##############ECHO OF PROBLEM################# ##############temp/mtest4postode.ode################# diff ( y2 , x , 3 ) = m1 * cos ( x ) ; diff ( y1 , x , 1 ) = m1 * y2 ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=5.0; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); array_y2_init[2 + 1] = exact_soln_y2pp(x_start); glob_max_iter=20; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=1000000000; glob_max_minutes=30.0; glob_subiter_method=3; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y2 (double x) { return(sin(x)); } double exact_soln_y2p (double x) { return( cos(x)); } double exact_soln_y2pp (double x) { return( -sin(x)); } double exact_soln_y1 (double x) { return( cos(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 4.9 estimated_steps = 4900000.000000001 step_error = 2.040816326530612e-17 est_needed_step_err = 2.040816326530612e-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 = 7.456680367024187e-160 estimated_step_error = 7.456680367024187e-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 = 3.358190142481625e-144 estimated_step_error = 3.358190142481625e-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 = 1.014950270158056e-120 estimated_step_error = 1.014950270158056e-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 = 4.570923134360029e-105 estimated_step_error = 4.570923134360029e-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 = 3.067488750234037e-97 estimated_step_error = 3.067488750234037e-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 = 2.058549011618172e-89 estimated_step_error = 2.058549011618172e-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 = 1.381458319740679e-81 estimated_step_error = 1.381458319740679e-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 = 9.270668118451431e-74 estimated_step_error = 9.270668118451431e-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 = 6.221249002141342e-66 estimated_step_error = 6.221249002141342e-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 = 4.174750875751545e-58 estimated_step_error = 4.174750875751545e-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 = 2.801274758009003e-50 estimated_step_error = 2.801274758009003e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (analytic) = 0.09983341664682815 y2[1] (numeric) = 0.09983341664682815 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9950041652780258 y1[1] (numeric) = 0.9950041652780258 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 Radius of convergence (three term test) for eq 1 = 0.09933 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09933 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.11 y2[1] (analytic) = 0.1097783008371748 y2[1] (numeric) = 0.1097783008371748 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9939560979566968 y1[1] (numeric) = 0.9939560979566969 absolute error = 1.110223024625157e-16 relative error = 1.116973905494893e-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 = 0.1091 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1091 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.12 y2[1] (analytic) = 0.1197122072889194 y2[1] (numeric) = 0.1197122072889194 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9928086358538663 y1[1] (numeric) = 0.9928086358538664 absolute error = 1.110223024625157e-16 relative error = 1.118264874549875e-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 = 0.1189 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1189 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.13 y2[1] (analytic) = 0.1296341426196949 y2[1] (numeric) = 0.1296341426196949 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9915618937147881 y1[1] (numeric) = 0.9915618937147882 absolute error = 1.110223024625157e-16 relative error = 1.119670926910892e-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 = 0.1285 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1285 Order of pole (three term test) = 22.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.14 y2[1] (analytic) = 0.1395431146442365 y2[1] (numeric) = 0.1395431146442365 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9902159962126371 y1[1] (numeric) = 0.9902159962126373 absolute error = 2.220446049250313e-16 relative error = 2.242385558042933e-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 = 0.1382 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1382 Order of pole (three term test) = 22.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.15 y2[1] (analytic) = 0.1494381324735992 y2[1] (numeric) = 0.1494381324735992 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9887710779360422 y1[1] (numeric) = 0.9887710779360425 absolute error = 2.220446049250313e-16 relative error = 2.245662417518588e-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 = 0.1478 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1478 Order of pole (three term test) = 22.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.16 y2[1] (analytic) = 0.159318206614246 y2[1] (numeric) = 0.159318206614246 absolute error = 2.775557561562891e-17 relative error = 1.742147128409055e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9872272833756269 y1[1] (numeric) = 0.9872272833756272 absolute error = 2.220446049250313e-16 relative error = 2.249174112832397e-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 = 0.1573 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1573 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.17 y2[1] (analytic) = 0.1691823490669961 y2[1] (numeric) = 0.169182349066996 absolute error = 2.775557561562891e-17 relative error = 1.640571594418383e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9855847669095607 y1[1] (numeric) = 0.9855847669095609 absolute error = 2.220446049250313e-16 relative error = 2.252922451523711e-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 = 0.1667 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1667 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.18 y2[1] (analytic) = 0.1790295734258242 y2[1] (numeric) = 0.1790295734258242 absolute error = 2.775557561562891e-17 relative error = 1.550334678484203e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9838436927881214 y1[1] (numeric) = 0.9838436927881216 absolute error = 1.110223024625157e-16 relative error = 1.128454685193832e-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 = 0.1761 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1761 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y2[1] (analytic) = 0.1888588949765006 y2[1] (numeric) = 0.1888588949765006 absolute error = 2.775557561562891e-17 relative error = 1.469646193740702e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9820042351172703 y1[1] (numeric) = 0.9820042351172704 absolute error = 1.110223024625157e-16 relative error = 1.130568468976689e-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 = 0.1855 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1855 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y2[1] (analytic) = 0.1986693307950613 y2[1] (numeric) = 0.1986693307950612 absolute error = 2.775557561562891e-17 relative error = 1.397073997508975e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9800665778412416 y1[1] (numeric) = 0.9800665778412417 absolute error = 1.110223024625157e-16 relative error = 1.132803678573149e-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 = 0.1947 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1947 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y2[1] (analytic) = 0.2084598998460996 y2[1] (numeric) = 0.2084598998460996 absolute error = 2.775557561562891e-17 relative error = 1.331458742718389e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9780309147241483 y1[1] (numeric) = 0.9780309147241484 absolute error = 1.110223024625157e-16 relative error = 1.135161484070565e-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 = 0.2039 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2039 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y2[1] (analytic) = 0.2182296230808694 y2[1] (numeric) = 0.2182296230808694 absolute error = 5.551115123125783e-17 relative error = 2.543703757884742e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9758974493306055 y1[1] (numeric) = 0.9758974493306056 absolute error = 1.110223024625157e-16 relative error = 1.137643125706178e-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 = 0.213 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.213 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y2[1] (analytic) = 0.2279775235351885 y2[1] (numeric) = 0.2279775235351884 absolute error = 5.551115123125783e-17 relative error = 2.43493965415804e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9736663950053748 y1[1] (numeric) = 0.973666395005375 absolute error = 2.220446049250313e-16 relative error = 2.280499830989911e-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 = 0.222 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.222 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y2[1] (analytic) = 0.2377026264271347 y2[1] (numeric) = 0.2377026264271346 absolute error = 5.551115123125783e-17 relative error = 2.335319220727004e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9713379748520296 y1[1] (numeric) = 0.9713379748520298 absolute error = 2.220446049250313e-16 relative error = 2.285966477928106e-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 = 0.2309 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2309 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y2[1] (analytic) = 0.247403959254523 y2[1] (numeric) = 0.247403959254523 absolute error = 8.326672684688674e-17 relative error = 3.365618201818023e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9689124217106447 y1[1] (numeric) = 0.968912421710645 absolute error = 2.220446049250313e-16 relative error = 2.291689113996544e-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 = 0.2397 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2397 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y2[1] (analytic) = 0.2570805518921552 y2[1] (numeric) = 0.2570805518921551 absolute error = 1.110223024625157e-16 relative error = 4.31858036889112e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9663899781345132 y1[1] (numeric) = 0.9663899781345134 absolute error = 2.220446049250313e-16 relative error = 2.297670815602401e-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 = 0.2484 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2484 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y2[1] (analytic) = 0.2667314366888313 y2[1] (numeric) = 0.2667314366888311 absolute error = 1.110223024625157e-16 relative error = 4.162325365196237e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9637708963658905 y1[1] (numeric) = 0.9637708963658908 absolute error = 2.220446049250313e-16 relative error = 2.303914817954134e-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 = 0.2571 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2571 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y2[1] (analytic) = 0.2763556485641139 y2[1] (numeric) = 0.2763556485641138 absolute error = 1.110223024625157e-16 relative error = 4.017370480370649e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9610554383107709 y1[1] (numeric) = 0.9610554383107712 absolute error = 3.33066907387547e-16 relative error = 3.465636779216113e-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 = 0.2656 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2656 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y2[1] (analytic) = 0.2859522251048357 y2[1] (numeric) = 0.2859522251048356 absolute error = 1.110223024625157e-16 relative error = 3.882547247947195e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9582438755126971 y1[1] (numeric) = 0.9582438755126974 absolute error = 3.33066907387547e-16 relative error = 3.475805229742204e-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 = 0.274 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.274 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y2[1] (analytic) = 0.2955202066613397 y2[1] (numeric) = 0.2955202066613397 absolute error = 5.551115123125783e-17 relative error = 1.878421508241313e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.955336489125606 y1[1] (numeric) = 0.9553364891256062 absolute error = 2.220446049250313e-16 relative error = 2.32425545818168e-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 = 0.2823 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 Radius of convergence (three term test) for eq 2 = 0.2823 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y2[1] (analytic) = 0.3050586364434437 y2[1] (numeric) = 0.3050586364434436 absolute error = 5.551115123125783e-17 relative error = 1.819687909132489e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9523335698857134 y1[1] (numeric) = 0.9523335698857136 absolute error = 2.220446049250313e-16 relative error = 2.3315843518115e-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 = 0.2905 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 Radius of convergence (three term test) for eq 2 = 0.2905 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y2[1] (analytic) = 0.3145665606161179 y2[1] (numeric) = 0.3145665606161179 absolute error = 5.551115123125783e-17 relative error = 1.764686975072376e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9492354180824408 y1[1] (numeric) = 0.9492354180824411 absolute error = 2.220446049250313e-16 relative error = 2.339194268304755e-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 = 0.2986 Order of pole (three term test) = 22.9 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2986 Order of pole (three term test) = 22.1 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y2[1] (analytic) = 0.3240430283948685 y2[1] (numeric) = 0.3240430283948685 absolute error = 5.551115123125783e-17 relative error = 1.713079633474284e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9460423435283869 y1[1] (numeric) = 0.9460423435283871 absolute error = 2.220446049250313e-16 relative error = 2.347089498096748e-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 = 0.3066 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 Radius of convergence (three term test) for eq 2 = 0.3066 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y2[1] (analytic) = 0.3334870921408146 y2[1] (numeric) = 0.3334870921408145 absolute error = 5.551115123125783e-17 relative error = 1.664566711560108e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9427546655283462 y1[1] (numeric) = 0.9427546655283464 absolute error = 2.220446049250313e-16 relative error = 2.355274527340485e-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 = 0.3144 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 Radius of convergence (three term test) for eq 2 = 0.3144 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y2[1] (analytic) = 0.3428978074554516 y2[1] (numeric) = 0.3428978074554515 absolute error = 1.110223024625157e-16 relative error = 3.237766472943674e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9393727128473789 y1[1] (numeric) = 0.9393727128473791 absolute error = 2.220446049250313e-16 relative error = 2.363754044462086e-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 = 0.3221 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3221 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y2[1] (analytic) = 0.3522742332750902 y2[1] (numeric) = 0.3522742332750901 absolute error = 5.551115123125783e-17 relative error = 1.575793685367538e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9358968236779348 y1[1] (numeric) = 0.935896823677935 absolute error = 2.220446049250313e-16 relative error = 2.372532947087363e-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 = 0.3297 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3297 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y2[1] (analytic) = 0.3616154319649622 y2[1] (numeric) = 0.3616154319649621 absolute error = 1.110223024625157e-16 relative error = 3.070176011550107e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9323273456060344 y1[1] (numeric) = 0.9323273456060346 absolute error = 2.220446049250313e-16 relative error = 2.381616349359539e-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 = 0.3371 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 Radius of convergence (three term test) for eq 2 = 0.3371 Order of pole (three term test) = 22.13 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y2[1] (analytic) = 0.3709204694129829 y2[1] (numeric) = 0.3709204694129828 absolute error = 1.110223024625157e-16 relative error = 2.993156528627796e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9286646355765101 y1[1] (numeric) = 0.9286646355765104 absolute error = 2.220446049250313e-16 relative error = 2.391009589669442e-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 = 0.3445 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3445 Order of pole (three term test) = 22.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y2[1] (analytic) = 0.3801884151231616 y2[1] (numeric) = 0.3801884151231615 absolute error = 1.110223024625157e-16 relative error = 2.920191622002741e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.924909059857313 y1[1] (numeric) = 0.9249090598573132 absolute error = 2.220446049250313e-16 relative error = 2.400718238821084e-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 = 0.3516 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3516 Order of pole (three term test) = 22.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y2[1] (analytic) = 0.3894183423086507 y2[1] (numeric) = 0.3894183423086506 absolute error = 1.110223024625157e-16 relative error = 2.850977737831364e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.921060994002885 y1[1] (numeric) = 0.9210609940028852 absolute error = 2.220446049250313e-16 relative error = 2.410748108657132e-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 = 0.3587 Order of pole (three term test) = 22.85 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3587 Order of pole (three term test) = 22.15 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y2[1] (analytic) = 0.3986093279844231 y2[1] (numeric) = 0.398609327984423 absolute error = 1.110223024625157e-16 relative error = 2.785240953188486e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.917120822816605 y1[1] (numeric) = 0.9171208228166052 absolute error = 2.220446049250313e-16 relative error = 2.421105261170514e-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 = 0.3656 Order of pole (three term test) = 22.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3656 Order of pole (three term test) = 22.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y2[1] (analytic) = 0.4077604530595704 y2[1] (numeric) = 0.4077604530595703 absolute error = 1.110223024625157e-16 relative error = 2.72273344875591e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9130889403123081 y1[1] (numeric) = 0.9130889403123084 absolute error = 2.220446049250313e-16 relative error = 2.431796018130329e-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 = 0.3723 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3723 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y2[1] (analytic) = 0.416870802429211 y2[1] (numeric) = 0.4168708024292109 absolute error = 1.110223024625157e-16 relative error = 2.663230473699784e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.908965749674885 y1[1] (numeric) = 0.9089657496748852 absolute error = 2.220446049250313e-16 relative error = 2.442826971252231e-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 = 0.3789 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3789 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y2[1] (analytic) = 0.4259394650659998 y2[1] (numeric) = 0.4259394650659997 absolute error = 1.110223024625157e-16 relative error = 2.606527724434096e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9047516632199633 y1[1] (numeric) = 0.9047516632199635 absolute error = 2.220446049250313e-16 relative error = 2.454204992945648e-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 = 0.3854 Order of pole (three term test) = 22.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3854 Order of pole (three term test) = 22.18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y2[1] (analytic) = 0.4349655341112305 y2[1] (numeric) = 0.4349655341112303 absolute error = 1.110223024625157e-16 relative error = 2.552439072888124e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.9004471023526768 y1[1] (numeric) = 0.900447102352677 absolute error = 2.220446049250313e-16 relative error = 2.465937247672584e-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 = 0.3917 Order of pole (three term test) = 22.81 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3917 Order of pole (three term test) = 22.19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y2[1] (analytic) = 0.44394810696552 y2[1] (numeric) = 0.4439481069655199 absolute error = 1.110223024625157e-16 relative error = 2.500794591092566e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8960524975255251 y1[1] (numeric) = 0.8960524975255253 absolute error = 2.220446049250313e-16 relative error = 2.478031203955281e-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 = 0.3978 Order of pole (three term test) = 22.8 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3978 Order of pole (three term test) = 22.2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y2[1] (analytic) = 0.4528862853790686 y2[1] (numeric) = 0.4528862853790684 absolute error = 1.110223024625157e-16 relative error = 2.451438827951907e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8915682881953289 y1[1] (numeric) = 0.891568288195329 absolute error = 1.110223024625157e-16 relative error = 1.245247323536393e-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 = 0.4038 Order of pole (three term test) = 22.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4038 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y2[1] (analytic) = 0.4617791755414832 y2[1] (numeric) = 0.4617791755414831 absolute error = 1.110223024625157e-16 relative error = 2.404229301425962e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.886994922779284 y1[1] (numeric) = 0.8869949227792843 absolute error = 2.220446049250313e-16 relative error = 2.503335692489459e-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 = 0.4096 Order of pole (three term test) = 22.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4096 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y2[1] (analytic) = 0.4706258881711583 y2[1] (numeric) = 0.4706258881711582 absolute error = 1.110223024625157e-16 relative error = 2.359035175348e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8823328586101213 y1[1] (numeric) = 0.8823328586101216 absolute error = 2.220446049250313e-16 relative error = 2.51656280006168e-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 = 0.4152 Order of pole (three term test) = 22.78 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4152 Order of pole (three term test) = 22.22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y2[1] (analytic) = 0.4794255386042033 y2[1] (numeric) = 0.4794255386042032 absolute error = 1.110223024625157e-16 relative error = 2.315736095030426e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8775825618903725 y1[1] (numeric) = 0.8775825618903728 absolute error = 2.220446049250313e-16 relative error = 2.530184789072519e-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 = 0.4207 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 Radius of convergence (three term test) for eq 2 = 0.4207 Order of pole (three term test) = 22.23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y2[1] (analytic) = 0.4881772468829078 y2[1] (numeric) = 0.4881772468829076 absolute error = 1.665334536937735e-16 relative error = 3.41133173979568e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8727445076457511 y1[1] (numeric) = 0.8727445076457513 absolute error = 2.220446049250313e-16 relative error = 2.544210854147932e-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 = 0.4261 Order of pole (three term test) = 22.76 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4261 Order of pole (three term test) = 22.24 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y2[1] (analytic) = 0.496880137843737 y2[1] (numeric) = 0.4968801378437369 absolute error = 1.665334536937735e-16 relative error = 3.351582021701707e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8678191796776498 y1[1] (numeric) = 0.8678191796776499 absolute error = 1.110223024625157e-16 relative error = 1.279325291056079e-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 = 0.4312 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 Radius of convergence (three term test) for eq 2 = 0.4312 Order of pole (three term test) = 22.25 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y2[1] (analytic) = 0.5055333412048473 y2[1] (numeric) = 0.5055333412048471 absolute error = 2.220446049250313e-16 relative error = 4.392284085473535e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8628070705147608 y1[1] (numeric) = 0.862807070514761 absolute error = 2.220446049250313e-16 relative error = 2.573513969844463e-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 = 0.4362 Order of pole (three term test) = 22.74 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4362 Order of pole (three term test) = 22.26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y2[1] (analytic) = 0.5141359916531134 y2[1] (numeric) = 0.5141359916531132 absolute error = 2.220446049250313e-16 relative error = 4.318791302882456e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8577086813638239 y1[1] (numeric) = 0.8577086813638242 absolute error = 2.220446049250313e-16 relative error = 2.588811443204271e-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 = 0.441 Order of pole (three term test) = 22.74 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.441 Order of pole (three term test) = 22.26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y2[1] (analytic) = 0.5226872289306594 y2[1] (numeric) = 0.5226872289306592 absolute error = 2.220446049250313e-16 relative error = 4.248135263976157e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8525245220595056 y1[1] (numeric) = 0.8525245220595058 absolute error = 2.220446049250313e-16 relative error = 2.604553877096954e-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 = 0.4456 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 Radius of convergence (three term test) for eq 2 = 0.4456 Order of pole (three term test) = 22.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y2[1] (analytic) = 0.5311861979208837 y2[1] (numeric) = 0.5311861979208835 absolute error = 2.220446049250313e-16 relative error = 4.180165181138672e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8472551110134159 y1[1] (numeric) = 0.8472551110134162 absolute error = 3.33066907387547e-16 relative error = 3.931128925137555e-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 = 0.4501 Order of pole (three term test) = 22.72 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4501 Order of pole (three term test) = 22.28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y2[1] (analytic) = 0.5396320487339695 y2[1] (numeric) = 0.5396320487339693 absolute error = 2.220446049250313e-16 relative error = 4.114740876602308e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8419009751622685 y1[1] (numeric) = 0.8419009751622688 absolute error = 3.33066907387547e-16 relative error = 3.956129250513713e-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 = 0.4543 Order of pole (three term test) = 22.71 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4543 Order of pole (three term test) = 22.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y2[1] (analytic) = 0.5480239367918739 y2[1] (numeric) = 0.5480239367918737 absolute error = 2.220446049250313e-16 relative error = 4.051731868226012e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8364626499151867 y1[1] (numeric) = 0.836462649915187 absolute error = 3.33066907387547e-16 relative error = 3.981850324354809e-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 = 0.4584 Order of pole (three term test) = 22.7 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4584 Order of pole (three term test) = 22.3 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y2[1] (analytic) = 0.5563610229127841 y2[1] (numeric) = 0.5563610229127839 absolute error = 2.220446049250313e-16 relative error = 3.991016548257359e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8309406791001632 y1[1] (numeric) = 0.8309406791001636 absolute error = 3.33066907387547e-16 relative error = 4.00831149280391e-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 = 0.4623 Order of pole (three term test) = 22.69 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4623 Order of pole (three term test) = 22.31 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y2[1] (analytic) = 0.5646424733950357 y2[1] (numeric) = 0.5646424733950355 absolute error = 2.220446049250313e-16 relative error = 3.932481444230361e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8253356149096781 y1[1] (numeric) = 0.8253356149096783 absolute error = 2.220446049250313e-16 relative error = 2.69035530411869e-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 = 0.466 Order of pole (three term test) = 22.68 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.466 Order of pole (three term test) = 22.32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y2[1] (analytic) = 0.5728674601004816 y2[1] (numeric) = 0.5728674601004814 absolute error = 2.220446049250313e-16 relative error = 3.876020552573966e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8196480178454792 y1[1] (numeric) = 0.8196480178454796 absolute error = 3.33066907387547e-16 relative error = 4.063535812153175e-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 = 0.4695 Order of pole (three term test) = 22.67 NO COMPLEX POLE (six term test) for Equation 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) = 22.33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y2[1] (analytic) = 0.5810351605373054 y2[1] (numeric) = 0.5810351605373052 absolute error = 2.220446049250313e-16 relative error = 3.82153473672227e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8138784566625337 y1[1] (numeric) = 0.813878456662534 absolute error = 3.33066907387547e-16 relative error = 4.092342101710769e-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 = 0.4729 Order of pole (three term test) = 22.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4729 Order of pole (three term test) = 22.34 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y2[1] (analytic) = 0.5891447579422698 y2[1] (numeric) = 0.5891447579422696 absolute error = 2.220446049250313e-16 relative error = 3.768931182559879e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8080275083121516 y1[1] (numeric) = 0.808027508312152 absolute error = 3.33066907387547e-16 relative error = 4.121974858049991e-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 = 0.476 Order of pole (three term test) = 22.65 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.476 Order of pole (three term test) = 22.35 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y2[1] (analytic) = 0.5971954413623924 y2[1] (numeric) = 0.5971954413623921 absolute error = 3.33066907387547e-16 relative error = 5.577184357397564e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.8020957578842923 y1[1] (numeric) = 0.8020957578842928 absolute error = 4.440892098500626e-16 relative error = 5.536610878250343e-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 = 0.479 Order of pole (three term test) = 22.64 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.479 Order of pole (three term test) = 22.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y2[1] (analytic) = 0.6051864057360399 y2[1] (numeric) = 0.6051864057360397 absolute error = 2.220446049250313e-16 relative error = 3.669028299718269e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.7960837985490555 y1[1] (numeric) = 0.796083798549056 absolute error = 4.440892098500626e-16 relative error = 5.578422907983566e-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 = 0.4818 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 Radius of convergence (three term test) for eq 2 = 0.4818 Order of pole (three term test) = 22.37 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y2[1] (analytic) = 0.6131168519734341 y2[1] (numeric) = 0.6131168519734339 absolute error = 2.220446049250313e-16 relative error = 3.621570736644054e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.7899922314973647 y1[1] (numeric) = 0.7899922314973652 absolute error = 4.440892098500626e-16 relative error = 5.621437681840597e-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 = 0.4844 Order of pole (three term test) = 22.62 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4844 Order of pole (three term test) = 22.38 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y2[1] (analytic) = 0.62098598703656 y2[1] (numeric) = 0.6209859870365598 absolute error = 2.220446049250313e-16 relative error = 3.575678188563675e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.783821665880849 y1[1] (numeric) = 0.7838216658808493 absolute error = 3.33066907387547e-16 relative error = 4.249268958561518e-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 = 0.4867 Order of pole (three term test) = 22.61 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4867 Order of pole (three term test) = 22.39 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y2[1] (analytic) = 0.6287930240184689 y2[1] (numeric) = 0.6287930240184687 absolute error = 2.220446049250313e-16 relative error = 3.531282893470991e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.7775727187509276 y1[1] (numeric) = 0.777572718750928 absolute error = 4.440892098500626e-16 relative error = 5.711224161303343e-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 = 0.4889 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 Radius of convergence (three term test) for eq 2 = 0.4889 Order of pole (three term test) = 22.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y2[1] (analytic) = 0.6365371822219683 y2[1] (numeric) = 0.6365371822219681 absolute error = 2.220446049250313e-16 relative error = 3.488321045911842e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.7712460149971063 y1[1] (numeric) = 0.7712460149971067 absolute error = 3.33066907387547e-16 relative error = 4.318555958941281e-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 = 0.4909 Order of pole (three term test) = 22.59 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4909 Order of pole (three term test) = 22.