##############ECHO OF PROBLEM################# ##############temp/mtest5postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.5; 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); 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_y1 (double x) { return( - cos(x)); } double exact_soln_y2 (double x) { return( - sin(x)); } double exact_soln_y2p (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 = 4.5 estimated_steps = 4500000 step_error = 2.222222222222222e-17 est_needed_step_err = 2.222222222222222e-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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.5 y1[1] (analytic) = -0.8775825618903728 y1[1] (numeric) = -0.8775825618903728 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.479425538604203 y2[1] (numeric) = -0.479425538604203 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.51 y1[1] (analytic) = -0.8727445076457513 y1[1] (numeric) = -0.8727445076457513 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.4881772468829075 y2[1] (numeric) = -0.4881772468829075 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.52 y1[1] (analytic) = -0.8678191796776499 y1[1] (numeric) = -0.8678191796776499 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.4968801378437367 y2[1] (numeric) = -0.4968801378437367 absolute error = 5.551115123125783e-17 relative error = 1.117194007233903e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.53 y1[1] (analytic) = -0.862807070514761 y1[1] (numeric) = -0.862807070514761 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.5055333412048469 y2[1] (numeric) = -0.5055333412048469 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.54 y1[1] (analytic) = -0.8577086813638242 y1[1] (numeric) = -0.8577086813638242 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.5141359916531132 y2[1] (numeric) = -0.5141359916531131 absolute error = 1.110223024625157e-16 relative error = 2.159395651441229e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.55 y1[1] (analytic) = -0.8525245220595057 y1[1] (numeric) = -0.8525245220595058 absolute error = 1.110223024625157e-16 relative error = 1.302276938548477e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.5226872289306592 y2[1] (numeric) = -0.5226872289306592 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5600000000000001 y1[1] (analytic) = -0.8472551110134161 y1[1] (numeric) = -0.8472551110134162 absolute error = 1.110223024625157e-16 relative error = 1.310376308379185e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.5311861979208834 y2[1] (numeric) = -0.5311861979208835 absolute error = 1.110223024625157e-16 relative error = 2.090082590569337e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5700000000000001 y1[1] (analytic) = -0.8419009751622687 y1[1] (numeric) = -0.8419009751622688 absolute error = 1.110223024625157e-16 relative error = 1.318709750171237e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.5396320487339693 y2[1] (numeric) = -0.5396320487339694 absolute error = 1.110223024625157e-16 relative error = 2.057370438301155e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5800000000000001 y1[1] (analytic) = -0.8364626499151869 y1[1] (numeric) = -0.836462649915187 absolute error = 1.110223024625157e-16 relative error = 1.327283441451603e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.5480239367918737 y2[1] (numeric) = -0.5480239367918738 absolute error = 1.110223024625157e-16 relative error = 2.025865934113007e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5900000000000001 y1[1] (analytic) = -0.8309406791001634 y1[1] (numeric) = -0.8309406791001636 absolute error = 1.110223024625157e-16 relative error = 1.336103830934636e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.5563610229127839 y2[1] (numeric) = -0.5563610229127841 absolute error = 2.220446049250313e-16 relative error = 3.99101654825736e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6000000000000001 y1[1] (analytic) = -0.8253356149096782 y1[1] (numeric) = -0.8253356149096783 absolute error = 1.110223024625157e-16 relative error = 1.345177652059345e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.5646424733950355 y2[1] (numeric) = -0.5646424733950358 absolute error = 3.33066907387547e-16 relative error = 5.898722166345543e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6100000000000001 y1[1] (analytic) = -0.8196480178454795 y1[1] (numeric) = -0.8196480178454796 absolute error = 1.110223024625157e-16 relative error = 1.354511937384391e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.5728674601004814 y2[1] (numeric) = -0.5728674601004818 absolute error = 4.440892098500626e-16 relative error = 7.752041105147935e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6200000000000001 y1[1] (analytic) = -0.8138784566625339 y1[1] (numeric) = -0.813878456662534 absolute error = 1.110223024625157e-16 relative error = 1.364114033903589e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.5810351605373052 y2[1] (numeric) = -0.5810351605373058 absolute error = 5.551115123125783e-16 relative error = 9.553836841805678e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6300000000000001 y1[1] (analytic) = -0.8080275083121518 y1[1] (numeric) = -0.808027508312152 absolute error = 2.220446049250313e-16 relative error = 2.747983238699994e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.5891447579422696 y2[1] (numeric) = -0.5891447579422703 absolute error = 6.661338147750939e-16 relative error = 1.130679354767964e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6400000000000001 