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5247729728653672 y2[1] (numeric) = 0.5247729728652231 absolute error = 1.441069485963453e-13 relative error = 2.746081754353546e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4031 Order of pole (three term test) = -6.351 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.929999999999833 y1[1] (analytic) = 0.124932971378325 y1[1] (numeric) = 0.1249329713784087 absolute error = 8.376632720796806e-14 relative error = 6.704901539106509e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.5159982485370197 y2[1] (numeric) = 0.5159982485368763 absolute error = 1.434408147815702e-13 relative error = 2.779870187316716e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4083 Order of pole (three term test) = -6.555 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.939999999999833 y1[1] (analytic) = 0.1298166612132205 y1[1] (numeric) = 0.1298166612133058 absolute error = 8.529288386682765e-14 relative error = 6.570257089476082e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.507271923980485 y2[1] (numeric) = 0.5072719239803424 absolute error = 1.426636586643326e-13 relative error = 2.812370484549445e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4133 Order of pole (three term test) = -6.761 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.949999999999832 y1[1] (analytic) = 0.1347873686568443 y1[1] (numeric) = 0.1347873686569311 absolute error = 8.681944052568724e-14 relative error = 6.441214884661872e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.4985948718209471 y2[1] (numeric) = 0.498594871820805 absolute error = 1.420530360007888e-13 relative error = 2.849067329593437e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4182 Order of pole (three term test) = -6.969 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.959999999999832 y1[1] (analytic) = 0.1398445966425942 y1[1] (numeric) = 0.1398445966426826 absolute error = 8.834599718454683e-14 relative error = 6.317440881204428e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.4899679597563908 y2[1] (numeric) = 0.4899679597562494 absolute error = 1.413869021860137e-13 relative error = 2.885635670061169e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4229 Order of pole (three term test) = -7.18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.969999999999832 y1[1] (analytic) = 0.1449878394518862 y1[1] (numeric) = 0.144987839451976 absolute error = 8.984479826779079e-14 relative error = 6.196712676555576e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.4813920504708336 y2[1] (numeric) = 0.4813920504706929 absolute error = 1.406652572200073e-13 relative error = 2.922051934227566e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4274 Order of pole (three term test) = -7.393 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.979999999999832 y1[1] (analytic) = 0.1502165827647252 y1[1] (numeric) = 0.1502165827648166 absolute error = 9.137135492665038e-14 relative error = 6.082641027040244e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.4728680015480574 y2[1] (numeric) = 0.4728680015479174 absolute error = 1.39943612254001e-13 relative error = 2.95946462428963e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4318 Order of pole (three term test) = -7.608 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.989999999999831 y1[1] (analytic) = 0.1555303037111372 y1[1] (numeric) = 0.1555303037112301 absolute error = 9.287015600989434e-14 relative error = 5.971193638403734e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.4643966653858512 y2[1] (numeric) = 0.4643966653857119 absolute error = 1.392219672879946e-13 relative error = 2.99791057225443e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.436 Order of pole (three term test) = -7.826 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.999999999999831 y1[1] (analytic) = 0.1609284709234557 y1[1] (numeric) = 0.1609284709235501 absolute error = 9.439671266875393e-14 relative error = 5.865755893104392e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.4559788891107718 y2[1] (numeric) = 0.4559788891106333 absolute error = 1.38444811170757e-13 relative error = 3.036210984257308e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.44 Order of pole (three term test) = -8.045 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y1 , x , 1 ) = m1 * y2 + 1.0; diff ( y2 , x , 1 ) = y1 - 1.0; Iterations = 991 Total Elapsed Time = 1 Seconds Elapsed Time(since restart) = 1 Seconds Time to Timeout = 2 Minutes 59 Seconds Percent Done = 100.2 %