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y2[1] (analytic) = 0.6442176872376915 y2[1] (numeric) = 0.6442176872376912 absolute error = 2.220446049250313e-16 relative error = 3.446732514860391e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.7648421872844881 y1[1] (numeric) = 0.7648421872844885 absolute error = 4.440892098500626e-16 relative error = 5.806285495662398e-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 = 0.4927 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 Radius of convergence (three term test) for eq 2 = 0.4927 Order of pole (three term test) = 22.42 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y2[1] (analytic) = 0.6518337710215371 y2[1] (numeric) = 0.6518337710215368 absolute error = 2.220446049250313e-16 relative error = 3.406460585450317e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.7583618759905079 y1[1] (numeric) = 0.7583618759905082 absolute error = 3.33066907387547e-16 relative error = 4.391925780189349e-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 = 0.4943 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 Radius of convergence (three term test) for eq 2 = 0.4943 Order of pole (three term test) = 22.42 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y2[1] (analytic) = 0.6593846719714735 y2[1] (numeric) = 0.6593846719714733 absolute error = 2.220446049250313e-16 relative error = 3.367451722241997e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.7518057291408946 y1[1] (numeric) = 0.7518057291408951 absolute error = 4.440892098500626e-16 relative error = 5.90696761991337e-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 = 0.4957 Order of pole (three term test) = 22.57 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4957 Order of pole (three term test) = 22.43 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y2[1] (analytic) = 0.6668696350036982 y2[1] (numeric) = 0.666869635003698 absolute error = 2.220446049250313e-16 relative error = 3.329655351960956e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.74517440234487 y1[1] (numeric) = 0.7451744023448704 absolute error = 4.440892098500626e-16 relative error = 5.95953388163401e-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 = 0.4969 Order of pole (three term test) = 22.56 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4969 Order of pole (three term test) = 22.44 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y2[1] (analytic) = 0.6742879116281455 y2[1] (numeric) = 0.6742879116281452 absolute error = 3.33066907387547e-16 relative error = 4.939535495799097e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.7384685587295875 y1[1] (numeric) = 0.7384685587295879 absolute error = 4.440892098500626e-16 relative error = 6.013650880601394e-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 = 0.4979 Order of pole (three term test) = 22.55 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4979 Order of pole (three term test) = 22.45 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y2[1] (analytic) = 0.6816387600233346 y2[1] (numeric) = 0.6816387600233342 absolute error = 3.33066907387547e-16 relative error = 4.886267139153664e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.7316888688738205 y1[1] (numeric) = 0.7316888688738209 absolute error = 4.440892098500626e-16 relative error = 6.069372225568812e-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 = 0.4987 Order of pole (three term test) = 22.54 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4987 Order of pole (three term test) = 22.46 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y2[1] (analytic) = 0.6889214451105518 y2[1] (numeric) = 0.6889214451105514 absolute error = 3.33066907387547e-16 relative error = 4.834613724850726e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.7248360107409048 y1[1] (numeric) = 0.7248360107409052 absolute error = 4.440892098500626e-16 relative error = 6.126754235018325e-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 = 0.4994 Order of pole (three term test) = 22.53 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4994 Order of pole (three term test) = 22.47 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y2[1] (analytic) = 0.6961352386273572 y2[1] (numeric) = 0.6961352386273568 absolute error = 3.33066907387547e-16 relative error = 4.784514400453135e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.717910669610943 y1[1] (numeric) = 0.7179106696109434 absolute error = 4.440892098500626e-16 relative error = 6.185856105060086e-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 = 0.4998 Order of pole (three term test) = 22.52 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4998 Order of pole (three term test) = 22.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y2[1] (analytic) = 0.7032794192004106 y2[1] (numeric) = 0.7032794192004103 absolute error = 3.33066907387547e-16 relative error = 4.735911478345626e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.710913538012277 y1[1] (numeric) = 0.7109135380122774 absolute error = 4.440892098500626e-16 relative error = 6.246740090106338e-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 = 0.5 Order of pole (three term test) = 22.51 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5 Order of pole (three term test) = 22.49 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y2[1] (analytic) = 0.7103532724176083 y2[1] (numeric) = 0.7103532724176079 absolute error = 3.33066907387547e-16 relative error = 4.688750236259077e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.7038453156522356 y1[1] (numeric) = 0.7038453156522362 absolute error = 5.551115123125783e-16 relative error = 7.886839621830409e-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 = 0.5 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y2[1] (analytic) = 0.7173560908995231 y2[1] (numeric) = 0.7173560908995229 absolute error = 2.220446049250313e-16 relative error = 3.09531915518554e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.6967067093471649 y1[1] (numeric) = 0.6967067093471655 absolute error = 5.551115123125783e-16 relative error = 7.967649871388987e-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 = 0.4998 Order of pole (three term test) = 22.49 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4998 Order of pole (three term test) = 22.51 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y2[1] (analytic) = 0.7242871743701429 y2[1] (numeric) = 0.7242871743701427 absolute error = 2.220446049250313e-16 relative error = 3.06569842435946e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.6894984329517466 y1[1] (numeric) = 0.6894984329517471 absolute error = 4.440892098500626e-16 relative error = 6.44075734804667e-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 = 0.4994 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 Radius of convergence (three term test) for eq 2 = 0.4994 Order of pole (three term test) = 22.52 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y2[1] (analytic) = 0.7311458297268963 y2[1] (numeric) = 0.731145829726896 absolute error = 3.33066907387547e-16 relative error = 4.555410067947141e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.6822212072876132 y1[1] (numeric) = 0.6822212072876136 absolute error = 4.440892098500626e-16 relative error = 6.50946064276835e-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 = 0.4988 Order of pole (three term test) = 22.47 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4988 Order of pole (three term test) = 22.53 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y2[1] (analytic) = 0.7379313711099631 y2[1] (numeric) = 0.7379313711099629 absolute error = 2.220446049250313e-16 relative error = 3.009014301574438e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.6748757600712666 y1[1] (numeric) = 0.6748757600712672 absolute error = 5.551115123125783e-16 relative error = 8.22538821447608e-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 = 0.498 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 Radius of convergence (three term test) for eq 2 = 0.498 Order of pole (three term test) = 22.54 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y2[1] (analytic) = 0.7446431199708597 y2[1] (numeric) = 0.7446431199708595 absolute error = 2.220446049250313e-16 relative error = 2.981892922528051e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.6674628258413077 y1[1] (numeric) = 0.6674628258413081 absolute error = 4.440892098500626e-16 relative error = 6.653392408638004e-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 = 0.497 Order of pole (three term test) = 22.45 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.497 Order of pole (three term test) = 22.55 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y2[1] (analytic) = 0.7512804051402932 y2[1] (numeric) = 0.7512804051402929 absolute error = 2.220446049250313e-16 relative error = 2.955548998826437e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.6599831458849816 y1[1] (numeric) = 0.6599831458849822 absolute error = 5.551115123125783e-16 relative error = 8.41099527728425e-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 = 0.4958 Order of pole (three term test) = 22.44 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4958 Order of pole (three term test) = 22.56 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y2[1] (analytic) = 0.7578425628952774 y2[1] (numeric) = 0.7578425628952772 absolute error = 2.220446049250313e-16 relative error = 2.929956903934341e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.6524374681640513 y1[1] (numeric) = 0.6524374681640519 absolute error = 5.551115123125783e-16 relative error = 8.50827151105612e-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 = 0.4944 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 Radius of convergence (three term test) for eq 2 = 0.4944 Order of pole (three term test) = 22.57 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y2[1] (analytic) = 0.7643289370255055 y2[1] (numeric) = 0.7643289370255053 absolute error = 2.220446049250313e-16 relative error = 2.905092221016116e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.6448265472400007 y1[1] (numeric) = 0.6448265472400012 absolute error = 5.551115123125783e-16 relative error = 8.608695077592223e-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 = 0.4929 Order of pole (three term test) = 22.42 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4929 Order of pole (three term test) = 22.58 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y2[1] (analytic) = 0.7707388788989697 y2[1] (numeric) = 0.7707388788989695 absolute error = 2.220446049250313e-16 relative error = 2.880931674839481e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.6371511441985797 y1[1] (numeric) = 0.6371511441985802 absolute error = 5.551115123125783e-16 relative error = 8.712399206483537e-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 = 0.4911 Order of pole (three term test) = 22.41 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4911 Order of pole (three term test) = 22.59 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y2[1] (analytic) = 0.7770717475268243 y2[1] (numeric) = 0.7770717475268241 absolute error = 2.220446049250313e-16 relative error = 2.857453068287834e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.6294120265736963 y1[1] (numeric) = 0.6294120265736969 absolute error = 5.551115123125783e-16 relative error = 8.819525030915208e-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 = 0.4891 Order of pole (three term test) = 22.4 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4891 Order of pole (three term test) = 22.6 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y2[1] (analytic) = 0.7833269096274839 y2[1] (numeric) = 0.7833269096274836 absolute error = 2.220446049250313e-16 relative error = 2.834635223123205e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.6216099682706639 y1[1] (numeric) = 0.6216099682706645 absolute error = 5.551115123125783e-16 relative error = 8.930222175440877e-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 = 0.4869 Order of pole (three term test) = 22.39 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4869 Order of pole (three term test) = 22.61 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y2[1] (analytic) = 0.7895037396899508 y2[1] (numeric) = 0.7895037396899507 absolute error = 1.110223024625157e-16 relative error = 1.406228962336716e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.613745749488811 y1[1] (numeric) = 0.6137457494888116 absolute error = 5.551115123125783e-16 relative error = 9.04464939716374e-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 = 0.4846 Order of pole (three term test) = 22.38 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4846 Order of pole (three term test) = 22.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y2[1] (analytic) = 0.7956016200363665 y2[1] (numeric) = 0.7956016200363664 absolute error = 1.110223024625157e-16 relative error = 1.395450935072768e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.6058201566434622 y1[1] (numeric) = 0.6058201566434629 absolute error = 6.661338147750939e-16 relative error = 1.099557034328139e-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 = 0.482 Order of pole (three term test) = 22.37 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.482 Order of pole (three term test) = 22.63 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y2[1] (analytic) = 0.8016199408837775 y2[1] (numeric) = 0.8016199408837775 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.5978339822872977 y1[1] (numeric) = 0.5978339822872983 absolute error = 6.661338147750939e-16 relative error = 1.114245483715199e-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 = 0.4792 Order of pole (three term test) = 22.36 NO COMPLEX POLE (six term test) for Equation 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) = 22.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y2[1] (analytic) = 0.8075581004051147 y2[1] (numeric) = 0.8075581004051147 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.5897880250310976 y1[1] (numeric) = 0.5897880250310983 absolute error = 6.661338147750939e-16 relative error = 1.129446150996319e-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 = 0.4763 Order of pole (three term test) = 22.35 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4763 Order of pole (three term test) = 22.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y2[1] (analytic) = 0.8134155047893742 y2[1] (numeric) = 0.8134155047893742 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.5816830894638829 y1[1] (numeric) = 0.5816830894638836 absolute error = 6.661338147750939e-16 relative error = 1.145183394258627e-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 = 0.4732 Order of pole (three term test) = 22.34 NO COMPLEX POLE (six term test) for Equation 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) = 22.66 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y2[1] (analytic) = 0.8191915683009987 y2[1] (numeric) = 0.8191915683009987 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.573519986072456 y1[1] (numeric) = 0.5735199860724568 absolute error = 7.771561172376096e-16 relative error = 1.355063705032639e-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 = 0.4698 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 Radius of convergence (three term test) for eq 2 = 0.4698 Order of pole (three term test) = 22.67 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y2[1] (analytic) = 0.8248857133384505 y2[1] (numeric) = 0.8248857133384505 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.5652995311603537 y1[1] (numeric) = 0.5652995311603545 absolute error = 7.771561172376096e-16 relative error = 1.374768727726329e-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 = 0.4663 Order of pole (three term test) = 22.32 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4663 Order of pole (three term test) = 22.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y2[1] (analytic) = 0.8304973704919709 y2[1] (numeric) = 0.8304973704919709 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.5570225467662167 y1[1] (numeric) = 0.5570225467662174 absolute error = 7.771561172376096e-16 relative error = 1.39519687622947e-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 = 0.4626 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 Radius of convergence (three term test) for eq 2 = 0.4626 Order of pole (three term test) = 22.69 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y2[1] (analytic) = 0.836025978600521 y2[1] (numeric) = 0.836025978600521 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.548689860581587 y1[1] (numeric) = 0.5486898605815878 absolute error = 7.771561172376096e-16 relative error = 1.416385052958439e-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 = 0.4587 Order of pole (three term test) = 22.3 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4587 Order of pole (three term test) = 22.7 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y2[1] (analytic) = 0.8414709848078968 y2[1] (numeric) = 0.8414709848078969 absolute error = 1.110223024625157e-16 relative error = 1.319383608786718e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.5403023058681392 y1[1] (numeric) = 0.5403023058681399 absolute error = 6.661338147750939e-16 relative error = 1.232890934464499e-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 = 0.4546 Order of pole (three term test) = 22.29 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4546 Order of pole (three term test) = 22.71 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.010000000000001 y2[1] (analytic) = 0.8468318446180155 y2[1] (numeric) = 0.8468318446180156 absolute error = 1.110223024625157e-16 relative error = 1.311031265157429e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.5318607213743549 y1[1] (numeric) = 0.5318607213743556 absolute error = 6.661338147750939e-16 relative error = 1.25245912699432e-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 = 0.4504 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 Radius of convergence (three term test) for eq 2 = 0.4504 Order of pole (three term test) = 22.72 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.020000000000001 y2[1] (analytic) = 0.8521080219493633 y2[1] (numeric) = 0.8521080219493634 absolute error = 1.110223024625157e-16 relative error = 1.302913475788322e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.523365951251649 y1[1] (numeric) = 0.5233659512516496 absolute error = 6.661338147750939e-16 relative error = 1.27278783264752e-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) = 22.27 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.446 Order of pole (three term test) = 22.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.030000000000001 y2[1] (analytic) = 0.8572989891886037 y2[1] (numeric) = 0.8572989891886039 absolute error = 2.220446049250313e-16 relative error = 2.590048602940578e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.5148188449699548 y1[1] (numeric) = 0.5148188449699554 absolute error = 6.661338147750939e-16 relative error = 1.293918863467342e-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 = 0.4414 Order of pole (three term test) = 22.27 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4414 Order of pole (three term test) = 22.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.040000000000001 y2[1] (analytic) = 0.8624042272433388 y2[1] (numeric) = 0.862404227243339 absolute error = 2.220446049250313e-16 relative error = 2.574716100763946e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.5062202572327777 y1[1] (numeric) = 0.5062202572327785 absolute error = 7.771561172376096e-16 relative error = 1.535213390088113e-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 = 0.4366 Order of pole (three term test) = 22.26 NO COMPLEX POLE (six term test) for Equation 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) = 22.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.050000000000001 y2[1] (analytic) = 0.8674232255940173 y2[1] (numeric) = 0.8674232255940175 absolute error = 2.220446049250313e-16 relative error = 2.559818533484317e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.4975710478917263 y1[1] (numeric) = 0.4975710478917271 absolute error = 7.771561172376096e-16 relative error = 1.561899794070659e-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 = 0.4316 Order of pole (three term test) = 22.25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4316 Order of pole (three term test) = 22.75 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.060000000000001 y2[1] (analytic) = 0.8723554823449866 y2[1] (numeric) = 0.8723554823449869 absolute error = 3.33066907387547e-16 relative error = 3.818018160351636e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.4888720818605269 y1[1] (numeric) = 0.4888720818605277 absolute error = 7.216449660063518e-16 relative error = 1.476142722775145e-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 = 0.4265 Order of pole (three term test) = 22.24 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4265 Order of pole (three term test) = 22.76 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.070000000000001 y2[1] (analytic) = 0.877200504274682 y2[1] (numeric) = 0.8772005042746823 absolute error = 3.33066907387547e-16 relative error = 3.796930186023378e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.4801242290285335 y1[1] (numeric) = 0.4801242290285342 absolute error = 7.771561172376096e-16 relative error = 1.61865631903243e-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 = 0.4212 Order of pole (three term test) = 22.23 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4212 Order of pole (three term test) = 22.77 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.080000000000001 y2[1] (analytic) = 0.8819578068849478 y2[1] (numeric) = 0.8819578068849482 absolute error = 3.33066907387547e-16 relative error = 3.776449449026713e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.4713283641737394 y1[1] (numeric) = 0.4713283641737401 absolute error = 7.771561172376096e-16 relative error = 1.648863459766527e-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 = 0.4157 Order of pole (three term test) = 22.22 NO COMPLEX POLE (six term test) for Equation 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) = 22.78 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.090000000000001 y2[1] (analytic) = 0.8866269144494876 y2[1] (numeric) = 0.8866269144494879 absolute error = 3.33066907387547e-16 relative error = 3.756562111520722e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.4624853668753002 y1[1] (numeric) = 0.462485366875301 absolute error = 7.216449660063518e-16 relative error = 1.560362808626827e-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 = 0.4101 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4101 Order of pole (three term test) = 22.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.100000000000001 y2[1] (analytic) = 0.8912073600614356 y2[1] (numeric) = 0.8912073600614361 absolute error = 4.440892098500626e-16 relative error = 4.983006534185817e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.4535961214255767 y1[1] (numeric) = 0.4535961214255775 absolute error = 7.771561172376096e-16 relative error = 1.713321786780579e-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 = 0.4042 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4042 Order of pole (three term test) = 22.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.110000000000001 y2[1] (analytic) = 0.895698685680048 y2[1] (numeric) = 0.8956986856800484 absolute error = 4.440892098500626e-16 relative error = 4.958020112677663e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.4446615167417062 y1[1] (numeric) = 0.444661516741707 absolute error = 7.771561172376096e-16 relative error = 1.747747641694485e-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 = 0.3983 Order of pole (three term test) = 22.2 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3983 Order of pole (three term test) = 22.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.120000000000001 y2[1] (analytic) = 0.9001004421765053 y2[1] (numeric) = 0.9001004421765058 absolute error = 4.440892098500626e-16 relative error = 4.933773932787147e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.4356824462767115 y1[1] (numeric) = 0.4356824462767123 absolute error = 7.771561172376096e-16 relative error = 1.783767337608137e-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 = 0.3922 Order of pole (three term test) = 22.19 NO COMPLEX POLE (six term test) for Equation 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) = 22.81 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.130000000000001 y2[1] (analytic) = 0.9044121893788263 y2[1] (numeric) = 0.9044121893788267 absolute error = 4.440892098500626e-16 relative error = 4.910252372373205e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.4266598079301566 y1[1] (numeric) = 0.4266598079301574 absolute error = 7.771561172376096e-16 relative error = 1.821488930508375e-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 = 0.3859 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 Radius of convergence (three term test) for eq 2 = 0.3859 Order of pole (three term test) = 22.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.140000000000001 y2[1] (analytic) = 0.9086334961158836 y2[1] (numeric) = 0.9086334961158841 absolute error = 4.440892098500626e-16 relative error = 4.887440444892262e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.4175945039583574 y1[1] (numeric) = 0.4175945039583582 absolute error = 7.771561172376096e-16 relative error = 1.861030520926367e-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 = 0.3794 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3794 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.150000000000001 y2[1] (analytic) = 0.9127639402605214 y2[1] (numeric) = 0.9127639402605219 absolute error = 4.440892098500626e-16 relative error = 4.865323773891753e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.4084874408841566 y1[1] (numeric) = 0.4084874408841574 absolute error = 8.326672684688674e-16 relative error = 2.03841583640023e-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 = 0.3729 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3729 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.160000000000001 y2[1] (analytic) = 0.9168031087717673 y2[1] (numeric) = 0.9168031087717677 absolute error = 4.440892098500626e-16 relative error = 4.843888568888088e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.3993395294062724 y1[1] (numeric) = 0.3993395294062733 absolute error = 8.326672684688674e-16 relative error = 2.085111057517535e-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 = 0.3661 Order of pole (three term test) = 22.16 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3661 Order of pole (three term test) = 22.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.170000000000001 y2[1] (analytic) = 0.920750597736136 y2[1] (numeric) = 0.9207505977361364 absolute error = 4.440892098500626e-16 relative error = 4.823121602548527e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.3901516843082294 y1[1] (numeric) = 0.3901516843082303 absolute error = 8.881784197001252e-16 relative error = 2.276495156684861e-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 = 0.3592 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 Radius of convergence (three term test) for eq 2 = 0.3592 Order of pole (three term test) = 22.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.180000000000001 y2[1] (analytic) = 0.9246060124080206 y2[1] (numeric) = 0.9246060124080211 absolute error = 4.440892098500626e-16 relative error = 4.803010189101928e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.380924824366881 y1[1] (numeric) = 0.3809248243668819 absolute error = 8.326672684688674e-16 relative error = 2.185909699775562e-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 = 0.3522 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 Radius of convergence (three term test) for eq 2 = 0.3522 Order of pole (three term test) = 22.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.190000000000001 y2[1] (analytic) = 0.928368967249167 y2[1] (numeric) = 0.9283689672491674 absolute error = 4.440892098500626e-16 relative error = 4.78354216390855e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.3716598722605322 y1[1] (numeric) = 0.371659872260533 absolute error = 8.326672684688674e-16 relative error = 2.240401320175805e-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 = 0.345 Order of pole (three term test) = 22.14 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.345 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.200000000000001 y2[1] (analytic) = 0.9320390859672266 y2[1] (numeric) = 0.9320390859672271 absolute error = 4.440892098500626e-16 relative error = 4.764705864123795e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.3623577544766728 y1[1] (numeric) = 0.3623577544766736 absolute error = 8.326672684688674e-16 relative error = 2.297914859505156e-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 = 0.3377 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 Radius of convergence (three term test) for eq 2 = 0.3377 Order of pole (three term test) = 22.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.210000000000001 y2[1] (analytic) = 0.9356160015533862 y2[1] (numeric) = 0.9356160015533866 absolute error = 4.440892098500626e-16 relative error = 4.746490110395177e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.3530194012193296 y1[1] (numeric) = 0.3530194012193304 absolute error = 8.326672684688674e-16 relative error = 2.358701152380955e-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 = 0.3303 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3303 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.220000000000001 y2[1] (analytic) = 0.9390993563190678 y2[1] (numeric) = 0.9390993563190683 absolute error = 4.440892098500626e-16 relative error = 4.728884189535949e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.3436457463160462 y1[1] (numeric) = 0.3436457463160471 absolute error = 8.326672684688674e-16 relative error = 2.423039648810537e-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 = 0.3227 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3227 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.230000000000001 y2[1] (analytic) = 0.9424888019316978 y2[1] (numeric) = 0.9424888019316982 absolute error = 3.33066907387547e-16 relative error = 3.533908378591901e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.3342377271245018 y1[1] (numeric) = 0.3342377271245026 absolute error = 8.326672684688674e-16 relative error = 2.491242612353881e-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 = 0.315 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.315 Order of pole (three term test) = 22.89 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.240000000000001 y2[1] (analytic) = 0.9457839994495393 y2[1] (numeric) = 0.9457839994495396 absolute error = 3.33066907387547e-16 relative error = 3.521595920224882e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.3247962844387754 y1[1] (numeric) = 0.3247962844387762 absolute error = 8.326672684688674e-16 relative error = 2.56366007975632e-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 = 0.3072 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3072 Order of pole (three term test) = 22.89 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.250000000000001 y2[1] (analytic) = 0.9489846193555865 y2[1] (numeric) = 0.9489846193555869 absolute error = 3.33066907387547e-16 relative error = 3.509718709811313e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.3153223623952678 y1[1] (numeric) = 0.3153223623952687 absolute error = 8.326672684688674e-16 relative error = 2.640685748209286e-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 = 0.2992 Order of pole (three term test) = 22.1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2992 Order of pole (three term test) = 22.9 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.260000000000001 y2[1] (analytic) = 0.9520903415905161 y2[1] (numeric) = 0.9520903415905164 absolute error = 3.33066907387547e-16 relative error = 3.498269994327865e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.3058169083782885 y1[1] (numeric) = 0.3058169083782893 absolute error = 8.881784197001252e-16 relative error = 2.904281599111155e-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 = 0.2912 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2912 Order of pole (three term test) = 22.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.270000000000001 y2[1] (analytic) = 0.9551008555846925 y2[1] (numeric) = 0.9551008555846929 absolute error = 4.440892098500626e-16 relative error = 4.649657753454745e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.2962808729253179 y1[1] (numeric) = 0.2962808729253187 absolute error = 8.881784197001252e-16 relative error = 2.997758211425293e-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 = 0.283 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.283 Order of pole (three term test) = 22.