y1[1] (analytic) = -0.8020957578842925 y1[1] (numeric) = -0.8020957578842927 absolute error = 1.110223024625157e-16 relative error = 1.384152719562585e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.5971954413623921 y2[1] (numeric) = -0.597195441362393 absolute error = 8.881784197001252e-16 relative error = 1.487249161972685e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6500000000000001 y1[1] (analytic) = -0.7960837985490558 y1[1] (numeric) = -0.7960837985490559 absolute error = 1.110223024625157e-16 relative error = 1.394605726995891e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6051864057360397 y2[1] (numeric) = -0.6051864057360407 absolute error = 9.992007221626409e-16 relative error = 1.651062734873222e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6600000000000001 y1[1] (analytic) = -0.789992231497365 y1[1] (numeric) = -0.7899922314973651 absolute error = 1.110223024625157e-16 relative error = 1.405359420460149e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6131168519734339 y2[1] (numeric) = -0.613116851973435 absolute error = 1.110223024625157e-15 relative error = 1.810785368322027e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6700000000000002 y1[1] (analytic) = -0.7838216658808492 y1[1] (numeric) = -0.7838216658808492 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6209859870365598 y2[1] (numeric) = -0.620985987036561 absolute error = 1.221245327087672e-15 relative error = 1.966623003710022e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6800000000000002 y1[1] (analytic) = -0.7775727187509278 y1[1] (numeric) = -0.7775727187509278 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6287930240184686 y2[1] (numeric) = -0.62879302401847 absolute error = 1.443289932012704e-15 relative error = 2.295333880756145e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6900000000000002 y1[1] (analytic) = -0.7712460149971065 y1[1] (numeric) = -0.7712460149971064 absolute error = 1.110223024625157e-16 relative error = 1.439518652980426e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6365371822219681 y2[1] (numeric) = -0.6365371822219696 absolute error = 1.554312234475219e-15 relative error = 2.44182473213829e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7000000000000002 y1[1] (analytic) = -0.7648421872844883 y1[1] (numeric) = -0.7648421872844883 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6442176872376912 y2[1] (numeric) = -0.644217687237693 absolute error = 1.77635683940025e-15 relative error = 2.757386011888314e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7100000000000002 y1[1] (analytic) = -0.7583618759905081 y1[1] (numeric) = -0.758361875990508 absolute error = 1.110223024625157e-16 relative error = 1.463975260063116e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6518337710215368 y2[1] (numeric) = -0.6518337710215388 absolute error = 1.998401444325282e-15 relative error = 3.065814526905287e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7200000000000002 y1[1] (analytic) = -0.7518057291408948 y1[1] (numeric) = -0.7518057291408947 absolute error = 1.110223024625157e-16 relative error = 1.476741904978342e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6593846719714733 y2[1] (numeric) = -0.6593846719714755 absolute error = 2.220446049250313e-15 relative error = 3.367451722241999e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7300000000000002 y1[1] (analytic) = -0.7451744023448702 y1[1] (numeric) = -0.7451744023448701 absolute error = 1.110223024625157e-16 relative error = 1.489883470408502e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.666869635003698 y2[1] (numeric) = -0.6668696350037006 absolute error = 2.55351295663786e-15 relative error = 3.829103654755101e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7400000000000002 y1[1] (analytic) = -0.7384685587295877 y1[1] (numeric) = -0.7384685587295876 absolute error = 1.110223024625157e-16 relative error = 1.503412720150348e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6742879116281453 y2[1] (numeric) = -0.6742879116281481 absolute error = 2.775557561562891e-15 relative error = 4.116279579832582e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7500000000000002 y1[1] (analytic) = -0.7316888688738208 y1[1] (numeric) = -0.7316888688738206 absolute error = 2.220446049250313e-16 relative error = 3.034686112784404e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6816387600233343 y2[1] (numeric) = -0.6816387600233375 absolute error = 3.108624468950438e-15 relative error = 4.560515996543421e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7600000000000002 y1[1] (analytic) = -0.724836010740905 y1[1] (numeric) = -0.7248360107409049 absolute error = 1.110223024625157e-16 relative error = 1.531688558754581e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6889214451105515 y2[1] (numeric) = -0.6889214451105549 absolute error = 3.33066907387547e-15 relative error = 4.834613724850728e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7700000000000002 y1[1] (analytic) = -0.7179106696109432 y1[1] (numeric) = -0.7179106696109431 absolute error = 1.110223024625157e-16 relative error = 1.546464026265021e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6961352386273569 y2[1] (numeric) = -0.6961352386273606 absolute error = 3.663735981263017e-15 relative error = 5.26296584049845e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7800000000000002 y1[1] (analytic) = -0.7109135380122772 y1[1] (numeric) = -0.7109135380122771 absolute error = 