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.280000000000001 y2[1] (analytic) = 0.9580158602892253 y2[1] (numeric) = 0.9580158602892257 absolute error = 4.440892098500626e-16 relative error = 4.635509997882415e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.2867152096319546 y1[1] (numeric) = 0.2867152096319555 absolute error = 8.881784197001252e-16 relative error = 3.097772248776917e-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 = 0.2747 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2747 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.290000000000001 y2[1] (analytic) = 0.9608350642060729 y2[1] (numeric) = 0.9608350642060733 absolute error = 4.440892098500626e-16 relative error = 4.621908862339537e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.2771208750565567 y1[1] (numeric) = 0.2771208750565576 absolute error = 8.881784197001252e-16 relative error = 3.205021705848972e-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 = 0.2663 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2663 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.300000000000001 y2[1] (analytic) = 0.9635581854171932 y2[1] (numeric) = 0.9635581854171936 absolute error = 4.440892098500626e-16 relative error = 4.608846840502783e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.2674988286245865 y1[1] (numeric) = 0.2674988286245874 absolute error = 8.881784197001252e-16 relative error = 3.320307697296923e-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 = 0.2578 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2578 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.310000000000001 y2[1] (analytic) = 0.9661849516127343 y2[1] (numeric) = 0.9661849516127347 absolute error = 3.33066907387547e-16 relative error = 3.447237579426166e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.2578500325326687 y1[1] (numeric) = 0.2578500325326696 absolute error = 8.881784197001252e-16 relative error = 3.444554227805249e-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 = 0.2491 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2491 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.320000000000001 y2[1] (analytic) = 0.9687151001182654 y2[1] (numeric) = 0.9687151001182659 absolute error = 4.440892098500626e-16 relative error = 4.584311835294464e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.248175451652372 y1[1] (numeric) = 0.2481754516523729 absolute error = 8.881784197001252e-16 relative error = 3.57883269189826e-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 = 0.2404 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2404 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.330000000000001 y2[1] (analytic) = 0.9711483779210448 y2[1] (numeric) = 0.9711483779210452 absolute error = 4.440892098500626e-16 relative error = 4.572825532600204e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.2384760534337223 y1[1] (numeric) = 0.2384760534337232 absolute error = 8.881784197001252e-16 relative error = 3.724392478454737e-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 = 0.2316 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2316 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.340000000000001 y2[1] (analytic) = 0.9734845416953196 y2[1] (numeric) = 0.9734845416953201 absolute error = 4.440892098500626e-16 relative error = 4.561851686691223e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.2287528078084585 y1[1] (numeric) = 0.2287528078084594 absolute error = 8.881784197001252e-16 relative error = 3.882699531469023e-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 = 0.2227 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2227 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.350000000000001 y2[1] (analytic) = 0.9757233578266593 y2[1] (numeric) = 0.9757233578266598 absolute error = 4.440892098500626e-16 relative error = 4.551384429693612e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.2190066870930406 y1[1] (numeric) = 0.2190066870930415 absolute error = 8.881784197001252e-16 relative error = 4.055485389461191e-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 = 0.2137 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2137 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.360000000000001 y2[1] (analytic) = 0.9778646024353164 y2[1] (numeric) = 0.9778646024353169 absolute error = 5.551115123125783e-16 relative error = 5.676772744714396e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.2092386658914184 y1[1] (numeric) = 0.2092386658914193 absolute error = 8.881784197001252e-16 relative error = 4.244810183224135e-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 = 0.2046 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2046 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.370000000000001 y2[1] (analytic) = 0.9799080613986144 y2[1] (numeric) = 0.979908061398615 absolute error = 5.551115123125783e-16 relative error = 5.664934642136451e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.199449720997572 y1[1] (numeric) = 0.1994497209975729 absolute error = 8.881784197001252e-16 relative error = 4.45314445795057e-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 = 0.1954 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1954 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.380000000000001 y2[1] (analytic) = 0.9818535303723599 y2[1] (numeric) = 0.9818535303723605 absolute error = 5.551115123125783e-16 relative error = 5.653709999922868e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.1896408312978334 y1[1] (numeric) = 0.1896408312978343 absolute error = 8.881784197001252e-16 relative error = 4.683476726091911e-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 = 0.1862 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1862 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.390000000000001 y2[1] (analytic) = 0.9837008148112767 y2[1] (numeric) = 0.9837008148112772 absolute error = 5.551115123125783e-16 relative error = 5.643092939991888e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.1798129776729985 y1[1] (numeric) = 0.1798129776729994 absolute error = 8.881784197001252e-16 relative error = 4.939456713270914e-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 = 0.1769 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1769 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.400000000000001 y2[1] (analytic) = 0.9854497299884604 y2[1] (numeric) = 0.9854497299884609 absolute error = 5.551115123125783e-16 relative error = 5.633077927973846e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.1699671429002399 y1[1] (numeric) = 0.1699671429002408 absolute error = 8.881784197001252e-16 relative error = 5.225588925863338e-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 = 0.1675 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1675 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.410000000000001 y2[1] (analytic) = 0.9871001010138505 y2[1] (numeric) = 0.987100101013851 absolute error = 5.551115123125783e-16 relative error = 5.623659766040174e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.1601043115548302 y1[1] (numeric) = 0.1601043115548311 absolute error = 8.881784197001252e-16 relative error = 5.547498446948163e-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 = 0.158 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.158 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.420000000000001 y2[1] (analytic) = 0.98865176285172 y2[1] (numeric) = 0.9886517628517205 absolute error = 5.551115123125783e-16 relative error = 5.614833586210224e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.1502254699116848 y1[1] (numeric) = 0.1502254699116856 absolute error = 8.881784197001252e-16 relative error = 5.912302489200211e-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 = 0.1485 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 Radius of convergence (three term test) for eq 2 = 0.1485 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.430000000000001 y2[1] (analytic) = 0.990104560337178 y2[1] (numeric) = 0.9901045603371785 absolute error = 5.551115123125783e-16 relative error = 5.606594844119658e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.1403316058467356 y1[1] (numeric) = 0.1403316058467365 absolute error = 8.881784197001252e-16 relative error = 6.329140284122145e-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 = 0.1389 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 Radius of convergence (three term test) for eq 2 = 0.1389 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.440000000000001 y2[1] (analytic) = 0.9914583481916867 y2[1] (numeric) = 0.9914583481916872 absolute error = 5.551115123125783e-16 relative error = 5.598939313235316e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.1304237087381444 y1[1] (numeric) = 0.1304237087381453 absolute error = 9.159339953157541e-16 relative error = 7.022756860523742e-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 = 0.1293 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 Radius of convergence (three term test) for eq 2 = 0.1293 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.450000000000001 y2[1] (analytic) = 0.9927129910375886 y2[1] (numeric) = 0.9927129910375893 absolute error = 6.661338147750939e-16 relative error = 6.710235695403235e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.1205027693673655 y1[1] (numeric) = 0.1205027693673664 absolute error = 9.159339953157541e-16 relative error = 7.60093730728654e-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 = 0.1196 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1196 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.460000000000001 y2[1] (analytic) = 0.993868363411645 y2[1] (numeric) = 0.9938683634116456 absolute error = 6.661338147750939e-16 relative error = 6.702435043695938e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.1105697798200685 y1[1] (numeric) = 0.1105697798200694 absolute error = 9.159339953157541e-16 relative error = 8.283764305276401e-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 = 0.1099 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1099 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.470000000000001 y2[1] (analytic) = 0.994924349777581 y2[1] (numeric) = 0.9949243497775817 absolute error = 6.661338147750939e-16 relative error = 6.695321256576046e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.1006257333869306 y1[1] (numeric) = 0.1006257333869315 absolute error = 9.159339953157541e-16 relative error = 9.102383301831584e-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 = 0.1001 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1001 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.480000000000001 y2[1] (analytic) = 0.9958808445376401 y2[1] (numeric) = 0.9958808445376409 absolute error = 7.771561172376096e-16 relative error = 7.803705849954585e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.09067162446430857 y1[1] (numeric) = 0.09067162446430949 absolute error = 9.159339953157541e-16 relative error = 1.010166080873843e-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 = 0.0903 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0903 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.490000000000001 y2[1] (analytic) = 0.9967377520431435 y2[1] (numeric) = 0.9967377520431443 absolute error = 7.771561172376096e-16 relative error = 7.796996909614101e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.08070844845479952 y1[1] (numeric) = 0.08070844845480044 absolute error = 9.159339953157541e-16 relative error = 1.134867554576668e-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 = 0.08045 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08045 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.500000000000001 y2[1] (analytic) = 0.9974949866040546 y2[1] (numeric) = 0.9974949866040553 absolute error = 7.771561172376096e-16 relative error = 7.791077926951965e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.0707372016677018 y1[1] (numeric) = 0.07073720166770273 absolute error = 9.298117831235686e-16 relative error = 1.314459380923059e-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 = 0.07056 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07056 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.510000000000001 y2[1] (analytic) = 0.9981524724975482 y2[1] (numeric) = 0.998152472497549 absolute error = 7.771561172376096e-16 relative error = 7.785945921598852e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.06075888121938479 y1[1] (numeric) = 0.06075888121938571 absolute error = 9.228728892196614e-16 relative error = 1.518910274018054e-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 = 0.06065 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06065 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.520000000000001 y2[1] (analytic) = 0.9987101439755831 y2[1] (numeric) = 0.9987101439755839 absolute error = 7.771561172376096e-16 relative error = 7.781598313840796e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.05077448493357807 y1[1] (numeric) = 0.05077448493357899 absolute error = 9.228728892196614e-16 relative error = 1.817591828704793e-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 = 0.05071 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05071 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.530000000000001 y2[1] (analytic) = 0.999167945271476 y2[1] (numeric) = 0.9991679452714769 absolute error = 8.881784197001252e-16 relative error = 8.889180481653715e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.04078501124158992 y1[1] (numeric) = 0.04078501124159085 absolute error = 9.228728892196614e-16 relative error = 2.262774634909442e-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 = 0.04075 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04075 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.540000000000001 y2[1] (analytic) = 0.9995258306054791 y2[1] (numeric) = 0.9995258306054799 absolute error = 8.881784197001252e-16 relative error = 8.885997665133843e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.03079145908246501 y1[1] (numeric) = 0.03079145908246594 absolute error = 9.26342336171615e-16 relative error = 3.008439235343493e-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 = 0.03078 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03078 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.550000000000001 y2[1] (analytic) = 0.999783764189357 y2[1] (numeric) = 0.9997837641893579 absolute error = 8.881784197001252e-16 relative error = 8.883705172190674e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.02079482780309132 y1[1] (numeric) = 0.02079482780309224 absolute error = 9.228728892196614e-16 relative error = 4.437992456386048e-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) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02079 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.560000000000001 y2[1] (analytic) = 0.9999417202299663 y2[1] (numeric) = 0.9999417202299672 absolute error = 8.881784197001252e-16 relative error = 8.882301855510762e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.01079611705826628 y1[1] (numeric) = 0.01079611705826721 absolute error = 9.246076126956382e-16 relative error = 8.56426072175359e-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 = 0.0108 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0108 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.570000000000001 y2[1] (analytic) = 0.9999996829318346 y2[1] (numeric) = 0.9999996829318355 absolute error = 8.881784197001252e-16 relative error = 8.881787013133166e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 0.0007963267107321531 y1[1] (numeric) = 0.0007963267107330765 absolute error = 9.234149903059041e-16 relative error = 1.159593139173875e-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 = 0.0007963 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0007963 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.580000000000001 y2[1] (analytic) = 0.9999576464987401 y2[1] (numeric) = 0.999957646498741 absolute error = 8.881784197001252e-16 relative error = 8.882160387592419e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.009203543268809447 y1[1] (numeric) = -0.009203543268808524 absolute error = 9.228728892196614e-16 relative error = 1.002736513824249e-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 = 0.009203 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.009203 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.590000000000001 y2[1] (analytic) = 0.9998156151342908 y2[1] (numeric) = 0.9998156151342918 absolute error = 9.992007221626409e-16 relative error = 9.993849936304832e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.01920249290169376 y1[1] (numeric) = -0.01920249290169284 absolute error = 9.228728892196614e-16 relative error = 4.80600562616669e-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 = 0.0192 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0192 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.600000000000001 y2[1] (analytic) = 0.9995736030415051 y2[1] (numeric) = 0.9995736030415061 absolute error = 9.992007221626409e-16 relative error = 9.996269600580391e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.02919952230128993 y1[1] (numeric) = -0.02919952230128901 absolute error = 9.194034422677078e-16 relative error = 3.148693436765888e-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 = 0.02919 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02919 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.610000000000001 y2[1] (analytic) = 0.9992316344213905 y2[1] (numeric) = 0.9992316344213915 absolute error = 9.992007221626409e-16 relative error = 9.999690639710706e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.03919363177298882 y1[1] (numeric) = -0.0391936317729879 absolute error = 9.159339953157541e-16 relative error = 2.336945962601483e-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 = 0.03916 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03916 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.620000000000001 y2[1] (analytic) = 0.998789743470524 y2[1] (numeric) = 0.998789743470525 absolute error = 9.992007221626409e-16 relative error = 1.000411476684461e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.04918382191417166 y1[1] (numeric) = -0.04918382191417075 absolute error = 9.089951014118469e-16 relative error = 1.848158736013015e-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 = 0.04912 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04912 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.630000000000001 y2[1] (analytic) = 0.9982479743776324 y2[1] (numeric) = 0.9982479743776334 absolute error = 9.992007221626409e-16 relative error = 1.000954419953221e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.05916909371414947 y1[1] (numeric) = -0.05916909371414856 absolute error = 9.089951014118469e-16 relative error = 1.536266730403669e-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 = 0.05907 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05907 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.640000000000001 y2[1] (analytic) = 0.9976063813191736 y2[1] (numeric) = 0.9976063813191746 absolute error = 9.992007221626409e-16 relative error = 1.001598166244044e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.06914844865406328 y1[1] (numeric) = -0.06914844865406236 absolute error = 9.159339953157541e-16 relative error = 1.324590808823493e-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 = 0.06898 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06898 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.650000000000001 y2[1] (analytic) = 0.9968650284539188 y2[1] (numeric) = 0.9968650284539198 absolute error = 9.992007221626409e-16 relative error = 1.002343039069536e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.07912088880673519 y1[1] (numeric) = -0.07912088880673428 absolute error = 9.159339953157541e-16 relative error = 1.157638657918849e-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 = 0.07887 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07887 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.660000000000001 y2[1] (analytic) = 0.9960239899165366 y2[1] (numeric) = 0.9960239899165376 absolute error = 9.992007221626409e-16 relative error = 1.003189413385887e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.08908541693646028 y1[1] (numeric) = -0.08908541693645938 absolute error = 9.020562075079397e-16 relative error = 1.012574491458379e-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 = 0.08873 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08873 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.670000000000001 y2[1] (analytic) = 0.9950833498101801 y2[1] (numeric) = 0.9950833498101811 absolute error = 9.992007221626409e-16 relative error = 1.004137716054887e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.09904103659872934 y1[1] (numeric) = -0.09904103659872844 absolute error = 9.020562075079397e-16 relative error = 9.107903536618605e-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 = 0.09855 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09855 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.680000000000001 y2[1] (analytic) = 0.9940432021980758 y2[1] (numeric) = 0.9940432021980768 absolute error = 9.992007221626409e-16 relative error = 1.005188426371369e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1089867522398724 y1[1] (numeric) = -0.1089867522398715 absolute error = 8.881784197001252e-16 relative error = 8.149416341403631e-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 = 0.1083 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1083 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.690000000000001 y2[1] (analytic) = 0.9929036510941184 y2[1] (numeric) = 0.9929036510941194 absolute error = 9.992007221626409e-16 relative error = 1.00634207665727e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1189215692966135 y1[1] (numeric) = -0.1189215692966127 absolute error = 8.881784197001252e-16 relative error = 7.468606619921364e-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 = 0.1181 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1181 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.700000000000001 y2[1] (analytic) = 0.9916648104524685 y2[1] (numeric) = 0.9916648104524695 absolute error = 9.992007221626409e-16 relative error = 1.007599252923711e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.128844494295526 y1[1] (numeric) = -0.1288444942955251 absolute error = 8.881784197001252e-16 relative error = 6.893413836240006e-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 = 0.1278 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 Radius of convergence (three term test) for eq 2 = 0.1278 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.710000000000001 y2[1] (analytic) = 0.9903268041561579 y2[1] (numeric) = 0.9903268041561589 absolute error = 9.992007221626409e-16 relative error = 1.008960595602625e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1387545349523789 y1[1] (numeric) = -0.138754534952378 absolute error = 8.881784197001252e-16 relative error = 6.401076692772252e-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 = 0.1374 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 Radius of convergence (three term test) for eq 2 = 0.1374 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.720000000000001 y2[1] (analytic) = 0.9888897660047012 y2[1] (numeric) = 0.9888897660047024 absolute error = 1.110223024625157e-15 relative error = 1.122696444832941e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.148650700271365 y1[1] (numeric) = -0.1486507002713641 absolute error = 8.881784197001252e-16 relative error = 5.974935994776593e-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 = 0.147 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 Radius of convergence (three term test) for eq 2 = 0.147 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.730000000000001 y2[1] (analytic) = 0.9873538397007162 y2[1] (numeric) = 0.9873538397007173 absolute error = 1.110223024625157e-15 relative error = 1.124442909911288e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1585320006441991 y1[1] (numeric) = -0.1585320006441982 absolute error = 8.881784197001252e-16 relative error = 5.602518205100474e-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 = 0.1565 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1565 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.740000000000001 y2[1] (analytic) = 0.9857191788355533 y2[1] (numeric) = 0.9857191788355544 absolute error = 1.110223024625157e-15 relative error = 1.126307622356178e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1683974479490783 y1[1] (numeric) = -0.1683974479490774 absolute error = 8.881784197001252e-16 relative error = 5.274298574695155e-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 = 0.166 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.166 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.750000000000001 y2[1] (analytic) = 0.9839859468739367 y2[1] (numeric) = 0.9839859468739378 absolute error = 1.110223024625157e-15 relative error = 1.128291545374471e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1782460556494934 y1[1] (numeric) = -0.1782460556494925 absolute error = 8.604228440844963e-16 relative error = 4.827163445212213e-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 = 0.1754 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1754 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.760000000000001 y2[1] (analytic) = 0.9821543171376182 y2[1] (numeric) = 0.9821543171376194 absolute error = 1.110223024625157e-15 relative error = 1.130395707938016e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1880768388928814 y1[1] (numeric) = -0.1880768388928805 absolute error = 8.881784197001252e-16 relative error = 4.722423159217305e-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 = 0.1847 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1847 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.770000000000001 y2[1] (analytic) = 0.9802244727880453 y2[1] (numeric) = 0.9802244727880464 absolute error = 1.110223024625157e-15 relative error = 1.13262120610737e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1978888146091103 y1[1] (numeric) = -0.1978888146091095 absolute error = 8.604228440844963e-16 relative error = 4.348011512343885e-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 = 0.194 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.194 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.780000000000001 y2[1] (analytic) = 0.9781966068080444 y2[1] (numeric) = 0.9781966068080455 absolute error = 1.110223024625157e-15 relative error = 1.134969204450553e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.2076810016087851 y1[1] (numeric) = -0.2076810016087842 absolute error = 8.604228440844963e-16 relative error = 4.143002188063887e-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 = 0.2032 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2032 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.790000000000001 y2[1] (analytic) = 0.9760709219825239 y2[1] (numeric) = 0.9760709219825251 absolute error = 1.221245327087672e-15 relative error = 1.251185031316339e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.2174524206813659 y1[1] (numeric) = -0.2174524206813651 absolute error = 8.604228440844963e-16 relative error = 3.956832678102388e-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 = 0.2122 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2122 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.800000000000001 y2[1] (analytic) = 0.9738476308781949 y2[1] (numeric) = 0.9738476308781961 absolute error = 1.221245327087672e-15 relative error = 1.254041482840985e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.2272020946930884 y1[1] (numeric) = -0.2272020946930875 absolute error = 8.604228440844963e-16 relative error = 3.787037462162407e-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 = 0.2213 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 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) = 22.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.810000000000001 y2[1] (analytic) = 0.971526955822315 y2[1] (numeric) = 0.9715269558223163 absolute error = 1.332267629550188e-15 relative error = 1.371313087677054e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.236929048684676 y1[1] (numeric) = -0.2369290486846751 absolute error = 8.604228440844963e-16 relative error = 3.63156332607242e-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 = 0.2302 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2302 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.820000000000001 y2[1] (analytic) = 0.9691091288804561 y2[1] (numeric) = 0.9691091288804573 absolute error = 1.221245327087672e-15 relative error = 1.260173174200197e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.2466323099688353 y1[1] (numeric) = -0.2466323099688345 absolute error = 8.604228440844963e-16 relative error = 3.488686637177506e-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 = 0.239 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.239 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.830000000000001 y2[1] (analytic) = 0.9665943918332972 y2[1] (numeric) = 0.9665943918332985 absolute error = 1.332267629550188e-15 relative error = 1.378310944907651e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.256310908227524 y1[1] (numeric) = -0.2563109082275232 absolute error = 8.326672684688674e-16 relative error = 3.248661066464323e-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 = 0.2477 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2477 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.840000000000001 y2[1] (analytic) = 0.9639829961524478 y2[1] (numeric) = 0.9639829961524491 absolute error = 1.332267629550188e-15 relative error = 1.38204474027828e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.2659638756089817 y1[1] (numeric) = -0.2659638756089808 absolute error = 8.326672684688674e-16 relative error = 3.130753251968133e-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 = 0.2564 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 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) = 22.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.850000000000001 y2[1] (analytic) = 0.9612752029752996 y2[1] (numeric) = 0.9612752029753009 absolute error = 1.332267629550188e-15 relative error = 1.385937789122832e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.2755902468245142 y1[1] (numeric) = -0.2755902468245134 absolute error = 8.326672684688674e-16 relative error = 3.021395996640909e-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 = 0.2649 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2649 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.860000000000001 y2[1] (analytic) = 0.9584712830789138 y2[1] (numeric) = 0.9584712830789152 absolute error = 1.332267629550188e-15 relative error = 1.389992223106071e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.2851890592450221 y1[1] (numeric) = -0.2851890592450213 absolute error = 8.326672684688674e-16 relative error = 2.919702707646564e-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 = 0.2733 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2733 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.870000000000001 y2[1] (analytic) = 0.9555715168529435 y2[1] (numeric) = 0.9555715168529449 absolute error = 1.443289932012704e-15 relative error = 1.510394467141507e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.2947593529972622 y1[1] (numeric) = -0.2947593529972615 absolute error = 7.771561172376096e-16 relative error = 2.63657831154497e-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 = 0.2817 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 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) = 22.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.880000000000001 y2[1] (analytic) = 0.9525761942715949 y2[1] (numeric) = 0.9525761942715963 absolute error = 1.443289932012704e-15 relative error = 1.515143818092517e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.3043001710598347 y1[1] (numeric) = -0.3043001710598339 absolute error = 8.326672684688674e-16 relative error = 2.73633519681834e-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 = 0.2899 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2899 Order of pole (three term test) = 22.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.890000000000001 y2[1] (analytic) = 0.94948561486463 y2[1] (numeric) = 0.9494856148646315 absolute error = 1.443289932012704e-15 relative error = 1.52007561717349e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.3138105593588837 y1[1] (numeric) = -0.3138105593588829 absolute error = 8.326672684688674e-16 relative error = 2.653407425709352e-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 = 0.298 Order of pole (three term test) = 22.1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.298 Order of pole (three term test) = 22.9 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y2[1] (analytic) = 0.946300087687414 y2[1] (numeric) = 0.9463000876874155 absolute error = 1.443289932012704e-15 relative error = 1.525192643213045e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.3232895668635048 y1[1] (numeric) = -0.323289566863504 absolute error = 7.771561172376096e-16 relative error = 2.403901012882765e-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 = 0.3059 Order of pole (three term test) = 22.1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3059 Order of pole (three term test) = 22.9 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.910000000000001 y2[1] (analytic) = 0.94301993129001 y2[1] (numeric) = 0.9430199312900115 absolute error = 1.443289932012704e-15 relative error = 1.530497801926992e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.3327362456808466 y1[1] (numeric) = -0.3327362456808458 absolute error = 8.326672684688674e-16 relative error = 2.502484413037297e-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 = 0.3138 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3138 Order of pole (three term test) = 22.89 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.920000000000001 y2[1] (analytic) = 0.9396454736853244 y2[1] (numeric) = 0.9396454736853259 absolute error = 1.554312234475219e-15 relative error = 1.654147524788417e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.3421496511508996 y1[1] (numeric) = -0.3421496511508988 absolute error = 7.771561172376096e-16 relative error = 2.271392399856218e-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 = 0.3215 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3215 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.930000000000001 y2[1] (analytic) = 0.9361770523163055 y2[1] (numeric) = 0.9361770523163071 absolute error = 1.554312234475219e-15 relative error = 1.660275938861685e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.3515288419409613 y1[1] (numeric) = -0.3515288419409605 absolute error = 7.771561172376096e-16 relative error = 2.210789057724406e-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 = 0.3291 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3291 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.940000000000002 y2[1] (analytic) = 0.9326150140221999 y2[1] (numeric) = 0.9326150140222016 absolute error = 1.665334536937735e-15 relative error = 1.785661298498132e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.3608728801397686 y1[1] (numeric) = -0.3608728801397678 absolute error = 7.771561172376096e-16 relative error = 2.153545361836588e-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 = 0.3366 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 Radius of convergence (three term test) for eq 2 = 0.3366 Order of pole (three term test) = 22.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.950000000000002 y2[1] (analytic) = 0.9289597150038688 y2[1] (numeric) = 0.9289597150038704 absolute error = 1.665334536937735e-15 relative error = 1.792687573035177e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.3701808313512883 y1[1] (numeric) = -0.3701808313512875 absolute error = 7.771561172376096e-16 relative error = 2.099395893625071e-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 = 0.3439 Order of pole (three term test) = 22.14 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3439 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.960000000000002 y2[1] (analytic) = 0.9252115207881677 y2[1] (numeric) = 0.9252115207881694 absolute error = 1.665334536937735e-15 relative error = 1.799950064952793e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.3794517647881559 y1[1] (numeric) = -0.3794517647881551 absolute error = 7.771561172376096e-16 relative error = 2.048102524102077e-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 = 0.3511 Order of pole (three term test) = 22.14 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3511 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.970000000000002 y2[1] (analytic) = 0.9213708061913948 y2[1] (numeric) = 0.9213708061913966 absolute error = 1.77635683940025e-15 relative error = 1.927949993057682e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.3886847533647534 y1[1] (numeric) = -0.3886847533647527 absolute error = 7.771561172376096e-16 relative error = 1.999450995980547e-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 = 0.3581 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 Radius of convergence (three term test) for eq 2 = 0.3581 Order of pole (three term test) = 22.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.980000000000002 y2[1] (analytic) = 0.9174379552818093 y2[1] (numeric) = 0.917437955281811 absolute error = 1.77635683940025e-15 relative error = 1.936214682609907e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.3978788737899174 y1[1] (numeric) = -0.3978788737899166 absolute error = 7.771561172376096e-16 relative error = 1.953248006949856e-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 = 0.365 Order of pole (three term test) = 22.16 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.365 Order of pole (three term test) = 22.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.990000000000002 y2[1] (analytic) = 0.9134133613412245 y2[1] (numeric) = 0.9134133613412264 absolute error = 1.887379141862766e-15 relative error = 2.066292460503757e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.407033206659267 y1[1] (numeric) = -0.4070332066592662 absolute error = 7.771561172376096e-16 relative error = 1.909318710422016e-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 = 0.3718 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3718 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.000000000000001 y2[1] (analytic) = 0.9092974268256812 y2[1] (numeric) = 0.9092974268256829 absolute error = 1.77635683940025e-15 relative error = 1.953548736634433e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.4161468365471436 y1[1] (numeric) = -0.416146836547143 absolute error = 5.551115123125783e-16 relative error = 1.33393183261575e-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 = 0.3784 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3784 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.010000000000001 y2[1] (analytic) = 0.9050905633252004 y2[1] (numeric) = 0.9050905633252022 absolute error = 1.77635683940025e-15 relative error = 1.962628836692448e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.4252188520981534 y1[1] (numeric) = -0.425218852098153 absolute error = 3.885780586188048e-16 relative error = 9.138307408089921e-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 = 0.3849 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 Radius of convergence (three term test) for eq 2 = 0.3849 Order of pole (three term test) = 22.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.020000000000001 y2[1] (analytic) = 0.9007931915226269 y2[1] (numeric) = 0.9007931915226286 absolute error = 1.665334536937735e-15 relative error = 1.848742366849809e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.4342483461183013 y1[1] (numeric) = -0.4342483461183011 absolute error = 1.665334536937735e-16 relative error = 3.834981875749163e-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 = 0.3912 Order of pole (three term test) = 22.19 NO COMPLEX POLE (six term test) for Equation 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) = 22.81 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.030000000000001 y2[1] (analytic) = 0.8964057411515596 y2[1] (numeric) = 0.8964057411515612 absolute error = 1.665334536937735e-15 relative error = 1.857791020836589e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.4432344156657097 y1[1] (numeric) = -0.4432344156657098 absolute error = 5.551115123125783e-17 relative error = 1.252410671853711e-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 = 0.3973 Order of pole (three term test) = 22.2 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3973 Order of pole (three term test) = 22.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.04 y2[1] (analytic) = 0.8919286509533794 y2[1] (numeric) = 0.891928650953381 absolute error = 1.665334536937735e-15 relative error = 1.867116316039029e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.4521761621409124 y1[1] (numeric) = -0.4521761621409126 absolute error = 2.220446049250313e-16 relative error = 4.910577414645648e-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 = 0.4033 Order of pole (three term test) = 22.2 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4033 Order of pole (three term test) = 22.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.05 y2[1] (analytic) = 0.8873623686333753 y2[1] (numeric) = 0.8873623686333768 absolute error = 1.554312234475219e-15 relative error = 1.751609364355863e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.4610726913767131 y1[1] (numeric) = -0.4610726913767136 absolute error = 4.440892098500626e-16 relative error = 9.631652842506467e-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 = 0.4091 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 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) = 22.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.06 y2[1] (analytic) = 0.8827073508159741 y2[1] (numeric) = 0.8827073508159754 absolute error = 1.332267629550188e-15 relative error = 1.509297082797193e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.4699231137276022 y1[1] (numeric) = -0.4699231137276029 absolute error = 6.661338147750939e-16 relative error = 1.417537880805812e-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 = 0.4148 Order of pole (three term test) = 22.22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4148 Order of pole (three term test) = 22.78 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.07 y2[1] (analytic) = 0.8779640629990781 y2[1] (numeric) = 0.8779640629990795 absolute error = 1.332267629550188e-15 relative error = 1.517451209790106e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.4787265441587198 y1[1] (numeric) = -0.4787265441587207 absolute error = 8.881784197001252e-16 relative error = 1.85529386355826e-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 = 0.4203 Order of pole (three term test) = 22.23 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4203 Order of pole (three term test) = 22.77 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.08 y2[1] (analytic) = 0.8731329795075167 y2[1] (numeric) = 0.8731329795075179 absolute error = 1.221245327087672e-15 relative error = 1.398693390068149e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.487482102334359 y1[1] (numeric) = -0.4874821023343601 absolute error = 1.054711873393899e-15 relative error = 2.163590967428959e-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 = 0.4256 Order of pole (three term test) = 22.24 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4256 Order of pole (three term test) = 22.76 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.089999999999999 y2[1] (analytic) = 0.8682145834456129 y2[1] (numeric) = 0.868214583445614 absolute error = 1.110223024625157e-15 relative error = 1.278742658547734e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.4961889127059985 y1[1] (numeric) = -0.4961889127059997 absolute error = 1.27675647831893e-15 relative error = 2.573125770497482e-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 = 0.4308 Order of pole (three term test) = 22.25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4308 Order of pole (three term test) = 22.75 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.099999999999999 y2[1] (analytic) = 0.8632093666488742 y2[1] (numeric) = 0.8632093666488752 absolute error = 9.992007221626409e-16 relative error = 1.157541566122838e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.5048461045998568 y1[1] (numeric) = -0.5048461045998582 absolute error = 1.443289932012704e-15 relative error = 2.858871087371589e-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 = 0.4358 Order of pole (three term test) = 22.25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4358 Order of pole (three term test) = 22.75 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.109999999999999 y2[1] (analytic) = 0.8581178296348094 y2[1] (numeric) = 0.8581178296348102 absolute error = 7.771561172376096e-16 relative error = 9.056519867071695e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.5134528123039588 y1[1] (numeric) = -0.5134528123039604 absolute error = 1.665334536937735e-15 relative error = 3.243403282699081e-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 = 0.4406 Order of pole (three term test) = 22.26 NO COMPLEX POLE (six term test) for Equation 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) = 22.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.119999999999999 y2[1] (analytic) = 0.8529404815528769 y2[1] (numeric) = 0.8529404815528776 absolute error = 6.661338147750939e-16 relative error = 7.809851087878021e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.5220081751547062 y1[1] (numeric) = -0.5220081751547081 absolute error = 1.887379141862766e-15 relative error = 3.615612229259453e-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 = 0.4452 Order of pole (three term test) = 22.27 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4452 Order of pole (three term test) = 22.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.129999999999999 y2[1] (analytic) = 0.8476778401335705 y2[1] (numeric) = 0.8476778401335711 absolute error = 5.551115123125783e-16 relative error = 6.548614179003525e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.5305113376229437 y1[1] (numeric) = -0.5305113376229457 absolute error = 1.998401444325282e-15 relative error = 3.766934469825842e-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 = 0.4497 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 Radius of convergence (three term test) for eq 2 = 0.4497 Order of pole (three term test) = 22.72 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.139999999999998 y2[1] (analytic) = 0.8423304316366466 y2[1] (numeric) = 0.842330431636647 absolute error = 4.440892098500626e-16 relative error = 5.272149659691127e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.5389614493995101 y1[1] (numeric) = -0.5389614493995123 absolute error = 2.220446049250313e-15 relative error = 4.119860616606713e-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 = 0.454 Order of pole (three term test) = 22.29 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.454 Order of pole (three term test) = 22.71 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.149999999999998 y2[1] (analytic) = 0.8368987907984987 y2[1] (numeric) = 0.836898790798499 absolute error = 3.33066907387547e-16 relative error = 3.979775225505612e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.5473576654802695 y1[1] (numeric) = -0.547357665480272 absolute error = 2.442490654175344e-15 relative error = 4.46233022430082e-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 = 0.4581 Order of pole (three term test) = 22.3 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4581 Order of pole (three term test) = 22.7 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.159999999999998 y2[1] (analytic) = 0.8313834607786843 y2[1] (numeric) = 0.8313834607786845 absolute error = 2.220446049250313e-16 relative error = 2.67078448634354e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.5556991462506109 y1[1] (numeric) = -0.5556991462506136 absolute error = 2.664535259100376e-15 relative error = 4.794924154694878e-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 = 0.462 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 Radius of convergence (three term test) for eq 2 = 0.462 Order of pole (three term test) = 22.69 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.169999999999998 y2[1] (analytic) = 0.8257849931056094 y2[1] (numeric) = 0.8257849931056094 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.5639850575694082 y1[1] (numeric) = -0.5639850575694111 absolute error = 2.886579864025407e-15 relative error = 5.118185003811316e-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 = 0.4657 Order of pole (three term test) = 22.32 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4657 Order of pole (three term test) = 22.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.179999999999997 y2[1] (analytic) = 0.8201039476213756 y2[1] (numeric) = 0.8201039476213755 absolute error = 1.110223024625157e-16 relative error = 1.35375890805701e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.5722145708524347 y1[1] (numeric) = -0.5722145708524377 absolute error = 2.997602166487923e-15 relative error = 5.238598104942277e-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 = 0.4693 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 Radius of convergence (three term test) for eq 2 = 0.4693 Order of pole (three term test) = 22.67 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.189999999999997 y2[1] (analytic) = 0.8143408924257975 y2[1] (numeric) = 0.8143408924257972 absolute error = 3.33066907387547e-16 relative error = 4.090018203499413e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.5803868631552197 y1[1] (numeric) = -0.5803868631552229 absolute error = 3.219646771412954e-15 relative error = 5.547414967164558e-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 = 0.4726 Order of pole (three term test) = 22.34 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4726 Order of pole (three term test) = 22.66 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.199999999999997 y2[1] (analytic) = 0.8084964038195919 y2[1] (numeric) = 0.8084964038195915 absolute error = 3.33066907387547e-16 relative error = 4.119584277852492e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.5885011172553434 y1[1] (numeric) = -0.5885011172553467 absolute error = 3.33066907387547e-15 relative error = 5.659579865216013e-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 = 0.4758 Order of pole (three term test) = 22.35 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4758 Order of pole (three term test) = 22.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.209999999999997 y2[1] (analytic) = 0.8025710662467491 y2[1] (numeric) = 0.8025710662467486 absolute error = 5.551115123125783e-16 relative error = 6.916664899328804e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.5965565217341574 y1[1] (numeric) = -0.596556521734161 absolute error = 3.552713678800501e-15 relative error = 5.955368099024306e-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 = 0.4788 Order of pole (three term test) = 22.36 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4788 Order of pole (three term test) = 22.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.219999999999997 y2[1] (analytic) = 0.7965654722360886 y2[1] (numeric) = 0.796565472236088 absolute error = 6.661338147750939e-16 relative error = 8.362574552787835e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.6045522710579269 y1[1] (numeric) = -0.6045522710579305 absolute error = 3.663735981263017e-15 relative error = 6.06024682506232e-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 = 0.4816 Order of pole (three term test) = 22.37 NO COMPLEX POLE (six term test) for Equation 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) = 22.63 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.229999999999996 y2[1] (analytic) = 0.790480222342007 y2[1] (numeric) = 0.7904802223420061 absolute error = 8.881784197001252e-16 relative error = 1.12359347469651e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.6124875656583824 y1[1] (numeric) = -0.6124875656583862 absolute error = 3.885780586188048e-15 relative error = 6.344260363899957e-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 = 0.4842 Order of pole (three term test) = 22.38 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4842 Order of pole (three term test) = 22.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.239999999999996 y2[1] (analytic) = 0.7843159250844224 y2[1] (numeric) = 0.7843159250844214 absolute error = 9.992007221626409e-16 relative error = 1.273977347910013e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.6203616120126767 y1[1] (numeric) = -0.6203616120126807 absolute error = 3.996802888650564e-15 relative error = 6.442698599101731e-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 = 0.4866 Order of pole (three term test) = 22.38 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4866 Order of pole (three term test) = 22.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.249999999999996 y2[1] (analytic) = 0.7780731968879238 y2[1] (numeric) = 0.7780731968879226 absolute error = 1.110223024625157e-15 relative error = 1.426887636106397e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.628173622722736 y1[1] (numeric) = -0.6281736227227401 absolute error = 4.107825191113079e-15 relative error = 6.539314995921431e-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 = 0.4888 Order of pole (three term test) = 22.39 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4888 Order of pole (three term test) = 22.61 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.259999999999996 y2[1] (analytic) = 0.7717526620201285 y2[1] (numeric) = 0.7717526620201273 absolute error = 1.221245327087672e-15 relative error = 1.582430987527738e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.6359228165939993 y1[1] (numeric) = -0.6359228165940036 absolute error = 4.329869796038111e-15 relative error = 6.808797676467846e-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 = 0.4908 Order of pole (three term test) = 22.4 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4908 Order of pole (three term test) = 22.6 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.269999999999996 y2[1] (analytic) = 0.7653549525292563 y2[1] (numeric) = 0.7653549525292549 absolute error = 1.443289932012704e-15 relative error = 1.885778523080155e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.6436084187135371 y1[1] (numeric) = -0.6436084187135416 absolute error = 4.440892098500626e-15 relative error = 6.899990692131106e-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 = 0.4926 Order of pole (three term test) = 22.41 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4926 Order of pole (three term test) = 22.59 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.279999999999995 y2[1] (analytic) = 0.7588807081809249 y2[1] (numeric) = 0.7588807081809233 absolute error = 1.554312234475219e-15 relative error = 2.048164115544568e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.6512296605275422 y1[1] (numeric) = -0.6512296605275467 absolute error = 4.551914400963142e-15 relative error = 6.989722177696527e-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 = 0.4942 Order of pole (three term test) = 22.42 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4942 Order of pole (three term test) = 22.58 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.289999999999995 y2[1] (analytic) = 0.7523305763941739 y2[1] (numeric) = 0.7523305763941721 absolute error = 1.77635683940025e-15 relative error = 2.361138700375712e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.6587857799181841 y1[1] (numeric) = -0.6587857799181888 absolute error = 4.662936703425657e-15 relative error = 7.078077344056753e-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 = 0.4956 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 Radius of convergence (three term test) for eq 2 = 0.4956 Order of pole (three term test) = 22.57 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.299999999999995 y2[1] (analytic) = 0.7457052121767236 y2[1] (numeric) = 0.7457052121767216 absolute error = 1.998401444325282e-15 relative error = 2.679881287797253e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.6662760212798204 y1[1] (numeric) = -0.6662760212798253 absolute error = 4.884981308350689e-15 relative error = 7.331768144630722e-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 = 0.4968 Order of pole (three term test) = 22.44 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4968 Order of pole (three term test) = 22.56 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.309999999999995 y2[1] (analytic) = 0.7390052780594745 y2[1] (numeric) = 0.7390052780594722 absolute error = 2.220446049250313e-15 relative error = 3.00464166518661e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.673699635594557 y1[1] (numeric) = -0.673699635594562 absolute error = 4.996003610813204e-15 relative error = 7.415773063917579e-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 = 0.4979 Order of pole (three term test) = 22.45 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4979 Order of pole (three term test) = 22.55 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.319999999999995 y2[1] (analytic) = 0.7322314440302551 y2[1] (numeric) = 0.7322314440302526 absolute error = 2.442490654175344e-15 relative error = 3.335681189449743e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.6810558805071486 y1[1] (numeric) = -0.6810558805071537 absolute error = 5.10702591327572e-15 relative error = 7.498688520937182e-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 = 0.4987 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 Radius of convergence (three term test) for eq 2 = 0.4987 Order of pole (three term test) = 22.54 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.329999999999994 y2[1] (analytic) = 0.7253843874668235 y2[1] (numeric) = 0.7253843874668209 absolute error = 2.664535259100376e-15 relative error = 3.67327351558451e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.6883440203992341 y1[1] (numeric) = -0.6883440203992394 absolute error = 5.218048215738236e-15 relative error = 7.5805818908862e-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 = 0.4993 Order of pole (three term test) = 22.47 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4993 Order of pole (three term test) = 22.53 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.339999999999994 y2[1] (analytic) = 0.7184647930691302 y2[1] (numeric) = 0.7184647930691275 absolute error = 2.775557561562891e-15 relative error = 3.863178249425827e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.6955633264628979 y1[1] (numeric) = -0.6955633264629032 absolute error = 5.329070518200751e-15 relative error = 7.661517385196717e-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 = 0.4997 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 Radius of convergence (three term test) for eq 2 = 0.4997 Order of pole (three term test) = 22.52 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.349999999999994 y2[1] (analytic) = 0.7114733527908488 y2[1] (numeric) = 0.7114733527908458 absolute error = 2.997602166487923e-15 relative error = 4.213231816384169e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.7027130767735495 y1[1] (numeric) = -0.702713076773555 absolute error = 5.440092820663267e-15 relative error = 7.741556263106721e-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 = 0.5 Order of pole (three term test) = 22.49 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5 Order of pole (three term test) = 22.51 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.359999999999994 y2[1] (analytic) = 0.7044107657701806 y2[1] (numeric) = 0.7044107657701775 absolute error = 3.108624468950438e-15 relative error = 4.413084836305087e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.7097925563621161 y1[1] (numeric) = -0.7097925563621217 absolute error = 5.551115123125783e-15 relative error = 7.820757027344424e-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 = 0.5 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.369999999999993 y2[1] (analytic) = 0.6972777382599425 y2[1] (numeric) = 0.6972777382599392 absolute error = 3.33066907387547e-15 relative error = 4.776674904589896e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.7168010572865383 y1[1] (numeric) = -0.716801057286544 absolute error = 5.662137425588298e-15 relative error = 7.899175605324033e-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 = 0.4998 Order of pole (three term test) = 22.51 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4998 Order of pole (three term test) = 22.49 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.379999999999993 y2[1] (analytic) = 0.6900749835569413 y2[1] (numeric) = 0.6900749835569377 absolute error = 3.552713678800501e-15 relative error = 5.148300928818339e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.723737878702564 y1[1] (numeric) = -0.7237378787025699 absolute error = 5.88418203051333e-15 relative error = 8.130266777057227e-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 = 0.4994 Order of pole (three term test) = 22.52 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4994 Order of pole (three term test) = 22.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.389999999999993 y2[1] (analytic) = 0.6828032219306449 y2[1] (numeric) = 0.6828032219306411 absolute error = 3.774758283725532e-15 relative error = 5.528325237031395e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.7306023269338324 y1[1] (numeric) = -0.7306023269338384 absolute error = 5.995204332975845e-15 relative error = 8.20583799416068e-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 = 0.4989 Order of pole (three term test) = 22.53 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4989 Order of pole (three term test) = 22.47 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.399999999999993 y2[1] (analytic) = 0.6754631805511563 y2[1] (numeric) = 0.6754631805511523 absolute error = 3.996802888650564e-15 relative error = 5.917129169630387e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.7373937155412407 y1[1] (numeric) = -0.7373937155412468 absolute error = 6.106226635438361e-15 relative error = 8.280822722982448e-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 = 0.4981 Order of pole (three term test) = 22.54 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4981 Order of pole (three term test) = 22.46 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.409999999999993 y2[1] (analytic) = 0.6680555934164966 y2[1] (numeric) = 0.6680555934164925 absolute error = 4.107825191113079e-15 relative error = 6.148927172520614e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.7441113653915875 y1[1] (numeric) = -0.7441113653915937 absolute error = 6.217248937900877e-15 relative error = 8.355266734340308e-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 = 0.4971 Order of pole (three term test) = 22.55 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4971 Order of pole (three term test) = 22.45 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.419999999999992 y2[1] (analytic) = 0.6605812012792064 y2[1] (numeric) = 0.6605812012792021 absolute error = 4.329869796038111e-15 relative error = 6.554636716354291e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.7507546047254859 y1[1] (numeric) = -0.7507546047254923 absolute error = 6.328271240363392e-15 relative error = 8.42921402084151e-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 = 0.4959 Order of pole (three term test) = 22.56 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4959 Order of pole (three term test) = 22.44 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.429999999999992 y2[1] (analytic) = 0.6530407515722708 y2[1] (numeric) = 0.6530407515722663 absolute error = 4.551914400963142e-15 relative error = 6.970337440663364e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.7573227692245386 y1[1] (numeric) = -0.757322769224545 absolute error = 6.439293542825908e-15 relative error = 8.502706909788846e-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 = 0.4946 Order of pole (three term test) = 22.57 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4946 Order of pole (three term test) = 22.43 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.439999999999992 y2[1] (analytic) = 0.6454349983343768 y2[1] (numeric) = 0.645434998334372 absolute error = 4.773959005888173e-15 relative error = 7.396498513727878e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.7638152020777689 y1[1] (numeric) = -0.7638152020777754 absolute error = 6.550315845288424e-15 relative error = 8.575786168526002e-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 = 0.493 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 Radius of convergence (three term test) for eq 2 = 0.493 Order of pole (three term test) = 22.42 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.449999999999992 y2[1] (analytic) = 0.6377647021345101 y2[1] (numeric) = 0.6377647021345051 absolute error = 4.996003610813204e-15 relative error = 7.833615742753201e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.7702312540473021 y1[1] (numeric) = -0.7702312540473086 absolute error = 6.550315845288424e-15 relative error = 8.5043495844511e-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 = 0.4912 Order of pole (three term test) = 22.59 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4912 Order of pole (three term test) = 22.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.459999999999992 y2[1] (analytic) = 0.6300306299958988 y2[1] (numeric) = 0.6300306299958935 absolute error = 5.218048215738236e-15 relative error = 8.282213542176835e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.7765702835332877 y1[1] (numeric) = -0.7765702835332944 absolute error = 6.661338147750939e-15 relative error = 8.577894736639637e-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 = 0.4893 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 Radius of convergence (three term test) for eq 2 = 0.4893 Order of pole (three term test) = 22.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.469999999999991 y2[1] (analytic) = 0.6222335553193116 y2[1] (numeric) = 0.6222335553193061 absolute error = 5.440092820663267e-15 relative error = 8.742847077527947e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.7828316566380599 y1[1] (numeric) = -0.7828316566380665 absolute error = 6.661338147750939e-15 relative error = 8.509285605999441e-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 = 0.4871 Order of pole (three term test) = 22.61 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4871 Order of pole (three term test) = 22.39 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.479999999999991 y2[1] (analytic) = 0.6143742578057187 y2[1] (numeric) = 0.6143742578057131 absolute error = 5.662137425588298e-15 relative error = 9.216104603423691e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.7890147472295257 y1[1] (numeric) = -0.7890147472295325 absolute error = 6.772360450213455e-15 relative error = 8.583312889896295e-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 = 0.4848 Order of pole (three term test) = 22.62 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4848 Order of pole (three term test) = 22.38 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.489999999999991 y2[1] (analytic) = 0.6064535233783221 y2[1] (numeric) = 0.6064535233783163 absolute error = 5.88418203051333e-15 relative error = 9.702610016567779e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.7951189370037787 y1[1] (numeric) = -0.7951189370037856 absolute error = 6.883382752675971e-15 relative error = 8.657047936267752e-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 = 0.4822 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 Radius of convergence (three term test) for eq 2 = 0.4822 Order of pole (three term test) = 22.37 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.499999999999991 y2[1] (analytic) = 0.598472144103964 y2[1] (numeric) = 0.5984721441039579 absolute error = 6.106226635438361e-15 relative error = 1.020302564721812e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8011436155469281 y1[1] (numeric) = -0.8011436155469351 absolute error = 6.994405055138486e-15 relative error = 8.730525862536539e-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 = 0.4795 Order of pole (three term test) = 22.64 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4795 Order of pole (three term test) = 22.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.50999999999999 y2[1] (analytic) = 0.5904309181139206 y2[1] (numeric) = 0.5904309181139142 absolute error = 6.328271240363392e-15 relative error = 1.071805531556257e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8070881803961404 y1[1] (numeric) = -0.8070881803961475 absolute error = 7.105427357601002e-15 relative error = 8.803780714659294e-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 = 0.4765 Order of pole (three term test) = 22.65 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4765 Order of pole (three term test) = 22.35 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.51999999999999 y2[1] (analytic) = 0.5823306495240899 y2[1] (numeric) = 0.5823306495240833 absolute error = 6.550315845288424e-15 relative error = 1.124844768284423e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8129520370998843 y1[1] (numeric) = -0.8129520370998915 absolute error = 7.216449660063518e-15 relative error = 8.87684553421798e-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 = 0.4734 Order of pole (three term test) = 22.66 NO COMPLEX POLE (six term test) for Equation 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) = 22.34 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.52999999999999 y2[1] (analytic) = 0.5741721483545806 y2[1] (numeric) = 0.5741721483545739 absolute error = 6.772360450213455e-15 relative error = 1.179499993098094e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.818734599277376 y1[1] (numeric) = -0.8187345992773832 absolute error = 7.216449660063518e-15 relative error = 8.814150112176563e-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 = 0.4701 Order of pole (three term test) = 22.67 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4701 Order of pole (three term test) = 22.33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.53999999999999 y2[1] (analytic) = 0.5659562304487112 y2[1] (numeric) = 0.5659562304487041 absolute error = 7.105427357601002e-15 relative error = 1.255472945667115e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8244352886772165 y1[1] (numeric) = -0.8244352886772238 absolute error = 7.327471962526033e-15 relative error = 8.887867929916923e-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 = 0.4666 Order of pole (three term test) = 22.68 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4666 Order of pole (three term test) = 22.32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.54999999999999 y2[1] (analytic) = 0.5576837173914255 y2[1] (numeric) = 0.5576837173914182 absolute error = 7.327471962526033e-15 relative error = 1.313911762889618e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8300535352352164 y1[1] (numeric) = -0.8300535352352237 absolute error = 7.327471962526033e-15 relative error = 8.827710083120857e-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 = 0.4629 Order of pole (three term test) = 22.69 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4629 Order of pole (three term test) = 22.31 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.559999999999989 y2[1] (analytic) = 0.5493554364271356 y2[1] (numeric) = 0.549355436427128 absolute error = 7.549516567451064e-15 relative error = 1.374249905771598e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8355887771314018 y1[1] (numeric) = -0.8355887771314091 absolute error = 7.327471962526033e-15 relative error = 8.769232142731066e-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 = 0.459 Order of pole (three term test) = 22.7 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.459 Order of pole (three term test) = 22.3 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.569999999999989 y2[1] (analytic) = 0.5409722203769975 y2[1] (numeric) = 0.5409722203769898 absolute error = 7.771561172376096e-15 relative error = 1.436591543824594e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8410404608461957 y1[1] (numeric) = -0.841040460846203 absolute error = 7.327471962526033e-15 relative error = 8.712389360142849e-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 = 0.455 Order of pole (three term test) = 22.71 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.455 Order of pole (three term test) = 22.