1.110223024625157e-16 relative error = 1.561685022526584e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7032794192004104 y2[1] (numeric) = -0.7032794192004144 absolute error = 3.996802888650564e-15 relative error = 5.683093774014752e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7900000000000003 y1[1] (analytic) = -0.703845315652236 y1[1] (numeric) = -0.7038453156522357 absolute error = 2.220446049250313e-16 relative error = 3.154735848732162e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.710353272417608 y2[1] (numeric) = -0.7103532724176123 absolute error = 4.218847493575595e-15 relative error = 5.939083632594834e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8000000000000003 y1[1] (analytic) = -0.6967067093471653 y1[1] (numeric) = -0.6967067093471651 absolute error = 2.220446049250313e-16 relative error = 3.187059948555593e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7173560908995229 y2[1] (numeric) = -0.7173560908995276 absolute error = 4.662936703425657e-15 relative error = 6.500170225889635e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8100000000000003 y1[1] (analytic) = -0.6894984329517468 y1[1] (numeric) = -0.6894984329517466 absolute error = 2.220446049250313e-16 relative error = 3.220378674023334e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7242871743701427 y2[1] (numeric) = -0.7242871743701477 absolute error = 4.996003610813204e-15 relative error = 6.897821454808789e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8200000000000003 y1[1] (analytic) = -0.6822212072876134 y1[1] (numeric) = -0.6822212072876132 absolute error = 2.220446049250313e-16 relative error = 3.254730321384174e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7311458297268961 y2[1] (numeric) = -0.7311458297269013 absolute error = 5.218048215738236e-15 relative error = 7.136809106450523e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8300000000000003 y1[1] (analytic) = -0.6748757600712669 y1[1] (numeric) = -0.6748757600712666 absolute error = 3.33066907387547e-16 relative error = 4.935232928685645e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7379313711099629 y2[1] (numeric) = -0.7379313711099685 absolute error = 5.662137425588298e-15 relative error = 7.672986469014819e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8400000000000003 y1[1] (analytic) = -0.6674628258413079 y1[1] (numeric) = -0.6674628258413076 absolute error = 3.33066907387547e-16 relative error = 4.990044306478501e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7446431199708595 y2[1] (numeric) = -0.7446431199708655 absolute error = 5.995204332975845e-15 relative error = 8.05111089082574e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8500000000000003 y1[1] (analytic) = -0.659983145884982 y1[1] (numeric) = -0.6599831458849815 absolute error = 4.440892098500626e-16 relative error = 6.728796221827396e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7512804051402929 y2[1] (numeric) = -0.7512804051402993 absolute error = 6.328271240363392e-15 relative error = 8.423314646655347e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8600000000000003 y1[1] (analytic) = -0.6524374681640516 y1[1] (numeric) = -0.6524374681640511 absolute error = 4.440892098500626e-16 relative error = 6.806617208844894e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7578425628952772 y2[1] (numeric) = -0.7578425628952838 absolute error = 6.661338147750939e-15 relative error = 8.789870711803026e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8700000000000003 y1[1] (analytic) = -0.644826547240001 y1[1] (numeric) = -0.6448265472400004 absolute error = 5.551115123125783e-16 relative error = 8.608695077592218e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7643289370255053 y2[1] (numeric) = -0.7643289370255123 absolute error = 6.994405055138486e-15 relative error = 9.151040496200768e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8800000000000003 y1[1] (analytic) = -0.63715114419858 y1[1] (numeric) = -0.6371511441985793 absolute error = 6.661338147750939e-16 relative error = 1.045487904778024e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7707388788989695 y2[1] (numeric) = -0.7707388788989769 absolute error = 7.327471962526033e-15 relative error = 9.507074526970291e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8900000000000003 y1[1] (analytic) = -0.6294120265736967 y1[1] (numeric) = -0.6294120265736959 absolute error = 7.771561172376096e-16 relative error = 1.234733504328128e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7770717475268241 y2[1] (numeric) = -0.7770717475268318 absolute error = 7.771561172376096e-15 relative error = 1.000108573900742e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9000000000000004 y1[1] (analytic) = -0.6216099682706642 y1[1] (numeric) = -0.6216099682706634 absolute error = 7.771561172376096e-16 relative error = 1.250231104561722e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7833269096274836 y2[1] (numeric) = -0.7833269096274917 absolute error = 8.104628079763643e-15 relative error = 1.03464185643997e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9100000000000004 y1[1] (analytic) = -0.6137457494888112 y1[1] (numeric) = -0.6137457494888104 absolute error = 7.771561172376096e-16 relative error = 1.266250915602923e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7895037396899507 y2[1] (numeric) = -0.7895037396899591 absolute error = 8.43769498715119e-15 relative error = 1.068734011375904e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9200000000000004 