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.579999999999989 y2[1] (analytic) = 0.5325349075556305 y2[1] (numeric) = 0.5325349075556225 absolute error = 7.993605777301127e-15 relative error = 1.50104822498722e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8464080412157696 y1[1] (numeric) = -0.8464080412157771 absolute error = 7.438494264988549e-15 relative error = 8.788307651595548e-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 = 0.4507 Order of pole (three term test) = 22.72 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4507 Order of pole (three term test) = 22.28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.589999999999989 y2[1] (analytic) = 0.5240443416872855 y2[1] (numeric) = 0.5240443416872773 absolute error = 8.215650382226158e-15 relative error = 1.567739545812844e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8516909814865598 y1[1] (numeric) = -0.8516909814865672 absolute error = 7.438494264988549e-15 relative error = 8.733794799617628e-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 = 0.4463 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 Radius of convergence (three term test) for eq 2 = 0.4463 Order of pole (three term test) = 22.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.599999999999989 y2[1] (analytic) = 0.515501371821474 y2[1] (numeric) = 0.5155013718214656 absolute error = 8.43769498715119e-15 relative error = 1.63679389587993e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8568887533689413 y1[1] (numeric) = -0.8568887533689488 absolute error = 7.438494264988549e-15 relative error = 8.68081677550719e-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 = 0.4417 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 Radius of convergence (three term test) for eq 2 = 0.4417 Order of pole (three term test) = 22.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.609999999999988 y2[1] (analytic) = 0.5069068522480634 y2[1] (numeric) = 0.5069068522480548 absolute error = 8.659739592076221e-15 relative error = 1.708349286199515e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8620008370900576 y1[1] (numeric) = -0.862000837090065 absolute error = 7.438494264988549e-15 relative error = 8.629335314916187e-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 = 0.437 Order of pole (three term test) = 22.74 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.437 Order of pole (three term test) = 22.26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.619999999999988 y2[1] (analytic) = 0.4982616424118489 y2[1] (numeric) = 0.4982616424118401 absolute error = 8.881784197001252e-15 relative error = 1.782554272893401e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8670267214457965 y1[1] (numeric) = -0.8670267214458039 absolute error = 7.438494264988549e-15 relative error = 8.579313740855192e-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 = 0.432 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 Radius of convergence (three term test) for eq 2 = 0.432 Order of pole (three term test) = 22.25 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.629999999999988 y2[1] (analytic) = 0.48956660682661 y2[1] (numeric) = 0.4895666068266009 absolute error = 9.103828801926284e-15 relative error = 1.859568989179565e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8719659038519106 y1[1] (numeric) = -0.8719659038519182 absolute error = 7.549516567451064e-15 relative error = 8.658041024426603e-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 = 0.4269 Order of pole (three term test) = 22.76 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4269 Order of pole (three term test) = 22.24 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.639999999999988 y2[1] (analytic) = 0.4808226149886591 y2[1] (numeric) = 0.4808226149886498 absolute error = 9.381384558082573e-15 relative error = 1.951111338285086e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8768178903942755 y1[1] (numeric) = -0.876817890394283 absolute error = 7.549516567451064e-15 relative error = 8.610130621372587e-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 = 0.4216 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 Radius of convergence (three term test) for eq 2 = 0.4216 Order of pole (three term test) = 22.23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.649999999999987 y2[1] (analytic) = 0.4720305412898936 y2[1] (numeric) = 0.472030541289884 absolute error = 9.658940314238862e-15 relative error = 2.046253254682287e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.88158219587828 y1[1] (numeric) = -0.8815821958782876 absolute error = 7.549516567451064e-15 relative error = 8.563599177419669e-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) = 22.78 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4161 Order of pole (three term test) = 22.22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.659999999999987 y2[1] (analytic) = 0.4631912649303566 y2[1] (numeric) = 0.4631912649303467 absolute error = 9.880984919163893e-15 relative error = 2.133240772718276e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.886258343877346 y1[1] (numeric) = -0.8862583438773537 absolute error = 7.66053886991358e-15 relative error = 8.643686034479538e-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 = 0.4105 Order of pole (three term test) = 22.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4105 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.669999999999987 y2[1] (analytic) = 0.4543056698303179 y2[1] (numeric) = 0.4543056698303078 absolute error = 1.015854067532018e-14 relative error = 2.236058528416423e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8908458667805706 y1[1] (numeric) = -0.8908458667805782 absolute error = 7.549516567451064e-15 relative error = 8.474548571162232e-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 = 0.4047 Order of pole (three term test) = 22.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4047 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.679999999999987 y2[1] (analytic) = 0.4453746445418831 y2[1] (numeric) = 0.4453746445418727 absolute error = 1.038058528024521e-14 relative error = 2.33075353692907e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8953443058394861 y1[1] (numeric) = -0.8953443058394938 absolute error = 7.66053886991358e-15 relative error = 8.555969831886028e-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 = 0.3988 Order of pole (three term test) = 22.8 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3988 Order of pole (three term test) = 22.2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.689999999999987 y2[1] (analytic) = 0.4363990821601383 y2[1] (numeric) = 0.4363990821601277 absolute error = 1.060262988517024e-14 relative error = 2.429571994672429e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8997532112139355 y1[1] (numeric) = -0.8997532112139431 absolute error = 7.66053886991358e-15 relative error = 8.51404448957518e-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 = 0.3927 Order of pole (three term test) = 22.81 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3927 Order of pole (three term test) = 22.19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.699999999999986 y2[1] (analytic) = 0.4273798802338422 y2[1] (numeric) = 0.4273798802338313 absolute error = 1.088018564132653e-14 relative error = 2.545787985006081e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9040721420170553 y1[1] (numeric) = -0.904072142017063 absolute error = 7.66053886991358e-15 relative error = 8.473371221042518e-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 = 0.3864 Order of pole (three term test) = 22.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3864 Order of pole (three term test) = 22.18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.709999999999986 y2[1] (analytic) = 0.4183179406756715 y2[1] (numeric) = 0.4183179406756603 absolute error = 1.115774139748282e-14 relative error = 2.667287322045218e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9083006663593644 y1[1] (numeric) = -0.908300666359372 absolute error = 7.66053886991358e-15 relative error = 8.433924088835501e-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 = 0.38 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.38 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.719999999999986 y2[1] (analytic) = 0.4092141696720303 y2[1] (numeric) = 0.4092141696720188 absolute error = 1.143529715363911e-14 relative error = 2.794452880945953e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9124383613919522 y1[1] (numeric) = -0.9124383613919598 absolute error = 7.549516567451064e-15 relative error = 8.274001715506623e-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 = 0.3734 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3734 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.729999999999986 y2[1] (analytic) = 0.4000694775924326 y2[1] (numeric) = 0.4000694775924209 absolute error = 1.165734175856414e-14 relative error = 2.91382932502538e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9164848133487636 y1[1] (numeric) = -0.9164848133487712 absolute error = 7.549516567451064e-15 relative error = 8.237470449581944e-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 = 0.3667 Order of pole (three term test) = 22.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3667 Order of pole (three term test) = 22.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.739999999999986 y2[1] (analytic) = 0.3908847788984657 y2[1] (numeric) = 0.3908847788984538 absolute error = 1.187938636348917e-14 relative error = 3.039101803085279e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.920439617587975 y1[1] (numeric) = -0.9204396175879824 absolute error = 7.438494264988549e-15 relative error = 8.081458167219299e-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 = 0.3598 Order of pole (three term test) = 22.85 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3598 Order of pole (three term test) = 22.15 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.749999999999985 y2[1] (analytic) = 0.3816609920523453 y2[1] (numeric) = 0.3816609920523331 absolute error = 1.221245327087672e-14 relative error = 3.199816990781643e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9243023786324579 y1[1] (numeric) = -0.9243023786324653 absolute error = 7.438494264988549e-15 relative error = 8.047684866930773e-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 = 0.3528 Order of pole (three term test) = 22.85 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3528 Order of pole (three term test) = 22.15 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.759999999999985 y2[1] (analytic) = 0.3723990394250693 y2[1] (numeric) = 0.3723990394250569 absolute error = 1.243449787580175e-14 relative error = 3.339025228152799e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9280727102093271 y1[1] (numeric) = -0.9280727102093345 absolute error = 7.327471962526033e-15 relative error = 7.89536410447121e-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 = 0.3456 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3456 Order of pole (three term test) = 22.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.769999999999985 y2[1] (analytic) = 0.3630998472041824 y2[1] (numeric) = 0.3630998472041697 absolute error = 1.271205363195804e-14 relative error = 3.500980165604327e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9317502352885667 y1[1] (numeric) = -0.931750235288574 absolute error = 7.327471962526033e-15 relative error = 7.864201891246839e-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 = 0.3383 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 Radius of convergence (three term test) for eq 2 = 0.3383 Order of pole (three term test) = 22.13 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.779999999999985 y2[1] (analytic) = 0.3537643453011572 y2[1] (numeric) = 0.3537643453011443 absolute error = 1.298960938811433e-14 relative error = 3.671825485142196e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9353345861207334 y1[1] (numeric) = -0.9353345861207406 absolute error = 7.216449660063518e-15 relative error = 7.715367064521246e-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 = 0.3309 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 Radius of convergence (three term test) for eq 2 = 0.3309 Order of pole (three term test) = 22.13 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.789999999999984 y2[1] (analytic) = 0.3443934672584046 y2[1] (numeric) = 0.3443934672583914 absolute error = 1.321165399303936e-14 relative error = 3.836209234226392e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9388254042737308 y1[1] (numeric) = -0.9388254042737381 absolute error = 7.216449660063518e-15 relative error = 7.686679149512487e-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 = 0.3233 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3233 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.799999999999984 y2[1] (analytic) = 0.3349881501559197 y2[1] (numeric) = 0.3349881501559063 absolute error = 1.343369859796439e-14 relative error = 4.010201134491384e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9422223406686528 y1[1] (numeric) = -0.9422223406686601 absolute error = 7.216449660063518e-15 relative error = 7.658966836789635e-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 = 0.3156 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 Radius of convergence (three term test) for eq 2 = 0.3156 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.809999999999984 y2[1] (analytic) = 0.3255493345175751 y2[1] (numeric) = 0.3255493345175614 absolute error = 1.371125435412068e-14 relative error = 4.21172857700327e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9455250556146907 y1[1] (numeric) = -0.9455250556146978 absolute error = 7.105427357601002e-15 relative error = 7.514795420182416e-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 = 0.3078 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 Radius of convergence (three term test) for eq 2 = 0.3078 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.819999999999984 y2[1] (analytic) = 0.316077964217069 y2[1] (numeric) = 0.316077964217055 absolute error = 1.393329895904571e-14 relative error = 4.408184225546617e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.948733218843102 y1[1] (numeric) = -0.948733218843109 absolute error = 6.994405055138486e-15 relative error = 7.372362341931652e-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 = 0.2999 Order of pole (three term test) = 22.9 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2999 Order of pole (three term test) = 22.1 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.829999999999984 y2[1] (analytic) = 0.3065749863835386 y2[1] (numeric) = 0.3065749863835243 absolute error = 1.426636586643326e-14 relative error = 4.653467014619849e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9518465095402373 y1[1] (numeric) = -0.9518465095402443 absolute error = 6.994405055138486e-15 relative error = 7.348248887855813e-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 = 0.2918 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 Radius of convergence (three term test) for eq 2 = 0.2918 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.839999999999983 y2[1] (analytic) = 0.2970413513068481 y2[1] (numeric) = 0.2970413513068336 absolute error = 1.454392162258955e-14 relative error = 4.896261600818488e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9548646163796215 y1[1] (numeric) = -0.9548646163796284 absolute error = 6.883382752675971e-15 relative error = 7.208752565127382e-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 = 0.2836 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 Radius of convergence (three term test) for eq 2 = 0.2836 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.849999999999983 y2[1] (analytic) = 0.2874780123425605 y2[1] (numeric) = 0.2874780123425458 absolute error = 1.476596622751458e-14 relative error = 5.136381077353272e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9577872375530855 y1[1] (numeric) = -0.9577872375530924 absolute error = 6.883382752675971e-15 relative error = 7.186755557801488e-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 = 0.2753 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2753 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.859999999999983 y2[1] (analytic) = 0.277885925816603 y2[1] (numeric) = 0.2778859258165879 absolute error = 1.504352198367087e-14 relative error = 5.413560236799895e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9606140808009476 y1[1] (numeric) = -0.9606140808009543 absolute error = 6.772360450213455e-15 relative error = 7.050032458994093e-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 = 0.2669 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2669 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.869999999999983 y2[1] (analytic) = 0.2682660509296346 y2[1] (numeric) = 0.2682660509296193 absolute error = 1.532107773982716e-14 relative error = 5.711150436939124e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9633448634412386 y1[1] (numeric) = -0.9633448634412453 absolute error = 6.661338147750939e-15 relative error = 6.914801127350655e-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 = 0.2584 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2584 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.879999999999983 y2[1] (analytic) = 0.2586193496611275 y2[1] (numeric) = 0.258619349661112 absolute error = 1.554312234475219e-14 relative error = 6.010038446511661e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9659793123979703 y1[1] (numeric) = -0.9659793123979769 absolute error = 6.550315845288424e-15 relative error = 6.781010484611479e-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 = 0.2498 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2498 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.889999999999982 y2[1] (analytic) = 0.2489467866731698 y2[1] (numeric) = 0.248946786673154 absolute error = 1.579292252529285e-14 relative error = 6.343894908764827e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9685171642284423 y1[1] (numeric) = -0.9685171642284487 absolute error = 6.439293542825908e-15 relative error = 6.64861066035489e-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 = 0.2411 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2411 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.899999999999982 y2[1] (analytic) = 0.2392493292139997 y2[1] (numeric) = 0.2392493292139836 absolute error = 1.604272270583351e-14 relative error = 6.70544103865967e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9709581651495862 y1[1] (numeric) = -0.9709581651495927 absolute error = 6.439293542825908e-15 relative error = 6.631895970341697e-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 = 0.2323 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2323 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.909999999999982 y2[1] (analytic) = 0.2295279470212819 y2[1] (numeric) = 0.2295279470212656 absolute error = 1.63202784619898e-14 relative error = 7.110366590991457e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9733020710633444 y1[1] (numeric) = -0.9733020710633508 absolute error = 6.328271240363392e-15 relative error = 6.501857366284733e-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 = 0.2234 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2234 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.919999999999982 y2[1] (analytic) = 0.2197836122251347 y2[1] (numeric) = 0.2197836122251181 absolute error = 1.657007864253046e-14 relative error = 7.539269409020791e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9755486475810786 y1[1] (numeric) = -0.9755486475810848 absolute error = 6.217248937900877e-15 relative error = 6.373079347008327e-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 = 0.2144 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2144 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.929999999999982 y2[1] (analytic) = 0.2100172992509174 y2[1] (numeric) = 0.2100172992509005 absolute error = 1.684763439868675e-14 relative error = 8.022022213778733e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9776976700470092 y1[1] (numeric) = -0.9776976700470154 absolute error = 6.106226635438361e-15 relative error = 6.245516198422324e-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 = 0.2053 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2053 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.939999999999981 y2[1] (analytic) = 0.2002299847217888 y2[1] (numeric) = 0.2002299847217717 absolute error = 1.709743457922741e-14 relative error = 8.538898208968842e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9797489235606806 y1[1] (numeric) = -0.9797489235606864 absolute error = 5.88418203051333e-15 relative error = 6.005806068281834e-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 = 0.1962 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1962 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.949999999999981 y2[1] (analytic) = 0.1904226473610458 y2[1] (numeric) = 0.1904226473610284 absolute error = 1.73749903353837e-14 relative error = 9.124434817062653e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9817022029984505 y1[1] (numeric) = -0.9817022029984562 absolute error = 5.773159728050814e-15 relative error = 5.880764767989348e-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 = 0.1869 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1869 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.959999999999981 y2[1] (analytic) = 0.1805962678942517 y2[1] (numeric) = 0.1805962678942341 absolute error = 1.762479051592436e-14 relative error = 9.759221893912321e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.983557313034003 y1[1] (numeric) = -0.9835573130340086 absolute error = 5.662137425588298e-15 relative error = 5.756794597075555e-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 = 0.1776 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1776 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.969999999999981 y2[1] (analytic) = 0.1707518289511646 y2[1] (numeric) = 0.1707518289511467 absolute error = 1.787459069646502e-14 relative error = 1.046816939312386e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9853140681578805 y1[1] (numeric) = -0.9853140681578859 absolute error = 5.440092820663267e-15 relative error = 5.521176441572517e-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 = 0.1682 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1682 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.97999999999998 y2[1] (analytic) = 0.1608903149674751 y2[1] (numeric) = 0.1608903149674569 absolute error = 1.812439087700568e-14 relative error = 1.126506022483058e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9869722926960345 y1[1] (numeric) = -0.9869722926960398 absolute error = 5.329070518200751e-15 relative error = 5.399412483651136e-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 = 0.1588 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1588 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.98999999999998 y2[1] (analytic) = 0.1510127120863636 y2[1] (numeric) = 0.1510127120863452 absolute error = 1.840194663316197e-14 relative error = 1.218569375976637e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.988531820827393 y1[1] (numeric) = -0.9885318208273982 absolute error = 5.218048215738236e-15 relative error = 5.27858396239665e-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 = 0.1493 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1493 Order of pole (three term test) = 22.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.99999999999998 y2[1] (analytic) = 0.141120008059887 y2[1] (numeric) = 0.1411200080598684 absolute error = 1.865174681370263e-14 relative error = 1.32169400144786e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9899924966004426 y1[1] (numeric) = -0.9899924966004476 absolute error = 4.996003610813204e-15 relative error = 5.04650654219006e-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 = 0.1397 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1397 Order of pole (three term test) = 22.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.00999999999998 y2[1] (analytic) = 0.131213192150204 y2[1] (numeric) = 0.1312131921501851 absolute error = 1.890154699424329e-14 relative error = 1.44052184727021e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9913541739488232 y1[1] (numeric) = -0.9913541739488281 absolute error = 4.884981308350689e-15 relative error = 4.927584345453986e-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 = 0.1301 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1301 Order of pole (three term test) = 22.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.01999999999998 y2[1] (analytic) = 0.12129325503065 y2[1] (numeric) = 0.1212932550306309 absolute error = 1.915134717478395e-14 relative error = 1.578929279286348e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9926167167059347 y1[1] (numeric) = -0.9926167167059393 absolute error = 4.662936703425657e-15 relative error = 4.697620566878953e-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 = 0.1204 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1204 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.029999999999979 y2[1] (analytic) = 0.1113611886866703 y2[1] (numeric) = 0.1113611886866509 absolute error = 1.940114735532461e-14 relative error = 1.742182135816846e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9937799986185533 y1[1] (numeric) = -0.9937799986185578 absolute error = 4.551914400963142e-15 relative error = 4.580404523426439e-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 = 0.1107 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1107 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.039999999999979 y2[1] (analytic) = 0.1014179863166226 y2[1] (numeric) = 0.101417986316603 absolute error = 1.965094753586527e-14 relative error = 1.937619573170764e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9948439033594574 y1[1] (numeric) = -0.9948439033594617 absolute error = 4.329869796038111e-15 relative error = 4.35231073077566e-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 = 0.1009 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1009 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.049999999999979 y2[1] (analytic) = 0.09146464223245798 y2[1] (numeric) = 0.09146464223243808 absolute error = 1.990074771640593e-14 relative error = 2.175785880824642e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9958083245390593 y1[1] (numeric) = -0.9958083245390634 absolute error = 4.107825191113079e-15 relative error = 4.125116340049189e-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 = 0.09108 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09108 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.059999999999979 y2[1] (analytic) = 0.08150215176029037 y2[1] (numeric) = 0.08150215176027023 absolute error = 2.013667010913878e-14 relative error = 2.470691837482235e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9966731657160448 y1[1] (numeric) = -0.9966731657160488 absolute error = 3.996802888650564e-15 relative error = 4.010143973103882e-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 = 0.08123 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08123 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.069999999999979 y2[1] (analytic) = 0.07153151114086496 y2[1] (numeric) = 0.07153151114084458 absolute error = 2.038647028967944e-14 relative error = 2.849998548126985e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.997438340407017 y1[1] (numeric) = -0.9974383404070207 absolute error = 3.774758283725532e-15 relative error = 3.784452763451218e-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 = 0.07135 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07135 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.079999999999978 y2[1] (analytic) = 0.06155371742993487 y2[1] (numeric) = 0.06155371742991424 absolute error = 2.062933157631619e-14 relative error = 3.351435532678927e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9981037720951443 y1[1] (numeric) = -0.9981037720951478 absolute error = 3.441691376337985e-15 relative error = 3.448230006298289e-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 = 0.06144 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 Radius of convergence (three term test) for eq 2 = 0.06144 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.089999999999978 y2[1] (analytic) = 0.05156976839855636 y2[1] (numeric) = 0.0515697683985355 absolute error = 2.086525396904904e-14 relative error = 4.04602436989675e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9986693942378124 y1[1] (numeric) = -0.9986693942378158 absolute error = 3.33066907387547e-15 relative error = 3.335106786182675e-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 = 0.0515 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 Radius of convergence (three term test) for eq 2 = 0.0515 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.099999999999978 y2[1] (analytic) = 0.04158066243331267 y2[1] (numeric) = 0.04158066243329157 absolute error = 2.110811525568579e-14 relative error = 5.076425920231337e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9991351502732786 y1[1] (numeric) = -0.9991351502732817 absolute error = 3.108624468950438e-15 relative error = 3.111315289127985e-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 = 0.04154 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 Radius of convergence (three term test) for eq 2 = 0.04154 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.109999999999978 y2[1] (analytic) = 0.03158739843647609 y2[1] (numeric) = 0.03158739843645474 absolute error = 2.135097654232254e-14 relative error = 6.759333658091682e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9995009936263272 y1[1] (numeric) = -0.9995009936263302 absolute error = 2.997602166487923e-15 relative error = 2.999098735872397e-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 = 0.03157 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 Radius of convergence (three term test) for eq 2 = 0.03157 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.119999999999977 y2[1] (analytic) = 0.0215909757261186 y2[1] (numeric) = 0.02159097572609702 absolute error = 2.157996004115148e-14 relative error = 9.994898014287611e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9997668877129279 y1[1] (numeric) = -0.9997668877129307 absolute error = 2.775557561562891e-15 relative error = 2.776204728996648e-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 = 0.02159 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 Radius of convergence (three term test) for eq 2 = 0.02159 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.129999999999977 y2[1] (analytic) = 0.01159239393618092 y2[1] (numeric) = 0.01159239393615911 absolute error = 2.181414771040835e-14 relative error = 1.881763838470361e-10 % Correct digits = 12 h = 0.01 y1[1] (analytic) = -0.9999328059438936 y1[1] (numeric) = -0.9999328059438961 absolute error = 2.55351295663786e-15 relative error = 2.553684549060728e-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 = 0.01159 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 Radius of convergence (three term test) for eq 2 = 0.01159 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.139999999999977 y2[1] (analytic) = 0.001592652916509921 y2[1] (numeric) = 0.001592652916487877 absolute error = 2.204399857097528e-14 relative error = 1.38410562291762e-09 % Correct digits = 11 h = 0.01 y1[1] (analytic) = -0.9999987317275395 y1[1] (numeric) = -0.9999987317275418 absolute error = 2.331468351712829e-15 relative error = 2.331471308653682e-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 = 0.001593 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 Radius of convergence (three term test) for eq 2 = 0.001593 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.149999999999977 y2[1] (analytic) = -0.008407247367125526 y2[1] (numeric) = -0.008407247367147798 absolute error = 2.227211470806623e-14 relative error = 2.649156583063781e-10 % Correct digits = 12 h = 0.01 y1[1] (analytic) = -0.9999646584713422 y1[1] (numeric) = -0.9999646584713443 absolute error = 2.109423746787797e-15 relative error = 2.109498299682409e-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 = 0.008407 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 Radius of convergence (three term test) for eq 2 = 0.008407 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.159999999999977 y2[1] (analytic) = -0.01840630693303028 y2[1] (numeric) = -0.01840630693305277 absolute error = 2.249589403646723e-14 relative error = 1.222184011073843e-10 % Correct digits = 12 h = 0.01 y1[1] (analytic) = -0.9998305895825987 y1[1] (numeric) = -0.9998305895826007 absolute error = 1.998401444325282e-15 relative error = 1.998740051711719e-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 = 0.0184 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 Radius of convergence (three term test) for eq 2 = 0.0184 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.169999999999976 