y1[1] (analytic) = -0.6058201566434626 y1[1] (numeric) = -0.6058201566434617 absolute error = 8.881784197001252e-16 relative error = 1.466076045770851e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7956016200363663 y2[1] (numeric) = -0.7956016200363751 absolute error = 8.881784197001252e-15 relative error = 1.116360748058215e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9300000000000004 y1[1] (analytic) = -0.5978339822872979 y1[1] (numeric) = -0.597833982287297 absolute error = 8.881784197001252e-16 relative error = 1.485660644953599e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8016199408837774 y2[1] (numeric) = -0.8016199408837867 absolute error = 9.325873406851315e-15 relative error = 1.163378420523027e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9400000000000004 y1[1] (analytic) = -0.589788025031098 y1[1] (numeric) = -0.589788025031097 absolute error = 9.992007221626409e-16 relative error = 1.694169226494478e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8075581004051146 y2[1] (numeric) = -0.8075581004051243 absolute error = 9.769962616701378e-15 relative error = 1.209815443842398e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9500000000000004 y1[1] (analytic) = -0.5816830894638831 y1[1] (numeric) = -0.5816830894638821 absolute error = 9.992007221626409e-16 relative error = 1.71777509138794e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.813415504789374 y2[1] (numeric) = -0.8134155047893842 absolute error = 1.021405182655144e-14 relative error = 1.255699180358785e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9600000000000004 y1[1] (analytic) = -0.5735199860724564 y1[1] (numeric) = -0.5735199860724552 absolute error = 1.110223024625157e-15 relative error = 1.935805292903768e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8191915683009985 y2[1] (numeric) = -0.8191915683010091 absolute error = 1.06581410364015e-14 relative error = 1.30105599823329e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9700000000000004 y1[1] (analytic) = -0.5652995311603539 y1[1] (numeric) = -0.5652995311603528 absolute error = 1.110223024625157e-15 relative error = 1.963955325323326e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8248857133384503 y2[1] (numeric) = -0.8248857133384614 absolute error = 1.110223024625157e-14 relative error = 1.345911326469577e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9800000000000004 y1[1] (analytic) = -0.557022546766217 y1[1] (numeric) = -0.5570225467662157 absolute error = 1.332267629550188e-15 relative error = 2.391766073536234e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8304973704919707 y2[1] (numeric) = -0.8304973704919822 absolute error = 1.154631945610163e-14 relative error = 1.390289706668404e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9900000000000004 y1[1] (analytic) = -0.5486898605815872 y1[1] (numeric) = -0.5486898605815858 absolute error = 1.443289932012704e-15 relative error = 2.630429384065671e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8360259786005207 y2[1] (numeric) = -0.8360259786005327 absolute error = 1.199040866595169e-14 relative error = 1.43421484174729e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1 y1[1] (analytic) = -0.5403023058681393 y1[1] (numeric) = -0.5403023058681378 absolute error = 1.554312234475219e-15 relative error = 2.876745513750498e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8414709848078967 y2[1] (numeric) = -0.8414709848079092 absolute error = 1.243449787580175e-14 relative error = 1.477709641841124e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.01 y1[1] (analytic) = -0.531860721374355 y1[1] (numeric) = -0.5318607213743534 absolute error = 1.665334536937735e-15 relative error = 3.1311478174858e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8468318446180154 y2[1] (numeric) = -0.8468318446180283 absolute error = 1.287858708565182e-14 relative error = 1.520796267582618e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.02 y1[1] (analytic) = -0.5233659512516492 y1[1] (numeric) = -0.5233659512516473 absolute error = 1.887379141862766e-15 relative error = 3.606232192501305e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8521080219493632 y2[1] (numeric) = -0.8521080219493765 absolute error = 1.332267629550188e-14 relative error = 1.563496170945986e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.03 y1[1] (analytic) = -0.5148188449699549 y1[1] (numeric) = -0.5148188449699529 absolute error = 1.998401444325282e-15 relative error = 3.881756590402027e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8572989891886036 y2[1] (numeric) = -0.8572989891886175 absolute error = 1.387778780781446e-14 relative error = 1.618780376837862e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.04 y1[1] (analytic) = -0.506220257232778 y1[1] (numeric) = -0.5062202572327759 absolute error = 2.109423746787797e-15 relative error = 4.167007773096306e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8624042272433387 y2[1] (numeric) = -0.862404227243353 absolute error = 1.432187701766452e-14 relative error = 1.660691884992745e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.05 y1[1] (analytic) = -0.4975710478917266 y1[1] (numeric) = -0.4975710478917243 absolute error = 2.275957200481571e-15 relative error = 4.574135111206929e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8674232255940172 y2[1] (numeric) = -0.867423225594032 absolute error = 1.476596622751458e-14 relative error = 1.702279324767071e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.06 y1[1] (analytic) = -0.4888720818605271 y1[1] (numeric) = -0.4888720818605247 absolute error = 2.386979502944087e-15 relative error = 4.882625929179324e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8723554823449865 y2[1] (numeric) = -0.8723554823450018 absolute error = 1.532107773982716e-14 relative error = 1.756288353761753e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.070000000000001 y1[1] (analytic) = -0.4801242290285337 y1[1] (numeric) = -0.4801242290285311 absolute error = 2.55351295663786e-15 relative error = 5.318442191106555e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8772005042746819 y2[1] (numeric) = -0.8772005042746976 absolute error = 1.576516694967722e-14 relative error = 1.797213621384399e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.080000000000001 y1[1] (analytic) = -0.4713283641737396 y1[1] (numeric) = -0.4713283641737369 absolute error = 2.720046410331634e-15 relative error = 5.771022109182843e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8819578068849477 y2[1] (numeric) = -0.8819578068849641 absolute error = 1.63202784619898e-14 relative error = 1.85046023002309e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.090000000000001 y1[1] (analytic) = -0.4624853668753004 y1[1] (numeric) = -0.4624853668752976 absolute error = 2.831068712794149e-15 relative error = 6.121423326151394e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8866269144494875 y2[1] (numeric) = -0.8866269144495044 absolute error = 1.687538997430238e-14 relative error = 1.903324803170499e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.100000000000001 y1[1] (analytic) = -0.4535961214255769 y1[1] (numeric) = -0.4535961214255739 absolute error = 2.997602166487923e-15 relative error = 6.608526891867944e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8912073600614355 y2[1] (numeric) = -0.891207360061453 absolute error = 1.743050148661496e-14 relative error = 1.955830064667934e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.110000000000001 y1[1] (analytic) = -0.4446615167417063 y1[1] (numeric) = -0.4446615167417032 absolute error = 3.108624468950438e-15 relative error = 6.990990566777936e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8956986856800478 y2[1] (numeric) = -0.8956986856800658 absolute error = 1.798561299892754e-14 relative error = 2.007998145634454e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.120000000000001 y1[1] (analytic) = -0.4356824462767117 y1[1] (numeric) = -0.4356824462767084 absolute error = 3.275157922644212e-15 relative error = 7.517305208491429e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9001004421765052 y2[1] (numeric) = -0.9001004421765237 absolute error = 1.854072451124011e-14 relative error = 2.059850616938634e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.130000000000001 y1[1] (analytic) = -0.4266598079301568 y1[1] (numeric) = -0.4266598079301533 absolute error = 3.441691376337985e-15 relative error = 8.066593835108514e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9044121893788262 y2[1] (numeric) = -0.9044121893788452 absolute error = 1.898481372109018e-14 relative error = 2.099132889189545e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.140000000000001 y1[1] (analytic) = -0.4175945039583576 y1[1] (numeric) = -0.417594503958354 absolute error = 3.608224830031759e-15 relative error = 8.640498847158127e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9086334961158835 y2[1] (numeric) = -0.908633496115903 absolute error = 1.953992523340276e-14 relative error = 2.150473795752596e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.150000000000001 y1[1] (analytic) = -0.4084874408841568 y1[1] (numeric) = -0.408487440884153 absolute error = 3.83026943495679e-15 relative error = 9.376712847441051e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9127639402605213 y2[1] (numeric) = -0.9127639402605414 absolute error = 2.009503674571533e-14 relative error = 2.201559007686018e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.160000000000001 y1[1] (analytic) = -0.3993395294062726 y1[1] (numeric) = -0.3993395294062686 absolute error = 3.996802888650564e-15 relative error = 1.000853307608416e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9168031087717672 y2[1] (numeric) = -0.9168031087717878 absolute error = 2.065014825802791e-14 relative error = 2.252408184532961e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.170000000000001 y1[1] (analytic) = -0.3901516843082297 y1[1] (numeric) = -0.3901516843082254 absolute error = 4.218847493575595e-15 relative error = 1.081335199425308e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9207505977361359 y2[1] (numeric) = -0.9207505977361571 absolute error = 2.120525977034049e-14 relative error = 2.303040565216922e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.180000000000001 y1[1] (analytic) = -0.3809248243668812 y1[1] (numeric) = -0.3809248243668768 absolute error = 4.385380947269368e-15 relative error = 1.151245775215129e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9246060124080205 y2[1] (numeric) = -0.9246060124080423 absolute error = 2.176037128265307e-14 relative error = 2.353474992659945e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.190000000000001 y1[1] (analytic) = -0.3716598722605324 y1[1] (numeric) = -0.3716598722605278 absolute error = 4.6074255521944e-15 relative error = 1.239688730497278e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.928368967249167 y2[1] (numeric) = -0.9283689672491892 absolute error = 