y2[1] (analytic) = -0.02840352588358026 y2[1] (numeric) = -0.02840352588360298 absolute error = 2.272140808834422e-14 relative error = 7.999502660857748e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9995965384680865 y1[1] (numeric) = -0.9995965384680883 absolute error = 1.77635683940025e-15 relative error = 1.777073820326123e-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 = 0.02839 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 Radius of convergence (three term test) for eq 2 = 0.02839 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.179999999999976 y2[1] (analytic) = -0.03839790450521142 y2[1] (numeric) = -0.03839790450523436 absolute error = 2.29399832463173e-14 relative error = 5.974279987910239e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9992625285327218 y1[1] (numeric) = -0.9992625285327233 absolute error = 1.554312234475219e-15 relative error = 1.555459341357982e-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 = 0.03837 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 Radius of convergence (three term test) for eq 2 = 0.03837 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.189999999999976 y2[1] (analytic) = -0.0483884433683902 y2[1] (numeric) = -0.04838844336841336 absolute error = 2.316202785124233e-14 relative error = 4.786685877639318e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9988285931772198 y1[1] (numeric) = -0.9988285931772212 absolute error = 1.332267629550188e-15 relative error = 1.333830087214781e-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 = 0.04833 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 Radius of convergence (three term test) for eq 2 = 0.04833 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.199999999999976 y2[1] (analytic) = -0.0583741434275557 y2[1] (numeric) = -0.05837414342757909 absolute error = 2.338407245616736e-14 relative error = 4.005895604307717e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9982947757947545 y1[1] (numeric) = -0.9982947757947556 absolute error = 1.110223024625157e-15 relative error = 1.112119437609292e-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 = 0.05827 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 Radius of convergence (three term test) for eq 2 = 0.05827 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.209999999999976 y2[1] (analytic) = -0.06835400612102341 y2[1] (numeric) = -0.06835400612104701 absolute error = 2.360611706109239e-14 relative error = 3.453508931034247e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9976611297666192 y1[1] (numeric) = -0.99766112976662 absolute error = 7.771561172376096e-16 relative error = 7.789780458013916e-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 = 0.06819 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 Radius of convergence (three term test) for eq 2 = 0.06819 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.219999999999975 y2[1] (analytic) = -0.07832703347084051 y2[1] (numeric) = -0.07832703347086431 absolute error = 2.380040609040179e-14 relative error = 3.038594088880205e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9969277184568889 y1[1] (numeric) = -0.9969277184568893 absolute error = 4.440892098500626e-16 relative error = 4.454577815706173e-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 = 0.07809 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07809 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.229999999999975 y2[1] (analytic) = -0.08829222818258282 y2[1] (numeric) = -0.08829222818260683 absolute error = 2.400857290751901e-14 relative error = 2.719217013967614e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9960946152060831 y1[1] (numeric) = -0.9960946152060833 absolute error = 2.220446049250313e-16 relative error = 2.229151744576917e-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 = 0.08795 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08795 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.239999999999975 y2[1] (analytic) = -0.09824859374508349 y2[1] (numeric) = -0.09824859374510771 absolute error = 2.421673972463623e-14 relative error = 2.464843393837184e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9951619033238328 y1[1] (numeric) = -0.9951619033238328 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 Radius of convergence (three term test) for eq 1 = 0.09777 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09777 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.249999999999975 y2[1] (analytic) = -0.1081951345300832 y2[1] (numeric) = -0.1081951345301076 absolute error = 2.441102875394563e-14 relative error = 2.25620392820513e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9941296760805489 y1[1] (numeric) = -0.9941296760805487 absolute error = 2.220446049250313e-16 relative error = 2.233557756775387e-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 = 0.1076 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1076 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.259999999999974 y2[1] (analytic) = -0.1181308558917922 y2[1] (numeric) = -0.1181308558918168 absolute error = 2.461919557106285e-14 relative error = 2.084061389821302e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9929980366980957 y1[1] (numeric) = -0.9929980366980952 absolute error = 5.551115123125783e-16 relative error = 5.590257903816486e-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 = 0.1173 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1173 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.269999999999974 y2[1] (analytic) = -0.1280547642663541 y2[1] (numeric) = -0.1280547642663789 absolute error = 2.481348460037225e-14 relative error = 1.937724437082259e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9917670983394682 y1[1] (numeric) = -0.9917670983394674 absolute error = 7.771561172376096e-16 relative error = 7.836074805655629e-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 = 0.127 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.127 Order of pole (three term test) = 22.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.279999999999974 y2[1] (analytic) = -0.1379658672712013 y2[1] (numeric) = -0.1379658672712263 absolute error = 2.500777362968165e-14 relative error = 1.812605836813502e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9904369840974767 y1[1] (numeric) = -0.9904369840974756 absolute error = 1.110223024625157e-15 relative error = 1.120942616694421e-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 = 0.1366 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1366 Order of pole (three term test) = 22.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.289999999999974 y2[1] (analytic) = -0.1478631738042926 y2[1] (numeric) = -0.1478631738043178 absolute error = 2.520206265899105e-14 relative error = 1.704417808070843e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9890078269824367 y1[1] (numeric) = -0.9890078269824354 absolute error = 1.332267629550188e-15 relative error = 1.347074910028843e-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 = 0.1462 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1462 Order of pole (three term test) = 22.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.299999999999974 y2[1] (analytic) = -0.1577456941432223 y2[1] (numeric) = -0.1577456941432477 absolute error = 2.536859611268483e-14 relative error = 1.608195789461731e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9874797699088691 y1[1] (numeric) = -0.9874797699088674 absolute error = 1.665334536937735e-15 relative error = 1.686449269833064e-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 = 0.1558 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1558 Order of pole (three term test) = 22.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.309999999999973 y2[1] (analytic) = -0.167612440044192 y2[1] (numeric) = -0.1676124400442176 absolute error = 2.556288514199423e-14 relative error = 1.525118609051597e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9858529656812075 y1[1] (numeric) = -0.9858529656812056 absolute error = 1.887379141862766e-15 relative error = 1.91446311728506e-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 = 0.1652 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1652 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.319999999999973 y2[1] (analytic) = -0.1774624248408339 y2[1] (numeric) = -0.1774624248408596 absolute error = 2.5729418595688e-14 relative error = 1.449851630212127e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9841275769785193 y1[1] (numeric) = -0.984127576978517 absolute error = 2.220446049250313e-15 relative error = 2.256258336005129e-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 = 0.1746 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1746 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.329999999999973 y2[1] (analytic) = -0.1872946635428766 y2[1] (numeric) = -0.1872946635429025 absolute error = 2.589595204938178e-14 relative error = 1.382631600897349e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9823037763382367 y1[1] (numeric) = -0.9823037763382343 absolute error = 2.442490654175344e-15 relative error = 2.486492175852454e-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 = 0.184 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.184 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.339999999999973 y2[1] (analytic) = -0.1971081729346433 y2[1] (numeric) = -0.1971081729346694 absolute error = 2.606248550307555e-14 relative error = 1.322242762187101e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9803817461389042 y1[1] (numeric) = -0.9803817461389014 absolute error = 2.775557561562891e-15 relative error = 2.831098776057423e-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 = 0.1932 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1932 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.349999999999973 y2[1] (analytic) = -0.2069019716733728 y2[1] (numeric) = -0.2069019716733991 absolute error = 2.625677453238495e-14 relative error = 1.269044191315653e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9783616785819398 y1[1] (numeric) = -0.9783616785819367 absolute error = 3.108624468950438e-15 relative error = 3.177377586432198e-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 = 0.2024 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2024 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.359999999999972 y2[1] (analytic) = -0.2166750803873528 y2[1] (numeric) = -0.2166750803873792 absolute error = 2.642330798607873e-14 relative error = 1.219489935752715e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9762437756724158 y1[1] (numeric) = -0.9762437756724125 absolute error = 3.33066907387547e-15 relative error = 3.411718626919159e-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 = 0.2115 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2115 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.369999999999972 y2[1] (analytic) = -0.2264265217738559 y2[1] (numeric) = -0.2264265217738825 absolute error = 2.661759701538813e-14 relative error = 1.17555120340419e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9740282491988584 y1[1] (numeric) = -0.9740282491988548 absolute error = 3.663735981263017e-15 relative error = 3.761426821323151e-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 = 0.2205 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2205 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.379999999999972 y2[1] (analytic) = -0.2361553206968698 y2[1] (numeric) = -0.2361553206968966 absolute error = 2.675637489346627e-14 relative error = 1.132999028542359e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9717153207120687 y1[1] (numeric) = -0.9717153207120647 absolute error = 3.996802888650564e-15 relative error = 4.113141784902315e-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 = 0.2295 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2295 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.389999999999972 y2[1] (analytic) = -0.2458605042846095 y2[1] (numeric) = -0.2458605042846364 absolute error = 2.692290834716005e-14 relative error = 1.095048121921768e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9693052215029678 y1[1] (numeric) = -0.9693052215029635 absolute error = 4.329869796038111e-15 relative error = 4.466982845015917e-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 = 0.2383 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2383 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.399999999999971 y2[1] (analytic) = -0.2555411020268037 y2[1] (numeric) = -0.2555411020268308 absolute error = 2.708944180085382e-14 relative error = 1.060081591023757e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9667981925794683 y1[1] (numeric) = -0.9667981925794636 absolute error = 4.662936703425657e-15 relative error = 4.823071390922544e-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 = 0.2471 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2471 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.409999999999971 y2[1] (analytic) = -0.2651961458717456 y2[1] (numeric) = -0.2651961458717728 absolute error = 2.725597525454759e-14 relative error = 1.027766642873051e-11 % Correct digits = 13 h = 0.01 y1[1] (analytic) = -0.9641944846423733 y1[1] (numeric) = -0.9641944846423683 absolute error = 4.996003610813204e-15 relative error = 5.181530998558095e-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 = 0.2557 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2557 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.419999999999971 y2[1] (analytic) = -0.2748246703230963 y2[1] (numeric) = -0.2748246703231236 absolute error = 2.736699755701011e-14 relative error = 9.957984312265793e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9614943580603068 y1[1] (numeric) = -0.9614943580603015 absolute error = 5.329070518200751e-15 relative error = 5.542487559626951e-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 = 0.2642 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 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) = 22.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.429999999999971 y2[1] (analytic) = -0.2844257125364344 y2[1] (numeric) = -0.2844257125364619 absolute error = 2.747801985947262e-14 relative error = 9.660877567794697e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9586980828436769 y1[1] (numeric) = -0.9586980828436712 absolute error = 5.662137425588298e-15 relative error = 5.906069415298449e-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 = 0.2727 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2727 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.439999999999971 y2[1] (analytic) = -0.2939983124155396 y2[1] (numeric) = -0.2939983124155672 absolute error = 2.76445533131664e-14 relative error = 9.402963263984101e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.955805938617675 y1[1] (numeric) = -0.955805938617669 absolute error = 5.995204332975845e-15 relative error = 6.272407494816731e-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 = 0.281 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 Radius of convergence (three term test) for eq 2 = 0.281 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.44999999999997 y2[1] (analytic) = -0.303541512708401 y2[1] (numeric) = -0.3035415127084288 absolute error = 2.781108676686017e-14 relative error = 9.162202072036541e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9528182145943137 y1[1] (numeric) = -0.9528182145943074 absolute error = 6.328271240363392e-15 relative error = 6.641635459349203e-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 = 0.2892 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 Radius of convergence (three term test) for eq 2 = 0.2892 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.45999999999997 y2[1] (analytic) = -0.3130543591029419 y2[1] (numeric) = -0.3130543591029699 absolute error = 2.792210906932269e-14 relative error = 8.919252601795279e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9497352095435054 y1[1] (numeric) = -0.9497352095434988 absolute error = 6.661338147750939e-15 relative error = 7.013889851417367e-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 = 0.2973 Order of pole (three term test) = 22.9 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2973 Order of pole (three term test) = 22.1 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.46999999999997 y2[1] (analytic) = -0.3225359003224504 y2[1] (numeric) = -0.3225359003224784 absolute error = 2.80331313717852e-14 relative error = 8.691476311244579e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9465572317631863 y1[1] (numeric) = -0.9465572317631792 absolute error = 7.105427357601002e-15 relative error = 7.506600889167014e-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 = 0.3053 Order of pole (three term test) = 22.9 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3053 Order of pole (three term test) = 22.1 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.47999999999997 y2[1] (analytic) = -0.3319851882207056 y2[1] (numeric) = -0.3319851882207338 absolute error = 2.814415367424772e-14 relative error = 8.477532936058981e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9432845990484858 y1[1] (numeric) = -0.9432845990484784 absolute error = 7.438494264988549e-15 relative error = 7.885737000786337e-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 = 0.3132 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 Radius of convergence (three term test) for eq 2 = 0.3132 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.48999999999997 y2[1] (analytic) = -0.3414012778767921 y2[1] (numeric) = -0.3414012778768204 absolute error = 2.825517597671023e-14 relative error = 8.276236150149152e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9399176386599484 y1[1] (numeric) = -0.9399176386599406 absolute error = 7.771561172376096e-15 relative error = 8.268342727833156e-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 = 0.3209 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3209 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.499999999999969 y2[1] (analytic) = -0.3507832276895911 y2[1] (numeric) = -0.3507832276896195 absolute error = 2.836619827917275e-14 relative error = 8.086532091629552e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9364566872908071 y1[1] (numeric) = -0.9364566872907989 absolute error = 8.215650382226158e-15 relative error = 8.77312372662343e-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 = 0.3285 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3285 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.509999999999969 y2[1] (analytic) = -0.3601300994719396 y2[1] (numeric) = -0.360130099471968 absolute error = 2.842170943040401e-14 relative error = 7.892067192405992e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9329020910333147 y1[1] (numeric) = -0.9329020910333061 absolute error = 8.548717289613705e-15 relative error = 9.163573939624094e-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 = 0.336 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 Radius of convergence (three term test) for eq 2 = 0.336 Order of pole (three term test) = 22.13 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.519999999999969 y2[1] (analytic) = -0.3694409585444482 y2[1] (numeric) = -0.3694409585444767 absolute error = 2.853273173286652e-14 relative error = 7.723218304023995e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9292542053441347 y1[1] (numeric) = -0.9292542053441258 absolute error = 8.881784197001252e-15 relative error = 9.557970408874312e-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 = 0.3433 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3433 Order of pole (three term test) = 22.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.529999999999969 y2[1] (analytic) = -0.3787148738289688 y2[1] (numeric) = -0.3787148738289974 absolute error = 2.858824288409778e-14 relative error = 7.548751015522167e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9255133950087963 y1[1] (numeric) = -0.925513395008787 absolute error = 9.214851104388799e-15 relative error = 9.956475134864168e-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 = 0.3505 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3505 Order of pole (three term test) = 22.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.539999999999969 y2[1] (analytic) = -0.3879509179417013 y2[1] (numeric) = -0.3879509179417299 absolute error = 2.864375403532904e-14 relative error = 7.383344828077822e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9216800341052156 y1[1] (numeric) = -0.9216800341052059 absolute error = 9.658940314238862e-15 relative error = 1.04797109157474e-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 = 0.3576 Order of pole (three term test) = 22.85 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3576 Order of pole (three term test) = 22.15 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.549999999999968 y2[1] (analytic) = -0.3971481672859308 y2[1] (numeric) = -0.3971481672859596 absolute error = 2.875477633779155e-14 relative error = 7.240314498817582e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9177545059662885 y1[1] (numeric) = -0.9177545059662785 absolute error = 9.992007221626409e-15 relative error = 1.088745100859624e-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 = 0.3645 Order of pole (three term test) = 22.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3645 Order of pole (three term test) = 22.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.559999999999968 y2[1] (analytic) = -0.4063057021443875 y2[1] (numeric) = -0.4063057021444164 absolute error = 2.881028748902281e-14 relative error = 7.090790834824315e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9137372031415577 y1[1] (numeric) = -0.9137372031415473 absolute error = 1.043609643147647e-14 relative error = 1.142133251836053e-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 = 0.3713 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3713 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.569999999999968 y2[1] (analytic) = -0.4154226067712168 y2[1] (numeric) = -0.4154226067712457 absolute error = 2.886579864025407e-14 relative error = 6.94853822824119e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9096285273579579 y1[1] (numeric) = -0.9096285273579471 absolute error = 1.076916333886402e-14 relative error = 1.18390782775287e-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 = 0.3779 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3779 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.579999999999968 y2[1] (analytic) = -0.4244979694835532 y2[1] (numeric) = -0.4244979694835822 absolute error = 2.897682094271659e-14 relative error = 6.826138880704179e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9054288894796434 y1[1] (numeric) = -0.9054288894796323 absolute error = 1.110223024625157e-14 relative error = 1.226184670629639e-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 = 0.3844 Order of pole (three term test) = 22.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3844 Order of pole (three term test) = 22.18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.589999999999967 y2[1] (analytic) = -0.4335308827526885 y2[1] (numeric) = -0.4335308827527175 absolute error = 2.903233209394784e-14 relative error = 6.696716023921551e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.9011387094669026 y1[1] (numeric) = -0.9011387094668911 absolute error = 1.143529715363911e-14 relative error = 1.26898301376977e-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 = 0.3907 Order of pole (three term test) = 22.81 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3907 Order of pole (three term test) = 22.19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.599999999999967 y2[1] (analytic) = -0.442520443294823 y2[1] (numeric) = -0.4425204432948521 absolute error = 2.90878432451791e-14 relative error = 6.573220217489418e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8967584163341615 y1[1] (numeric) = -0.8967584163341497 absolute error = 1.187938636348917e-14 relative error = 1.324703080239899e-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 = 0.3968 Order of pole (three term test) = 22.8 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3968 Order of pole (three term test) = 22.2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.609999999999967 y2[1] (analytic) = -0.4514657521613938 y2[1] (numeric) = -0.451465752161423 absolute error = 2.914335439641036e-14 relative error = 6.45527468183056e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8922884481070832 y1[1] (numeric) = -0.892288448107071 absolute error = 1.221245327087672e-14 relative error = 1.368666522219854e-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 = 0.4028 Order of pole (three term test) = 22.8 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4028 Order of pole (three term test) = 22.2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.619999999999967 y2[1] (analytic) = -0.4603659148289687 y2[1] (numeric) = -0.4603659148289979 absolute error = 2.919886554764162e-14 relative error = 6.342534190110347e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8877292517787654 y1[1] (numeric) = -0.8877292517787528 absolute error = 1.254552017826427e-14 relative error = 1.413214688276464e-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) = 22.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4087 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.629999999999967 y2[1] (analytic) = -0.4692200412886977 y2[1] (numeric) = -0.469220041288727 absolute error = 2.925437669887287e-14 relative error = 6.234681838935667e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8830812832650416 y1[1] (numeric) = -0.8830812832650287 absolute error = 1.298960938811433e-14 relative error = 1.470941535538776e-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 = 0.4144 Order of pole (three term test) = 22.78 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4144 Order of pole (three term test) = 22.22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.639999999999966 y2[1] (analytic) = -0.4780272461353132 y2[1] (numeric) = -0.4780272461353425 absolute error = 2.930988785010413e-14 relative error = 6.131426207829062e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8783450073588901 y1[1] (numeric) = -0.8783450073588767 absolute error = 1.343369859796439e-14 relative error = 1.529433022948283e-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 = 0.4199 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 Radius of convergence (three term test) for eq 2 = 0.4199 Order of pole (three term test) = 22.23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.649999999999966 y2[1] (analytic) = -0.4867866486556699 y2[1] (numeric) = -0.4867866486556993 absolute error = 2.936539900133539e-14 relative error = 6.032498853950101e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8735208976839544 y1[1] (numeric) = -0.8735208976839405 absolute error = 1.387778780781446e-14 relative error = 1.588718466222148e-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 = 0.4252 Order of pole (three term test) = 22.76 NO COMPLEX POLE (six term test) for Equation 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) = 22.24 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.659999999999966 y2[1] (analytic) = -0.4954973729168152 y2[1] (numeric) = -0.4954973729168446 absolute error = 2.936539900133539e-14 relative error = 5.926448979632692e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8686094366471818 y1[1] (numeric) = -0.8686094366471676 absolute error = 1.4210854715202e-14 relative error = 1.636046549304791e-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 = 0.4304 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 Radius of convergence (three term test) for eq 2 = 0.4304 Order of pole (three term test) = 22.25 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.669999999999966 y2[1] (analytic) = -0.5041585478535819 y2[1] (numeric) = -0.5041585478536114 absolute error = 2.942091015256665e-14 relative error = 5.835646400884011e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8636111153905833 y1[1] (numeric) = -0.8636111153905688 absolute error = 1.454392162258955e-14 relative error = 1.684082263810582e-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 = 0.4354 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 Radius of convergence (three term test) for eq 2 = 0.4354 Order of pole (three term test) = 22.25 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.679999999999966 y2[1] (analytic) = -0.512769307355694 y2[1] (numeric) = -0.5127693073557235 absolute error = 2.942091015256665e-14 relative error = 5.737650387907903e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8585264337421193 y1[1] (numeric) = -0.8585264337421045 absolute error = 1.48769885299771e-14 relative error = 1.732851540182837e-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 = 0.4402 Order of pole (three term test) = 22.74 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4402 Order of pole (three term test) = 22.26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.689999999999965 y2[1] (analytic) = -0.521328790354377 y2[1] (numeric) = -0.5213287903544064 absolute error = 2.942091015256665e-14 relative error = 5.643446265948131e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8533559001657175 y1[1] (numeric) = -0.8533559001657022 absolute error = 1.532107773982716e-14 relative error = 1.795391317602876e-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 = 0.4449 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 Radius of convergence (three term test) for eq 2 = 0.4449 Order of pole (three term test) = 22.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.699999999999965 y2[1] (analytic) = -0.5298361409084636 y2[1] (numeric) = -0.5298361409084931 absolute error = 2.942091015256665e-14 relative error = 5.552831881592899e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8481000317104267 y1[1] (numeric) = -0.8481000317104109 absolute error = 1.576516694967722e-14 relative error = 1.858880599011703e-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 = 0.4494 Order of pole (three term test) = 22.72 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4494 Order of pole (three term test) = 22.28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.709999999999965 y2[1] (analytic) = -0.538290508289988 y2[1] (numeric) = -0.5382905082900176 absolute error = 2.953193245502916e-14 relative error = 5.486244323505647e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8427593539587124 y1[1] (numeric) = -0.8427593539586963 absolute error = 1.609823385706477e-14 relative error = 1.910181569797615e-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 = 0.4536 Order of pole (three term test) = 22.71 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4536 Order of pole (three term test) = 22.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.719999999999965 y2[1] (analytic) = -0.5466910470692574 y2[1] (numeric) = -0.546691047069287 absolute error = 2.953193245502916e-14 relative error = 5.401941848754643e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8373344009738994 y1[1] (numeric) = -0.8373344009738829 absolute error = 1.654232306691483e-14 relative error = 1.975593388695668e-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 = 0.4578 Order of pole (three term test) = 22.7 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4578 Order of pole (three term test) = 22.3 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.729999999999964 y2[1] (analytic) = -0.5550369171993943 y2[1] (numeric) = -0.5550369171994237 absolute error = 2.942091015256665e-14 relative error = 5.30071230234895e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8318257152467654 y1[1] (numeric) = -0.8318257152467484 absolute error = 1.69864122767649e-14 relative error = 2.042063856095839e-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 = 0.4617 Order of pole (three term test) = 22.69 NO COMPLEX POLE (six term test) for Equation 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) = 22.31 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.739999999999964 y2[1] (analytic) = -0.5633272841003404 y2[1] (numeric) = -0.5633272841003698 absolute error = 2.942091015256665e-14 relative error = 5.222702855508445e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8262338476412924 y1[1] (numeric) = -0.8262338476412751 absolute error = 1.731947918415244e-14 relative error = 2.09619579657691e-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 = 0.4654 Order of pole (three term test) = 22.68 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4654 Order of pole (three term test) = 22.32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.749999999999964 y2[1] (analytic) = -0.5715613187423143 y2[1] (numeric) = -0.5715613187423437 absolute error = 2.942091015256665e-14 relative error = 5.147463480787251e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8205593573395813 y1[1] (numeric) = -0.8205593573395635 absolute error = 1.77635683940025e-14 relative error = 2.16481211689494e-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 = 0.469 Order of pole (three term test) = 22.67 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.469 Order of pole (three term test) = 22.33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.759999999999964 y2[1] (analytic) = -0.5797381977287135 y2[1] (numeric) = -0.5797381977287429 absolute error = 2.942091015256665e-14 relative error = 5.074861423282318e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8148028117859334 y1[1] (numeric) = -0.8148028117859152 absolute error = 1.820765760385257e-14 relative error = 2.234609078476784e-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 = 0.4724 Order of pole (three term test) = 22.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4724 Order of pole (three term test) = 22.34 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.769999999999964 y2[1] (analytic) = -0.5878571033784533 y2[1] (numeric) = -0.5878571033784827 absolute error = 2.942091015256665e-14 relative error = 5.004772415521178e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.808964786630107 y1[1] (numeric) = -0.8089647866300883 absolute error = 1.865174681370263e-14 relative error = 2.305631483837504e-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 = 0.4756 Order of pole (three term test) = 22.65 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4756 Order of pole (three term test) = 22.35 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.779999999999963 y2[1] (analytic) = -0.5959172238077346 y2[1] (numeric) = -0.595917223807764 absolute error = 2.942091015256665e-14 relative error = 4.937080013323955e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.8030458656697526 y1[1] (numeric) = -0.8030458656697336 absolute error = 1.898481372109018e-14 relative error = 2.364100798309515e-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 = 0.4785 Order of pole (three term test) = 22.64 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4785 Order of pole (three term test) = 22.