2.220446049250313e-14 relative error = 2.391771081954275e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.200000000000001 y1[1] (analytic) = -0.362357754476673 y1[1] (numeric) = -0.3623577544766682 absolute error = 4.829470157119431e-15 relative error = 1.33279061851299e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9320390859672266 y2[1] (numeric) = -0.9320390859672494 absolute error = 2.275957200481571e-14 relative error = 2.441911755363445e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.210000000000001 y1[1] (analytic) = -0.3530194012193297 y1[1] (numeric) = -0.3530194012193247 absolute error = 4.996003610813204e-15 relative error = 1.415220691428572e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9356160015533862 y2[1] (numeric) = -0.9356160015534095 absolute error = 2.331468351712829e-14 relative error = 2.491907307957468e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.220000000000001 y1[1] (analytic) = -0.3436457463160464 y1[1] (numeric) = -0.3436457463160412 absolute error = 5.273559366969494e-15 relative error = 1.534591777580006e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9390993563190678 y2[1] (numeric) = -0.9390993563190917 absolute error = 2.386979502944087e-14 relative error = 2.541775251875572e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.230000000000001 y1[1] (analytic) = -0.334237727124502 y1[1] (numeric) = -0.3342377271244965 absolute error = 5.495603971894525e-15 relative error = 1.64422012415356e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9424888019316977 y2[1] (numeric) = -0.9424888019317222 absolute error = 2.453592884421596e-14 relative error = 2.603312505562701e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.240000000000001 y1[1] (analytic) = -0.3247962844387756 y1[1] (numeric) = -0.3247962844387699 absolute error = 5.717648576819556e-15 relative error = 1.760379921432672e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9457839994495392 y2[1] (numeric) = -0.9457839994495643 absolute error = 2.509104035652854e-14 relative error = 2.652935593236078e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.250000000000001 y1[1] (analytic) = -0.315322362395268 y1[1] (numeric) = -0.3153223623952621 absolute error = 5.939693181744587e-15 relative error = 1.883689167055956e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9489846193555864 y2[1] (numeric) = -0.9489846193556121 absolute error = 2.564615186884112e-14 relative error = 2.702483406554712e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.260000000000001 y1[1] (analytic) = -0.3058169083782887 y1[1] (numeric) = -0.3058169083782825 absolute error = 6.217248937900877e-15 relative error = 2.032997119377807e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.952090341590516 y2[1] (numeric) = -0.9520903415905422 absolute error = 2.620126338115369e-14 relative error = 2.751972395537921e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.270000000000001 y1[1] (analytic) = -0.2962808729253181 y1[1] (numeric) = -0.2962808729253116 absolute error = 6.494804694057166e-15 relative error = 2.192110692104744e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9551008555846925 y2[1] (numeric) = -0.9551008555847192 absolute error = 2.675637489346627e-14 relative error = 2.801418796456484e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.280000000000001 y1[1] (analytic) = -0.2867152096319548 y1[1] (numeric) = -0.2867152096319481 absolute error = 6.772360450213455e-15 relative error = 2.362051339692397e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9580158602892251 y2[1] (numeric) = -0.9580158602892526 absolute error = 2.742250870824137e-14 relative error = 2.862427423692392e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.290000000000001 y1[1] (analytic) = -0.277120875056557 y1[1] (numeric) = -0.2771208750565499 absolute error = 7.049916206369744e-15 relative error = 2.543985979017619e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9608350642060729 y2[1] (numeric) = -0.9608350642061009 absolute error = 2.797762022055394e-14 relative error = 2.911802583273908e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.300000000000001 y1[1] (analytic) = -0.2674988286245867 y1[1] (numeric) = -0.2674988286245794 absolute error = 7.327471962526033e-15 relative error = 2.73925385026996e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9635581854171932 y2[1] (numeric) = -0.9635581854172218 absolute error = 2.864375403532904e-14 relative error = 2.972706212124296e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.310000000000001 y1[1] (analytic) = -0.257850032532669 y1[1] (numeric) = -0.2578500325326614 absolute error = 7.605027718682322e-15 relative error = 2.949399557558242e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9661849516127342 y2[1] (numeric) = -0.9661849516127635 absolute error = 2.930988785010413e-14 relative error = 3.033569069895026e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.320000000000001 y1[1] (analytic) = -0.2481754516523723 y1[1] (numeric) = -0.2481754516523644 absolute error = 7.882583474838611e-15 relative error = 3.176214014059703e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9687151001182654 y2[1] (numeric) = -0.9687151001182953 absolute error = 2.986499936241671e-14 relative error = 3.082949709235527e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.330000000000001 y1[1] (analytic) = -0.2384760534337225 y1[1] (numeric) = -0.2384760534337143 absolute error = 8.187894806610529e-15 relative error = 