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.789999999999963 y2[1] (analytic) = -0.6039177530112312 y2[1] (numeric) = -0.6039177530112606 absolute error = 2.942091015256665e-14 relative error = 4.871674993137601e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.7970466407920339 y1[1] (numeric) = -0.7970466407920145 absolute error = 1.942890293094024e-14 relative error = 2.43761179541934e-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 = 0.4814 Order of pole (three term test) = 22.64 NO COMPLEX POLE (six term test) for Equation 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) = 22.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.799999999999963 y2[1] (analytic) = -0.6118578909426898 y2[1] (numeric) = -0.6118578909427191 absolute error = 2.930988785010413e-14 relative error = 4.790309691838144e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.7909677119144394 y1[1] (numeric) = -0.7909677119144195 absolute error = 1.98729921407903e-14 relative error = 2.512490945134813e-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 = 0.484 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 Radius of convergence (three term test) for eq 2 = 0.484 Order of pole (three term test) = 22.37 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.809999999999963 y2[1] (analytic) = -0.619736843594934 y2[1] (numeric) = -0.6197368435949633 absolute error = 2.930988785010413e-14 relative error = 4.729408643850351e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.7848096869247909 y1[1] (numeric) = -0.7848096869247706 absolute error = 2.031708135064036e-14 relative error = 2.58879084816742e-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 = 0.4864 Order of pole (three term test) = 22.62 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4864 Order of pole (three term test) = 22.38 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.819999999999963 y2[1] (analytic) = -0.6275538230792643 y2[1] (numeric) = -0.6275538230792935 absolute error = 2.919886554764162e-14 relative error = 4.652806575915577e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.778573181620456 y1[1] (numeric) = -0.7785731816204352 absolute error = 2.076117056049043e-14 relative error = 2.666566361466483e-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 = 0.4886 Order of pole (three term test) = 22.61 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4886 Order of pole (three term test) = 22.39 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.829999999999962 y2[1] (analytic) = -0.6353080477042465 y2[1] (numeric) = -0.6353080477042756 absolute error = 2.90878432451791e-14 relative error = 4.578541598881225e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.7722588196467677 y1[1] (numeric) = -0.7722588196467466 absolute error = 2.109423746787797e-14 relative error = 2.731498421413498e-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 = 0.4906 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 Radius of convergence (three term test) for eq 2 = 0.4906 Order of pole (three term test) = 22.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.839999999999962 y2[1] (analytic) = -0.6429987420538799 y2[1] (numeric) = -0.6429987420539089 absolute error = 2.90878432451791e-14 relative error = 4.52377918380775e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.7658672324346617 y1[1] (numeric) = -0.7658672324346402 absolute error = 2.153832667772804e-14 relative error = 2.812279435073694e-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 = 0.4925 Order of pole (three term test) = 22.59 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4925 Order of pole (three term test) = 22.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.849999999999962 y2[1] (analytic) = -0.6506251370651384 y2[1] (numeric) = -0.6506251370651673 absolute error = 2.897682094271659e-14 relative error = 4.45368912019388e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.7593990591375327 y1[1] (numeric) = -0.7593990591375108 absolute error = 2.187139358511558e-14 relative error = 2.880092267951377e-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 = 0.4941 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 Radius of convergence (three term test) for eq 2 = 0.4941 Order of pole (three term test) = 22.42 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.859999999999962 y2[1] (analytic) = -0.6581864701048762 y2[1] (numeric) = -0.6581864701049051 absolute error = 2.886579864025407e-14 relative error = 4.38565664159802e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.7528549465673204 y1[1] (numeric) = -0.7528549465672981 absolute error = 2.231548279496565e-14 relative error = 2.964114521225397e-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 = 0.4955 Order of pole (three term test) = 22.57 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4955 Order of pole (three term test) = 22.43 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.869999999999961 y2[1] (analytic) = -0.6656819850460903 y2[1] (numeric) = -0.6656819850461192 absolute error = 2.886579864025407e-14 relative error = 4.336274570845637e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.7462355491298286 y1[1] (numeric) = -0.7462355491298057 absolute error = 2.287059430727822e-14 relative error = 3.064795604276317e-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 = 0.4968 Order of pole (three term test) = 22.56 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4968 Order of pole (three term test) = 22.44 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.879999999999961 y2[1] (analytic) = -0.673110932343533 y2[1] (numeric) = -0.6731109323435618 absolute error = 2.875477633779155e-14 relative error = 4.271922346837785e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.7395415287592845 y1[1] (numeric) = -0.7395415287592613 absolute error = 2.320366121466577e-14 relative error = 3.137573795699362e-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 = 0.4978 Order of pole (three term test) = 22.55 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4978 Order of pole (three term test) = 22.45 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.889999999999961 y2[1] (analytic) = -0.6804725691086654 y2[1] (numeric) = -0.680472569108694 absolute error = 2.864375403532904e-14 relative error = 4.209391434080701e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.7327735548521471 y1[1] (numeric) = -0.7327735548521235 absolute error = 2.364775042451583e-14 relative error = 3.227156639036636e-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 = 0.4986 Order of pole (three term test) = 22.54 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4986 Order of pole (three term test) = 22.46 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.899999999999961 y2[1] (analytic) = -0.6877661591839453 y2[1] (numeric) = -0.6877661591839739 absolute error = 2.853273173286652e-14 relative error = 4.148609429507471e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.7259323042001671 y1[1] (numeric) = -0.725932304200143 absolute error = 2.40918396343659e-14 relative error = 3.318744667370921e-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 = 0.4993 Order of pole (three term test) = 22.53 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4993 Order of pole (three term test) = 22.47 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.909999999999961 y2[1] (analytic) = -0.6949909732164435 y2[1] (numeric) = -0.694990973216472 absolute error = 2.842170943040401e-14 relative error = 4.089507709555896e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.7190184609227086 y1[1] (numeric) = -0.7190184609226841 absolute error = 2.453592884421596e-14 relative error = 3.412419872047412e-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 = 0.4997 Order of pole (three term test) = 22.52 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4997 Order of pole (three term test) = 22.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.91999999999996 y2[1] (analytic) = -0.7021462887307773 y2[1] (numeric) = -0.7021462887308056 absolute error = 2.831068712794149e-14 relative error = 4.032021187367781e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.7120327163983379 y1[1] (numeric) = -0.712032716398313 absolute error = 2.486899575160351e-14 relative error = 3.492675993513036e-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 = 0.5 Order of pole (three term test) = 22.51 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5 Order of pole (three term test) = 22.49 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.92999999999996 y2[1] (analytic) = -0.7092313902013579 y2[1] (numeric) = -0.7092313902013861 absolute error = 2.819966482547898e-14 relative error = 3.976088088468956e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.7049757691956861 y1[1] (numeric) = -0.7049757691956606 absolute error = 2.542410726391608e-14 relative error = 3.606380300548869e-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 = 0.5 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.93999999999996 y2[1] (analytic) = -0.7162455691239427 y2[1] (numeric) = -0.7162455691239707 absolute error = 2.808864252301646e-14 relative error = 3.921649743309737e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.6978483250035924 y1[1] (numeric) = -0.6978483250035666 absolute error = 2.575717417130363e-14 relative error = 3.690941605566086e-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 = 0.4998 Order of pole (three term test) = 22.49 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4998 Order of pole (three term test) = 22.51 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.94999999999996 y2[1] (analytic) = -0.7231881240864843 y2[1] (numeric) = -0.7231881240865122 absolute error = 2.797762022055394e-14 relative error = 3.868650395205905e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.6906510965605368 y1[1] (numeric) = -0.6906510965605106 absolute error = 2.620126338115369e-14 relative error = 3.793704739142061e-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 = 0.4995 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 Radius of convergence (three term test) for eq 2 = 0.4995 Order of pole (three term test) = 22.52 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.95999999999996 y2[1] (analytic) = -0.730058360839272 y2[1] (numeric) = -0.7300583608392998 absolute error = 2.775557561562891e-14 relative error = 3.801829703548798e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.6833848035833657 y1[1] (numeric) = -0.6833848035833392 absolute error = 2.653433028854124e-14 relative error = 3.882780265145936e-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 = 0.4989 Order of pole (three term test) = 22.47 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4989 Order of pole (three term test) = 22.53 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.969999999999959 y2[1] (analytic) = -0.7368555923643557 y2[1] (numeric) = -0.7368555923643834 absolute error = 2.76445533131664e-14 relative error = 3.751692136102686e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.6760501726953219 y1[1] (numeric) = -0.6760501726952949 absolute error = 2.69784194983913e-14 relative error = 3.990594276580382e-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 = 0.4982 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 Radius of convergence (three term test) for eq 2 = 0.4982 Order of pole (three term test) = 22.54 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.979999999999959 y2[1] (analytic) = -0.7435791389442473 y2[1] (numeric) = -0.7435791389442747 absolute error = 2.742250870824137e-14 relative error = 3.687907214177168e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.6686479373533817 y1[1] (numeric) = -0.6686479373533543 absolute error = 2.742250870824137e-14 relative error = 4.101187961004435e-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 = 0.4972 Order of pole (three term test) = 22.45 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4972 Order of pole (three term test) = 22.55 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.989999999999959 y2[1] (analytic) = -0.7502283282298917 y2[1] (numeric) = -0.7502283282299189 absolute error = 2.720046410331634e-14 relative error = 3.625624770460724e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.6611788377749109 y1[1] (numeric) = -0.6611788377748831 absolute error = 2.786659791809143e-14 relative error = 4.21468388369354e-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 = 0.496 Order of pole (three term test) = 22.44 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.496 Order of pole (three term test) = 22.56 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.999999999999959 y2[1] (analytic) = -0.7568024953079012 y2[1] (numeric) = -0.7568024953079283 absolute error = 2.708944180085382e-14 relative error = 3.579459894596756e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.6536436208636431 y1[1] (numeric) = -0.6536436208636149 absolute error = 2.819966482547898e-14 relative error = 4.314226273365822e-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 = 0.4947 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 Radius of convergence (three term test) for eq 2 = 0.4947 Order of pole (three term test) = 22.57 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.009999999999959 y2[1] (analytic) = -0.7633009827670469 y2[1] (numeric) = -0.7633009827670736 absolute error = 2.664535259100376e-14 relative error = 3.490805487294347e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.6460430401349899 y1[1] (numeric) = -0.6460430401349616 absolute error = 2.831068712794149e-14 relative error = 4.382167343220044e-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 = 0.4931 Order of pole (three term test) = 22.42 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4931 Order of pole (three term test) = 22.58 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.019999999999959 y2[1] (analytic) = -0.7697231407639977 y2[1] (numeric) = -0.7697231407640241 absolute error = 2.642330798607873e-14 relative error = 3.432832740334656e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.6383778556406909 y1[1] (numeric) = -0.6383778556406622 absolute error = 2.875477633779155e-14 relative error = 4.504350532167597e-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 = 0.4914 Order of pole (three term test) = 22.41 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4914 Order of pole (three term test) = 22.59 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.029999999999959 y2[1] (analytic) = -0.776068327088306 y2[1] (numeric) = -0.7760683270883322 absolute error = 2.620126338115369e-14 relative error = 3.37615419501231e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.6306488338928077 y1[1] (numeric) = -0.6306488338927785 absolute error = 2.919886554764162e-14 relative error = 4.62997217760726e-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 = 0.4894 Order of pole (three term test) = 22.4 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4894 Order of pole (three term test) = 22.6 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.039999999999958 y2[1] (analytic) = -0.7823359072266267 y2[1] (numeric) = -0.7823359072266528 absolute error = 2.609024107869118e-14 relative error = 3.334915454817974e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.6228567477870741 y1[1] (numeric) = -0.6228567477870445 absolute error = 2.964295475749168e-14 relative error = 4.759193002694295e-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 = 0.4873 Order of pole (three term test) = 22.39 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4873 Order of pole (three term test) = 22.61 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.049999999999958 y2[1] (analytic) = -0.7885252544261693 y2[1] (numeric) = -0.7885252544261951 absolute error = 2.586819647376615e-14 relative error = 3.280579325590671e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.6150023765256074 y1[1] (numeric) = -0.6150023765255773 absolute error = 3.008704396734174e-14 relative error = 4.892183366398582e-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 = 0.4849 Order of pole (three term test) = 22.38 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4849 Order of pole (three term test) = 22.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.059999999999958 y2[1] (analytic) = -0.7946357497573715 y2[1] (numeric) = -0.794635749757397 absolute error = 2.55351295663786e-14 relative error = 3.213438304805103e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.6070865055389884 y1[1] (numeric) = -0.6070865055389578 absolute error = 3.05311331771918e-14 relative error = 5.029124004343568e-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 = 0.4824 Order of pole (three term test) = 22.37 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4824 Order of pole (three term test) = 22.63 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.069999999999958 y2[1] (analytic) = -0.8006667821757921 y2[1] (numeric) = -0.8006667821758174 absolute error = 2.531308496145357e-14 relative error = 3.161500579887415e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.5991099264077191 y1[1] (numeric) = -0.5991099264076882 absolute error = 3.086420008457935e-14 relative error = 5.151675631489201e-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 = 0.4797 Order of pole (three term test) = 22.36 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4797 Order of pole (three term test) = 22.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.079999999999957 y2[1] (analytic) = -0.8066177485832153 y2[1] (numeric) = -0.8066177485832404 absolute error = 2.509104035652854e-14 relative error = 3.110648185041765e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.5910734367830658 y1[1] (numeric) = -0.5910734367830345 absolute error = 3.130828929442941e-14 relative error = 5.296852699865127e-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 = 0.4768 Order of pole (three term test) = 22.35 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4768 Order of pole (three term test) = 22.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.089999999999957 y2[1] (analytic) = -0.8124880538879594 y2[1] (numeric) = -0.8124880538879843 absolute error = 2.486899575160351e-14 relative error = 3.060844480432557e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.5829778403072937 y1[1] (numeric) = -0.582977840307262 absolute error = 3.175237850427948e-14 relative error = 5.446584125314688e-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 = 0.4737 Order of pole (three term test) = 22.34 NO COMPLEX POLE (six term test) for Equation 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) = 22.66 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.099999999999957 y2[1] (analytic) = -0.8182771110643858 y2[1] (numeric) = -0.8182771110644105 absolute error = 2.464695114667848e-14 relative error = 3.012054328956922e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.574823946533304 y1[1] (numeric) = -0.574823946533272 absolute error = 3.208544541166702e-14 relative error = 5.581786493964037e-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 = 0.4704 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 Radius of convergence (three term test) for eq 2 = 0.4704 Order of pole (three term test) = 22.67 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.109999999999957 y2[1] (analytic) = -0.8239843412116011 y2[1] (numeric) = -0.8239843412116256 absolute error = 2.442490654175344e-14 relative error = 2.964244017773278e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.5666125708436796 y1[1] (numeric) = -0.566612570843647 absolute error = 3.252953462151709e-14 relative error = 5.741054169179654e-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 = 0.4669 Order of pole (three term test) = 22.32 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4669 Order of pole (three term test) = 22.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.119999999999957 y2[1] (analytic) = -0.8296091736113466 y2[1] (numeric) = -0.8296091736113708 absolute error = 2.420286193682841e-14 relative error = 2.917381184621147e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.5583445343691462 y1[1] (numeric) = -0.5583445343691132 absolute error = 3.297362383136715e-14 relative error = 5.905605195656277e-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 = 0.4632 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 Radius of convergence (three term test) for eq 2 = 0.4632 Order of pole (three term test) = 22.69 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.129999999999956 y2[1] (analytic) = -0.8351510457850696 y2[1] (numeric) = -0.8351510457850935 absolute error = 2.386979502944087e-14 relative error = 2.858141069200538e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.5500206639064614 y1[1] (numeric) = -0.5500206639064281 absolute error = 3.33066907387547e-14 relative error = 6.055534441596718e-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 = 0.4594 Order of pole (three term test) = 22.3 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4594 Order of pole (three term test) = 22.7 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.139999999999956 y2[1] (analytic) = -0.8406094035501709 y2[1] (numeric) = -0.8406094035501946 absolute error = 2.375877272697835e-14 relative error = 2.82637484503947e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.5416417918357351 y1[1] (numeric) = -0.5416417918357014 absolute error = 3.375077994860476e-14 relative error = 6.231199375184187e-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 = 0.4553 Order of pole (three term test) = 22.29 NO COMPLEX POLE (six term test) for Equation 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) = 22.71 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.149999999999956 y2[1] (analytic) = -0.8459837010754229 y2[1] (numeric) = -0.8459837010754463 absolute error = 2.34257058195908e-14 relative error = 2.769049307901773e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.533208756037192 y1[1] (numeric) = -0.5332087560371578 absolute error = 3.419486915845482e-14 relative error = 6.413035939730458e-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 = 0.4511 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 Radius of convergence (three term test) for eq 2 = 0.4511 Order of pole (three term test) = 22.72 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.159999999999956 y2[1] (analytic) = -0.8512734009355513 y2[1] (numeric) = -0.8512734009355745 absolute error = 2.320366121466577e-14 relative error = 2.725758985205564e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.5247223998073841 y1[1] (numeric) = -0.5247223998073496 absolute error = 3.452793606584237e-14 relative error = 6.580229103715971e-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 = 0.4467 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 Radius of convergence (three term test) for eq 2 = 0.4467 Order of pole (three term test) = 22.72 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.169999999999956 y2[1] (analytic) = -0.8564779741649782 y2[1] (numeric) = -0.8564779741650012 absolute error = 2.298161660974074e-14 relative error = 2.683270008449036e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.5161835717748627 y1[1] (numeric) = -0.5161835717748279 absolute error = 3.486100297322992e-14 relative error = 6.753605670432843e-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 = 0.4421 Order of pole (three term test) = 22.27 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4421 Order of pole (three term test) = 22.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.179999999999955 y2[1] (analytic) = -0.861596900310718 y2[1] (numeric) = -0.8615969003107407 absolute error = 2.264854970235319e-14 relative error = 2.628671214367814e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.5075931258153156 y1[1] (numeric) = -0.5075931258152802 absolute error = 3.541611448554249e-14 relative error = 6.977264404173278e-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 = 0.4373 Order of pole (three term test) = 22.26 NO COMPLEX POLE (six term test) for Equation 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) = 22.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.189999999999955 y2[1] (analytic) = -0.8666296674844217 y2[1] (numeric) = -0.866629667484444 absolute error = 2.231548279496565e-14 relative error = 2.574973328543104e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.4989519209661796 y1[1] (numeric) = -0.4989519209661438 absolute error = 3.574918139293004e-14 relative error = 7.164854947086821e-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 = 0.4324 Order of pole (three term test) = 22.25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4324 Order of pole (three term test) = 22.75 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.199999999999955 y2[1] (analytic) = -0.871575772413566 y2[1] (numeric) = -0.871575772413588 absolute error = 2.19824158875781e-14 relative error = 2.522146276129778e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.4902608213407389 y1[1] (numeric) = -0.4902608213407028 absolute error = 3.613775945154885e-14 relative error = 7.371129382258458e-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 = 0.4273 Order of pole (three term test) = 22.24 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4273 Order of pole (three term test) = 22.76 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.209999999999955 y2[1] (analytic) = -0.8764347204917796 y2[1] (numeric) = -0.8764347204918013 absolute error = 2.164934898019055e-14 relative error = 2.470161036984341e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.4815206960417135 y1[1] (numeric) = -0.4815206960416769 absolute error = 3.658184866139891e-14 relative error = 7.597149813521176e-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 = 0.422 Order of pole (three term test) = 22.23 NO COMPLEX POLE (six term test) for Equation 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) = 22.77 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.219999999999954 y2[1] (analytic) = -0.8812060258283039 y2[1] (numeric) = -0.8812060258283252 absolute error = 2.131628207280301e-14 relative error = 2.418989594716675e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.4727324190743498 y1[1] (numeric) = -0.4727324190743128 absolute error = 3.697042672001771e-14 relative error = 7.820582051979626e-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 = 0.4166 Order of pole (three term test) = 22.22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4166 Order of pole (three term test) = 22.78 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.229999999999954 y2[1] (analytic) = -0.8858892112965813 y2[1] (numeric) = -0.8858892112966023 absolute error = 2.098321516541546e-14 relative error = 2.368604888494417e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.4638968692590211 y1[1] (numeric) = -0.4638968692589837 absolute error = 3.735900477863652e-14 relative error = 8.053299613405404e-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 = 0.411 Order of pole (three term test) = 22.22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.411 Order of pole (three term test) = 22.78 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.239999999999954 y2[1] (analytic) = -0.8904838085819675 y2[1] (numeric) = -0.8904838085819882 absolute error = 2.065014825802791e-14 relative error = 2.318980767422578e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.4550149301433458 y1[1] (numeric) = -0.4550149301433081 absolute error = 3.769207168602406e-14 relative error = 8.283699981921413e-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 = 0.4052 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4052 Order of pole (three term test) = 22.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.249999999999954 y2[1] (analytic) = -0.894989358228563 y2[1] (numeric) = -0.8949893582285833 absolute error = 2.031708135064036e-14 relative error = 2.270091947333722e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.4460874899138341 y1[1] (numeric) = -0.446087489913796 absolute error = 3.808064974464287e-14 relative error = 8.536587688661365e-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 = 0.3992 Order of pole (three term test) = 22.2 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3992 Order of pole (three term test) = 22.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.259999999999954 y2[1] (analytic) = -0.8994054096851575 y2[1] (numeric) = -0.8994054096851775 absolute error = 1.998401444325282e-14 relative error = 2.221913969835733e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.4371154413070694 y1[1] (numeric) = -0.4371154413070309 absolute error = 3.846922780326167e-14 relative error = 8.800702095590673e-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 = 0.3931 Order of pole (three term test) = 22.19 NO COMPLEX POLE (six term test) for Equation 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) = 22.81 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.269999999999953 y2[1] (analytic) = -0.9037315213502856 y2[1] (numeric) = -0.9037315213503052 absolute error = 1.965094753586527e-14 relative error = 2.174423163474961e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.4280996815204356 y1[1] (numeric) = -0.4280996815203967 absolute error = 3.891331701311174e-14 relative error = 9.089779481943901e-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 = 0.3869 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 Radius of convergence (three term test) for eq 2 = 0.3869 Order of pole (three term test) = 22.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.279999999999953 y2[1] (analytic) = -0.9079672606163857 y2[1] (numeric) = -0.907967260616405 absolute error = 1.931788062847772e-14 relative error = 2.127596606882447e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.4190411121223983 y1[1] (numeric) = -0.419041112122359 absolute error = 3.930189507173054e-14 relative error = 9.379006960121564e-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 = 0.3805 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 Radius of convergence (three term test) for eq 2 = 0.3805 Order of pole (three term test) = 22.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.289999999999953 y2[1] (analytic) = -0.912112203913061 y2[1] (numeric) = -0.91211220391308 absolute error = 1.898481372109018e-14 relative error = 2.081412093780047e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.4099406389623485 y1[1] (numeric) = -0.4099406389623089 absolute error = 3.963496197911809e-14 relative error = 9.668463726710054e-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 = 0.3739 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3739 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.299999999999953 y2[1] (analytic) = -0.916165936749436 y2[1] (numeric) = -0.9161659367494547 absolute error = 1.865174681370263e-14 relative error = 2.035848099731712e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.4007991720800186 y1[1] (numeric) = -0.4007991720799786 absolute error = 4.002354003773689e-14 relative error = 9.985933810698164e-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 = 0.3672 Order of pole (three term test) = 22.16 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3672 Order of pole (three term test) = 22.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.309999999999953 y2[1] (analytic) = -0.9201280537556052 y2[1] (numeric) = -0.9201280537556235 absolute error = 1.820765760385257e-14 relative error = 1.97881778840847e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.3916176256144788 y1[1] (numeric) = -0.3916176256144384 absolute error = 4.04121180963557e-14 relative error = 1.031927968843228e-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 = 0.3603 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 Radius of convergence (three term test) for eq 2 = 0.3603 Order of pole (three term test) = 22.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.319999999999952 y2[1] (analytic) = -0.9239981587231696 y2[1] (numeric) = -0.9239981587231875 absolute error = 1.787459069646502e-14 relative error = 1.934483367495569e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.3823969177127246 y1[1] (numeric) = -0.3823969177126838 absolute error = 4.08006961549745e-14 relative error = 1.066972411781467e-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 = 0.3533 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 Radius of convergence (three term test) for eq 2 = 0.3533 Order of pole (three term test) = 22.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.329999999999952 y2[1] (analytic) = -0.9277758646448576 y2[1] (numeric) = -0.927775864644875 absolute error = 1.743050148661496e-14 relative error = 1.878740561254756e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.3731379704378621 y1[1] (numeric) = -0.3731379704378209 absolute error = 4.113376306236205e-14 relative error = 1.10237409004753e-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 = 0.3462 Order of pole (three term test) = 22.14 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3462 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.339999999999952 y2[1] (analytic) = -0.9314607937532251 y2[1] (numeric) = -0.9314607937532421 absolute error = 1.69864122767649e-14 relative error = 1.82363148193494e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.3638417096769031 y1[1] (numeric) = -0.3638417096768616 absolute error = 4.152234112098085e-14 relative error = 1.141219932092264e-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 = 0.3389 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 Radius of convergence (three term test) for eq 2 = 0.3389 Order of pole (three term test) = 22.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.349999999999952 y2[1] (analytic) = -0.9350525775584321 y2[1] (numeric) = -0.9350525775584486 absolute error = 1.654232306691483e-14 relative error = 1.769132930482841e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.3545090650481768 y1[1] (numeric) = -0.354509065048135 absolute error = 4.18554080283684e-14 relative error = 1.180658328798457e-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 = 0.3315 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 Radius of convergence (three term test) for eq 2 = 0.3315 Order of pole (three term test) = 22.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.359999999999951 y2[1] (analytic) = -0.938550856885091 y2[1] (numeric) = -0.9385508568851072 absolute error = 1.620925615952729e-14 relative error = 1.727051447518078e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.3451409698083689 y1[1] (numeric) = -0.3451409698083267 absolute error = 4.224398608698721e-14 relative error = 1.223963243495611e-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 = 0.3239 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 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) = 22.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.369999999999951 y2[1] (analytic) = -0.9419552819081846 y2[1] (numeric) = -0.9419552819082003 absolute error = 1.576516694967722e-14 relative error = 1.673664053110953e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.3357383607591968 y1[1] (numeric) = -0.3357383607591541 absolute error = 4.263256414560601e-14 relative error = 1.269815103916099e-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 = 0.3163 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3163 Order of pole (three term test) = 22.89 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.379999999999951 y2[1] (analytic) = -0.9452655121880474 y2[1] (numeric) = -0.9452655121880628 absolute error = 1.532107773982716e-14 relative error = 1.620822672813143e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.3263021781537297 y1[1] (numeric) = -0.3263021781536867 absolute error = 4.296563105299356e-14 relative error = 1.316743617713496e-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 = 0.3084 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3084 Order of pole (three term test) = 22.89 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.389999999999951 y2[1] (analytic) = -0.9484812167044101 y2[1] (numeric) = -0.948481216704425 absolute error = 1.48769885299771e-14 relative error = 1.568506394008374e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.3168333656023649 y1[1] (numeric) = -0.3168333656023215 absolute error = 4.335420911161236e-14 relative error = 1.368359958844207e-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 = 0.3005 Order of pole (three term test) = 22.1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3005 Order of pole (three term test) = 22.9 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.399999999999951 y2[1] (analytic) = -0.9516020738895008 y2[1] (numeric) = -0.9516020738895151 absolute error = 1.432187701766452e-14 relative error = 1.505027932434662e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.3073328699784666 y1[1] (numeric) = -0.307332869978423 absolute error = 4.368727601899991e-14 relative error = 1.421497024449772e-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 = 0.2925 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2925 Order of pole (three term test) = 22.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.40999999999995 y2[1] (analytic) = -0.9546277716602015 y2[1] (numeric) = -0.9546277716602154 absolute error = 1.387778780781446e-14 relative error = 1.453738118646965e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.2978016413236805 y1[1] (numeric) = -0.2978016413236365 absolute error = 4.407585407761871e-14 relative error = 1.480040670081891e-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 = 0.2843 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2843 Order of pole (three term test) = 22.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.41999999999995 y2[1] (analytic) = -0.9575580074492568 y2[1] (numeric) = -0.9575580074492702 absolute error = 1.343369859796439e-14 relative error = 1.402912251107281e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.2882406327529292 y1[1] (numeric) = -0.2882406327528848 absolute error = 4.440892098500626e-14 relative error = 1.540689130497163e-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 = 0.276 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.276 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.42999999999995 y2[1] (analytic) = -0.9603924882355295 y2[1] (numeric) = -0.9603924882355425 absolute error = 1.298960938811433e-14 relative error = 1.352531339762908e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.2786508003591023 y1[1] (numeric) = -0.2786508003590576 absolute error = 4.474198789239381e-14 relative error = 1.605665149166412e-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 = 0.2676 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2676 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.43999999999995 y2[1] (analytic) = -0.963130930573303 y2[1] (numeric) = -0.9631309305733156 absolute error = 1.254552017826427e-14 relative error = 1.302576812770052e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.2690331031174478 y1[1] (numeric) = -0.2690331031174027 absolute error = 4.513056595101261e-14 relative error = 1.677509772145423e-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 = 0.2591 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2591 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.44999999999995 y2[1] (analytic) = -0.9657730606206257 y2[1] (numeric) = -0.9657730606206377 absolute error = 1.199040866595169e-14 relative error = 1.241534803036068e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.259388502789675 y1[1] (numeric) = -0.2593885027896295 absolute error = 4.546363285840016e-14 relative error = 1.752723515863165e-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 = 0.2505 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2505 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.459999999999949 y2[1] (analytic) = -0.9683186141666945 y2[1] (numeric) = -0.9683186141667059 absolute error = 1.143529715363911e-14 relative error = 1.180943646681829e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.2497179638277796 y1[1] (numeric) = -0.2497179638277338 absolute error = 4.579669976578771e-14 relative error = 1.833936936846555e-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 = 0.2418 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2418 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.469999999999949 y2[1] (analytic) = -0.9707673366582761 y2[1] (numeric) = -0.9707673366582871 absolute error = 1.099120794378905e-14 relative error = 1.132218558323632e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.2400224532775991 y1[1] (numeric) = -0.2400224532775529 absolute error = 4.612976667317525e-14 relative error = 1.921893807985691e-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 = 0.233 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.233 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.479999999999949 y2[1] (analytic) = -0.973118983225162 y2[1] (numeric) = -0.9731189832251724 absolute error = 1.043609643147647e-14 relative error = 1.072437863342118e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.2303029406821088 y1[1] (numeric) = -0.2303029406820624 absolute error = 4.643507800494717e-14 relative error = 2.016260750619e-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 = 0.2241 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2241 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.489999999999949 y2[1] (analytic) = -0.9753733187046552 y2[1] (numeric) = -0.975373318704665 absolute error = 9.880984919163893e-15 relative error = 1.013046464330841e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = -0.2205603979844688 y1[1] (numeric) = -0.220560397984422 absolute error = 4.676814491233472e-14 relative error = 2.120423491239257e-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 = 0.2151 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2151 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.499999999999948 y2[1] (analytic) = -0.9775301176650862 y2[1] (numeric) = -0.9775301176650956 absolute error = 9.325873406851315e-15 relative error = 9.540241511051298e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.2107957994308301 y1[1] (numeric) = -0.210795799430783 absolute error = 4.707345624410664e-14 relative error = 2.233130658732751e-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 = 0.2061 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2061 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.509999999999948 y2[1] (analytic) = -0.9795891644283565 y2[1] (numeric) = -0.9795891644283653 absolute error = 8.770761894538737e-15 relative error = 8.953510525667107e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.2010101214729108 y1[1] (numeric) = -0.2010101214728635 absolute error = 4.737876757587856e-14 relative error = 2.357033925889327e-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 = 0.1969 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1969 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.519999999999948 y2[1] (analytic) = -0.9815502530915056 y2[1] (numeric) = -0.9815502530915138 absolute error = 8.215650382226158e-15 relative error = 8.370076169151831e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1912043426703522 y1[1] (numeric) = -0.1912043426703045 absolute error = 4.768407890765047e-14 relative error = 2.493880538574414e-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 = 0.1877 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 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) = 22.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.529999999999948 y2[1] (analytic) = -0.9834131875473012 y2[1] (numeric) = -0.9834131875473089 absolute error = 7.66053886991358e-15 relative error = 7.789745924619417e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1813794435928629 y1[1] (numeric) = -0.181379443592815 absolute error = 4.796163466380676e-14 relative error = 2.64427069097559e-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 = 0.1784 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1784 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.539999999999948 y2[1] (analytic) = -0.9851777815038505 y2[1] (numeric) = -0.9851777815038576 absolute error = 7.105427357601002e-15 relative error = 7.212330090062258e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1715364067221634 y1[1] (numeric) = -0.1715364067221152 absolute error = 4.823919041996305e-14 relative error = 2.812183800614164e-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 = 0.169 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.169 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.549999999999947 y2[1] (analytic) = -0.9868438585032281 y2[1] (numeric) = -0.9868438585032346 absolute error = 6.550315845288424e-15 relative error = 6.637641597347993e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1616762163537382 y1[1] (numeric) = -0.1616762163536897 absolute error = 4.851674617611934e-14 relative error = 3.000858584540815e-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 = 0.1595 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1595 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.559999999999947 y2[1] (analytic) = -0.9884112519391225 y2[1] (numeric) = -0.9884112519391285 absolute error = 5.995204332975845e-15 relative error = 6.06549583608453e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1517998584984074 y1[1] (numeric) = -0.1517998584983586 absolute error = 4.876654635666e-14 relative error = 3.212555455522486e-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 = 0.15 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 Radius of convergence (three term test) for eq 2 = 0.15 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.569999999999947 y2[1] (analytic) = -0.9898798050734964 y2[1] (numeric) = -0.9898798050735017 absolute error = 5.329070518200751e-15 relative error = 5.383553125225219e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1419083207837261 y1[1] (numeric) = -0.1419083207836771 absolute error = 4.904410211281629e-14 relative error = 3.456041325974213e-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 = 0.1405 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 Radius of convergence (three term test) for eq 2 = 0.1405 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.579999999999947 y2[1] (analytic) = -0.9912493710522599 y2[1] (numeric) = -0.9912493710522646 absolute error = 4.773959005888173e-15 relative error = 4.816102935652187e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1320025923552231 y1[1] (numeric) = -0.1320025923551738 absolute error = 4.932165786897258e-14 relative error = 3.736415852822531e-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 = 0.1308 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 Radius of convergence (three term test) for eq 2 = 0.1308 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.589999999999947 y2[1] (analytic) = -0.9925198129199566 y2[1] (numeric) = -0.9925198129199607 absolute error = 4.107825191113079e-15 relative error = 4.138784070242396e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1220836637774863 y1[1] (numeric) = -0.1220836637774367 absolute error = 4.957145804951324e-14 relative error = 4.060449737146143e-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 = 0.1212 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1212 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.599999999999946 y2[1] (analytic) = -0.9936910036334584 y2[1] (numeric) = -0.993691003633462 absolute error = 3.552713678800501e-15 relative error = 3.575270044520787e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.1121525269351078 y1[1] (numeric) = -0.112152526935058 absolute error = 4.98212582300539e-14 relative error = 4.442276923361771e-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 = 0.1114 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1114 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.609999999999946 y2[1] (analytic) = -0.99476282607467 y2[1] (numeric) = -0.9947628260746729 absolute error = 2.886579864025407e-15 relative error = 2.90177697473461e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.102210174933496 y1[1] (numeric) = -0.1022101749334459 absolute error = 5.007105841059456e-14 relative error = 4.898833060717662e-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 = 0.1017 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1017 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.619999999999946 y2[1] (analytic) = -0.9957351730622404 y2[1] (numeric) = -0.9957351730622427 absolute error = 2.331468351712829e-15 relative error = 2.341454248866928e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.09225760199956561 y1[1] (numeric) = -0.0922576019995153 absolute error = 5.030698080332741e-14 relative error = 5.452881899484475e-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 = 0.09186 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09186 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.629999999999946 y2[1] (analytic) = -0.9966079473622811 y2[1] (numeric) = -0.9966079473622828 absolute error = 1.665334536937735e-15 relative error = 1.671002665938366e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.08229580338231637 y1[1] (numeric) = -0.08229580338226583 absolute error = 5.054290319606025e-14 relative error = 6.141613681229444e-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 = 0.08202 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08202 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.639999999999946 y2[1] (analytic) = -0.9973810616980894 y2[1] (numeric) = -0.9973810616980904 absolute error = 9.992007221626409e-16 relative error = 1.001824438556567e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.07232577525330852 y1[1] (numeric) = -0.07232577525325776 absolute error = 5.076494780098528e-14 relative error = 7.018928953500994e-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 = 0.07214 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07214 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.649999999999945 y2[1] (analytic) = -0.998054438758876 y2[1] (numeric) = -0.9980544387588763 absolute error = 3.33066907387547e-16 relative error = 3.337161726385688e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.06234851460704662 y1[1] (numeric) = -0.06234851460699563 absolute error = 5.098699240591031e-14 relative error = 8.177739714772254e-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 = 0.06223 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06223 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.659999999999945 y2[1] (analytic) = -0.998628011207496 y2[1] (numeric) = -0.9986280112074957 absolute error = 3.33066907387547e-16 relative error = 3.335244992625607e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = -0.05236501916128092 y1[1] (numeric) = -0.05236501916122972 absolute error = 5.120209811693144e-14 relative error = 9.777920248483484e-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 = 0.05229 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05229 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.669999999999945 y2[1] (analytic) = -0.9991017216871825 y2[1] (numeric) = -0.9991017216871815 absolute error = 9.992007221626409e-16 relative error = 1.000099089485394e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.04237628725723648 y1[1] (numeric) = -0.04237628725718507 absolute error = 5.141026493404866e-14 relative error = 1.213184737539022e-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 = 0.04234 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04234 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.679999999999945 y2[1] (analytic) = -0.9994755228272822 y2[1] (numeric) = -0.9994755228272806 absolute error = 1.665334536937735e-15 relative error = 1.666208425221754e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.03238331775977977 y1[1] (numeric) = -0.03238331775972816 absolute error = 5.161149285726196e-14 relative error = 1.59376791594108e-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 = 0.03237 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03237 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.689999999999944 y2[1] (analytic) = -0.9997493772479927 y2[1] (numeric) = -0.9997493772479904 absolute error = 2.331468351712829e-15 relative error = 2.332052817207704e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.02238710995753308 y1[1] (numeric) = -0.02238710995748128 absolute error = 5.180231243961941e-14 relative error = 2.31393478380573e-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 = 0.02238 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02238 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.699999999999944 y2[1] (analytic) = -0.9999232575641002 y2[1] (numeric) = -0.9999232575640972 absolute error = 2.997602166487923e-15 relative error = 2.997832227435475e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.01238866346294651 y1[1] (numeric) = -0.01238866346289452 absolute error = 5.198966257502491e-14 relative error = 4.19655136573221e-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 = 0.01239 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.01239 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.709999999999944 y2[1] (analytic) = -0.9999971463877179 y2[1] (numeric) = -0.9999971463877141 absolute error = 3.774758283725532e-15 relative error = 3.774769055452871e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = -0.002388978112337493 y1[1] (numeric) = -0.002388978112285323 absolute error = 5.21700738165265e-14 relative error = 2.183781992271195e-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 = 0.002389 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.002389 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.719999999999944 y2[1] (analytic) = -0.9999710363300249 y2[1] (numeric) = -0.9999710363300204 absolute error = 4.551914400963142e-15 relative error = 4.552046244928291e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = 0.007610946134091949 y1[1] (numeric) = 0.007610946134144292 absolute error = 5.234267880238619e-14 relative error = 6.877289351441602e-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 = 0.007611 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.007611 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.729999999999944 y2[1] (analytic) = -0.9998449300020054 y2[1] (numeric) = -0.9998449300020001 absolute error = 5.218048215738236e-15 relative error = 5.21885750396091e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = 0.01761010929225042 y1[1] (numeric) = 0.01761010929230292 absolute error = 5.2506610170866e-14 relative error = 2.981617507278748e-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 = 0.01761 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.01761 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.739999999999943 y2[1] (analytic) = -0.999618840014187 y2[1] (numeric) = -0.999618840014181 absolute error = 5.995204332975845e-15 relative error = 5.997490336307345e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = 0.0276075114541547 y1[1] (numeric) = 0.02760751145420737 absolute error = 5.266620473065586e-14 relative error = 1.907676641486281e-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 = 0.0276 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0276 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.749999999999943 y2[1] (analytic) = -0.9992927889753801 y2[1] (numeric) = -0.9992927889753733 absolute error = 6.772360450213455e-15 relative error = 6.777153327762388e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = 0.03760215288791975 y1[1] (numeric) = 0.03760215288797257 absolute error = 5.281886039654182e-14 relative error = 1.404676496954265e-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 = 0.03758 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03758 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.759999999999943 y2[1] (analytic) = -0.9988668094904168 y2[1] (numeric) = -0.9988668094904094 absolute error = 7.438494264988549e-15 relative error = 7.446933058856346e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = 0.04759303413773103 y1[1] (numeric) = 0.04759303413778399 absolute error = 5.295763827461997e-14 relative error = 1.112718262957645e-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 = 0.04754 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04754 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.769999999999943 y2[1] (analytic) = -0.9983409441568909 y2[1] (numeric) = -0.9983409441568826 absolute error = 8.326672684688674e-15 relative error = 8.34051005663264e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = 0.05757915612378928 y1[1] (numeric) = 0.05757915612384237 absolute error = 5.30894772587942e-14 relative error = 9.220259696869694e-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 = 0.05748 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05748 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.779999999999943 y2[1] (analytic) = -0.9977152455608972 y2[1] (numeric) = -0.9977152455608881 absolute error = 9.103828801926284e-15 relative error = 9.124676446943815e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = 0.0675595202422176 y1[1] (numeric) = 0.06755952024227083 absolute error = 5.322131624296844e-14 relative error = 7.877693040471106e-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 = 0.06741 Order of pole (three term test) = 22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06741 Order of pole (three term test) = 23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.789999999999942 y2[1] (analytic) = -0.996989776271774 y2[1] (numeric) = -0.9969897762717641 absolute error = 9.880984919163893e-15 relative error = 9.910818700783137e-13 % Correct digits = 15 h = 0.01 y1[1] (analytic) = 0.07753312846492112 y1[1] (numeric) = 0.07753312846497447 absolute error = 5.334621633323877e-14 relative error = 6.880441611146207e-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 = 0.0773 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0773 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.799999999999942 y2[1] (analytic) = -0.9961646088358458 y2[1] (numeric) = -0.996164608835835 absolute error = 1.076916333886402e-14 relative error = 1.081062631952891e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.08749898343938889 y1[1] (numeric) = 0.08749898343944233 absolute error = 5.344336084789347e-14 relative error = 6.107883628718273e-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 = 0.08716 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08716 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.809999999999942 y2[1] (analytic) = -0.9952398257691683 y2[1] (numeric) = -0.9952398257691567 absolute error = 1.154631945610163e-14 relative error = 1.160154483084325e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.09745608858842827 y1[1] (numeric) = 0.09745608858848183 absolute error = 5.355438315035599e-14 relative error = 5.495232152864682e-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 = 0.09699 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09699 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.819999999999942 y2[1] (analytic) = -0.9942155195492777 y2[1] (numeric) = -0.9942155195492652 absolute error = 1.243449787580175e-14 relative error = 1.250684346733882e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.107403448209822 y1[1] (numeric) = 0.1074034482098756 absolute error = 5.363764987720288e-14 relative error = 4.994034248548247e-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 = 0.1068 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1068 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.829999999999941 y2[1] (analytic) = -0.9930917926059423 y2[1] (numeric) = -0.9930917926059291 absolute error = 1.321165399303936e-14 relative error = 1.330355772890949e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.1173400675758972 y1[1] (numeric) = 0.117340067575951 absolute error = 5.373479439185758e-14 relative error = 4.579407145568682e-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 = 0.1165 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1165 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.839999999999941 y2[1] (analytic) = -0.9918687573109201 y2[1] (numeric) = -0.991868757310906 absolute error = 1.409983241273949e-14 relative error = 1.421542145451369e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.127264953032998 y1[1] (numeric) = 0.1272649530330518 absolute error = 5.379030554308883e-14 relative error = 4.226639326943512e-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 = 0.1262 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 Radius of convergence (three term test) for eq 2 = 0.1262 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.849999999999941 y2[1] (analytic) = -0.9905465359667213 y2[1] (numeric) = -0.9905465359667064 absolute error = 1.48769885299771e-14 relative error = 1.501896982099679e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.1371771121008492 y1[1] (numeric) = 0.1371771121009031 absolute error = 5.384581669432009e-14 relative error = 3.925277028337932e-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 = 0.1359 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 Radius of convergence (three term test) for eq 2 = 0.1359 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.859999999999941 y2[1] (analytic) = -0.9891252607943786 y2[1] (numeric) = -0.9891252607943628 absolute error = 1.576516694967722e-14 relative error = 1.59384939143259e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.1470755535718042 y1[1] (numeric) = 0.1470755535718582 absolute error = 5.392908342116698e-14 relative error = 3.666760526237835e-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 = 0.1455 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 Radius of convergence (three term test) for eq 2 = 0.1455 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.869999999999941 y2[1] (analytic) = -0.9876050739202247 y2[1] (numeric) = -0.987605073920208 absolute error = 1.665334536937735e-14 relative error = 1.686235298819713e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.1569592876099646 y1[1] (numeric) = 0.1569592876100186 absolute error = 5.398459457239824e-14 relative error = 3.439401095304857e-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 = 0.155 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 Radius of convergence (three term test) for eq 2 = 0.155 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.87999999999994 y2[1] (analytic) = -0.9859861273616802 y2[1] (numeric) = -0.9859861273616628 absolute error = 1.743050148661496e-14 relative error = 1.767824212015621e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.166827325850163 y1[1] (numeric) = 0.166827325850217 absolute error = 5.401235014801387e-14 relative error = 3.237620088481511e-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 = 0.1645 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1645 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.88999999999994 y2[1] (analytic) = -0.984268583012052 y2[1] (numeric) = -0.9842685830120337 absolute error = 1.831867990631508e-14 relative error = 1.861146461696094e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.1766786814967987 y1[1] (numeric) = 0.1766786814968527 absolute error = 5.404010572362949e-14 relative error = 3.058665893689538e-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) = 22.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1739 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.89999999999994 y2[1] (analytic) = -0.9824526126243437 y2[1] (numeric) = -0.9824526126243245 absolute error = 1.920685832601521e-14 relative error = 1.954990813725817e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.1865123694225164 y1[1] (numeric) = 0.1865123694225705 absolute error = 5.406786129924512e-14 relative error = 2.898888768967505e-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 = 0.1832 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1832 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.90999999999994 y2[1] (analytic) = -0.9805383977940807 y2[1] (numeric) = -0.9805383977940606 absolute error = 2.009503674571533e-14 relative error = 2.049388049557588e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.1963274062667184 y1[1] (numeric) = 0.1963274062667724 absolute error = 5.409561687486075e-14 relative error = 2.755377759199333e-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 = 0.1925 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1925 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.91999999999994 y2[1] (analytic) = -0.978526129941151 y2[1] (numeric) = -0.97852612994113 absolute error = 2.098321516541546e-14 relative error = 2.144369426974566e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.2061228105338992 y1[1] (numeric) = 0.2061228105339533 absolute error = 5.409561687486075e-14 relative error = 2.624436215222483e-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 = 0.2017 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2017 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.929999999999939 y2[1] (analytic) = -0.9764160102906628 y2[1] (numeric) = -0.976416010290641 absolute error = 2.187139358511558e-14 relative error = 2.239966710357897e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.2158976026917952 y1[1] (numeric) = 0.2158976026918493 absolute error = 5.409561687486075e-14 relative error = 2.505614522829371e-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 = 0.2108 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2108 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.939999999999939 y2[1] (analytic) = -0.9742082498528229 y2[1] (numeric) = -0.9742082498528001 absolute error = 2.287059430727822e-14 relative error = 2.34760835896569e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.225650805269336 y1[1] (numeric) = 0.2256508052693901 absolute error = 5.406786129924512e-14 relative error = 2.396085457559521e-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 = 0.2198 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2198 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.949999999999939 y2[1] (analytic) = -0.9719030694018352 y2[1] (numeric) = -0.9719030694018115 absolute error = 2.375877272697835e-14 relative error = 2.444561960443325e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.2353814429543916 y1[1] (numeric) = 0.2353814429544457 absolute error = 5.404010572362949e-14 relative error = 2.295852427674194e-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 = 0.2288 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2288 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.959999999999939 y2[1] (analytic) = -0.9695006994538239 y2[1] (numeric) = -0.9695006994537992 absolute error = 2.464695114667848e-14 relative error = 2.542231394011736e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.2450885426913023 y1[1] (numeric) = 0.2450885426913563 absolute error = 5.398459457239824e-14 relative error = 2.202656802296701e-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 = 0.2376 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2376 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.969999999999938 y2[1] (analytic) = -0.9670013802437817 y2[1] (numeric) = -0.9670013802437561 absolute error = 2.55351295663786e-14 relative error = 2.640650787896619e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.2547711337781837 y1[1] (numeric) = 0.2547711337782376 absolute error = 5.395683899678261e-14 relative error = 2.117855276483563e-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 = 0.2464 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2464 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.979999999999938 y2[1] (analytic) = -0.9644053617015469 y2[1] (numeric) = -0.9644053617015205 absolute error = 2.642330798607873e-14 relative error = 2.739854944341953e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.2644282479639958 y1[1] (numeric) = 0.2644282479640497 absolute error = 5.390132784555135e-14 relative error = 2.038410353680916e-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 = 0.255 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.255 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.989999999999938 y2[1] (analytic) = -0.9617129034268105 y2[1] (numeric) = -0.9617129034267831 absolute error = 2.742250870824137e-14 relative error = 2.851423601630849e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.2740589195453677 y1[1] (numeric) = 0.2740589195454214 absolute error = 5.379030554308883e-14 relative error = 1.962727782490013e-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 = 0.2636 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2636 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.999999999999938 y2[1] (analytic) = -0.9589242746631561 y2[1] (numeric) = -0.9589242746631277 absolute error = 2.842170943040401e-14 relative error = 2.963915940118189e-12 % Correct digits = 14 h = 0.01 y1[1] (analytic) = 0.2836621854631666 y1[1] (numeric) = 0.2836621854632204 absolute error = 5.373479439185758e-14 relative error = 1.89432349976853e-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 = 0.272 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.272 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 3 ) = m1 * cos ( x ) ; diff ( y1 , x , 1 ) = m1 * y2 ; Iterations = 491 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 30 Minutes 0.0 Seconds Percent Done = 100.4 %