3.433424316075458e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9711483779210447 y2[1] (numeric) = -0.9711483779210752 absolute error = 3.05311331771918e-14 relative error = 3.143817553662641e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.340000000000001 y1[1] (analytic) = -0.2287528078084587 y1[1] (numeric) = -0.2287528078084503 absolute error = 8.493206138382448e-15 relative error = 3.712831426967249e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9734845416953195 y2[1] (numeric) = -0.9734845416953506 absolute error = 3.108624468950438e-14 relative error = 3.193296180683856e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.350000000000001 y1[1] (analytic) = -0.2190066870930409 y1[1] (numeric) = -0.2190066870930321 absolute error = 8.798517470154366e-15 relative error = 4.017465213934989e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9757233578266592 y2[1] (numeric) = -0.9757233578266908 absolute error = 3.164135620181696e-14 relative error = 3.242861406156699e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.360000000000001 y1[1] (analytic) = -0.2092386658914186 y1[1] (numeric) = -0.2092386658914095 absolute error = 9.103828801926284e-15 relative error = 4.350930437804733e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9778646024353164 y2[1] (numeric) = -0.9778646024353486 absolute error = 3.219646771412954e-14 relative error = 3.29252819193435e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.370000000000001 y1[1] (analytic) = -0.1994497209975722 y1[1] (numeric) = -0.1994497209975628 absolute error = 9.409140133698202e-15 relative error = 4.71754991014138e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9799080613986144 y2[1] (numeric) = -0.9799080613986472 absolute error = 3.275157922644212e-14 relative error = 3.342311438860506e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.380000000000001 y1[1] (analytic) = -0.1896408312978336 y1[1] (numeric) = -0.1896408312978239 absolute error = 9.742207041085749e-15 relative error = 5.13718853393206e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9818535303723599 y2[1] (numeric) = -0.9818535303723933 absolute error = 3.341771304121721e-14 relative error = 3.403533419953567e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.390000000000001 y1[1] (analytic) = -0.1798129776729987 y1[1] (numeric) = -0.1798129776729886 absolute error = 1.00752739484733e-14 relative error = 5.603196209116686e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9837008148112767 y2[1] (numeric) = -0.9837008148113107 absolute error = 3.397282455352979e-14 relative error = 3.453572879275035e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.400000000000001 y1[1] (analytic) = -0.1699671429002401 y1[1] (numeric) = -0.1699671429002297 absolute error = 1.040834085586084e-14 relative error = 6.123737022496091e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9854497299884604 y2[1] (numeric) = -0.9854497299884949 absolute error = 3.452793606584237e-14 relative error = 3.503774471199733e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.410000000000001 y1[1] (analytic) = -0.1601043115548304 y1[1] (numeric) = -0.1601043115548196 absolute error = 1.076916333886402e-14 relative error = 6.726341866924638e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9871001010138505 y2[1] (numeric) = -0.9871001010138857 absolute error = 3.519406988061746e-14 relative error = 3.56540029166947e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.420000000000001 y1[1] (analytic) = -0.150225469911685 y1[1] (numeric) = -0.1502254699116738 absolute error = 1.112998582186719e-14 relative error = 7.408854056779005e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.98865176285172 y2[1] (numeric) = -0.9886517628517557 absolute error = 3.574918139293004e-14 relative error = 3.615952829519384e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.430000000000001 y1[1] (analytic) = -0.1403316058467358 y1[1] (numeric) = -0.1403316058467244 absolute error = 1.146305272925474e-14 relative error = 8.168546679195132e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9901045603371779 y2[1] (numeric) = -0.9901045603372143 absolute error = 3.641531520770513e-14 relative error = 3.677926217742496e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.440000000000001 y1[1] (analytic) = -0.1304237087381447 y1[1] (numeric) = -0.1304237087381329 absolute error = 1.179611963664229e-14 relative error = 9.044459593098743e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9914583481916865 y2[1] (numeric) = -0.9914583481917235 absolute error = 3.697042672001771e-14 relative error = 3.728893582614721e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.450000000000001 y1[1] (analytic) = -0.1205027693673657 y1[1] (numeric) = -0.1205027693673536 absolute error = 1.217081990745328e-14 relative error = 1.010003336134891e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9927129910375886 y2[1] (numeric) = -0.9927129910376261 absolute error = 3.752553823233029e-14 relative error = 3.780099441743823e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.460000000000001 y1[1] (analytic) = -0.1105697798200687 y1[1] (numeric) = -0.1105697798200562 absolute error = 1.254552017826427e-14 relative error = 1.134624686662099e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.993868363411645 y2[1] (numeric) = -0.9938683634116831 absolute error = 3.808064974464287e-14 relative error = 3.831558699979511e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.470000000000001 y1[1] (analytic) = -0.1006257333869308 y1[1] (numeric) = -0.1006257333869179 absolute error = 1.292022044907526e-14 relative error = 1.283987705152301e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9949243497775809 y2[1] (numeric) = -0.9949243497776197 absolute error = 3.874678355941796e-14 relative error = 3.894445197575067e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.480000000000001 y1[1] (analytic) = -0.09067162446430879 y1[1] (numeric) = -0.09067162446429548 absolute error = 1.330879850769406e-14 relative error = 1.46780192660305e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9958808445376401 y2[1] (numeric) = -0.9958808445376794 absolute error = 3.930189507173054e-14 relative error = 3.946445529834177e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.490000000000001 y1[1] (analytic) = -0.08070844845479974 y1[1] (numeric) = -0.08070844845478604 absolute error = 1.369737656631287e-14 relative error = 1.697142842980558e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9967377520431434 y2[1] (numeric) = -0.9967377520431834 absolute error = 3.996802888650564e-14 relative error = 4.009884124944395e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.500000000000001 y1[1] (analytic) = -0.07073720166770202 y1[1] (numeric) = -0.07073720166768793 absolute error = 1.408595462493167e-14 relative error = 1.991307868114777e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9974949866040544 y2[1] (numeric) = -0.997494986604095 absolute error = 4.052314039881821e-14 relative error = 4.06249063333924e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.510000000000001 y1[1] (analytic) = -0.06075888121938501 y1[1] (numeric) = -0.06075888121937052 absolute error = 1.448841047135829e-14 relative error = 2.384574926428335e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9981524724975481 y2[1] (numeric) = -0.9981524724975892 absolute error = 4.107825191113079e-14 relative error = 4.115428558559394e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.520000000000001 y1[1] (analytic) = -0.05077448493357829 y1[1] (numeric) = -0.0507744849335634 absolute error = 1.489086631778491e-14 relative error = 2.932745913083059e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.998710143975583 y2[1] (numeric) = -0.9987101439756246 absolute error = 4.163336342344337e-14 relative error = 4.168713382414713e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.530000000000001 y1[1] (analytic) = -0.04078501124159015 y1[1] (numeric) = -0.04078501124157485 absolute error = 1.530026105811544e-14 relative error = 3.75144215787616e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.999167945271476 y2[1] (numeric) = -0.9991679452715182 absolute error = 4.218847493575595e-14 relative error = 4.222360728785515e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.540000000000001 y1[1] (analytic) = -0.03079145908246523 y1[1] (numeric) = -0.03079145908244952 absolute error = 1.571312524539792e-14 relative error = 5.103079137404713e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9995258306054791 y2[1] (numeric) = -0.9995258306055218 absolute error = 4.274358644806853e-14 relative error = 4.276386376345662e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.550000000000001 y1[1] (analytic) = -0.02079482780309154 y1[1] (numeric) = -0.02079482780307541 absolute error = 1.613292832658431e-14 relative error = 7.75814470759207e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.999783764189357 y2[1] (numeric) = -0.9997837641894003 absolute error = 4.329869796038111e-14 relative error = 4.330806271442953e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.560000000000001 y1[1] (analytic) = -0.0107961170582665 y1[1] (numeric) = -0.01079611705824994 absolute error = 1.656140502515058e-14 relative error = 1.534014955170353e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = -0.9999417202299663 y2[1] (numeric) = -0.9999417202300102 absolute error = 4.385380947269368e-14 relative error = 4.385636541158439e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.570000000000001 y1[1] (analytic) = -0.0007963267107323752 y1[1] (numeric) = -0.0007963267107153806 absolute error = 1.699454379305854e-14 relative error = 2.134117010520568e-09 % Correct digits = 11 h = 0.01 y2[1] (analytic) = -0.9999996829318346 y2[1] (numeric) = -0.999999682931879 absolute error = 4.440892098500626e-14 relative error = 4.440893506566583e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.580000000000001 y1[1] (analytic) = 0.009203543268809225 y1[1] (numeric) = 0.009203543268826655 absolute error = 1.743050148661496e-14 relative error = 1.893890317839529e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = -0.9999576464987401 y2[1] (numeric) = -0.999957646498785 absolute error = 4.496403249731884e-14 relative error = 4.496593696218662e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.590000000000001 y1[1] (analytic) = 0.01920249290169354 y1[1] (numeric) = 0.01920249290171141 absolute error = 1.787112124951307e-14 relative error = 9.306667285858987e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9998156151342908 y2[1] (numeric) = -0.9998156151343364 absolute error = 4.551914400963142e-14 relative error = 4.552753859872201e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.600000000000001 y1[1] (analytic) = 0.0291995223012897 y1[1] (numeric) = 0.02919952230130803 absolute error = 1.832214935326704e-14 relative error = 6.274811335683315e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9995736030415051 y2[1] (numeric) = -0.9995736030415512 absolute error = 4.6074255521944e-14 relative error = 4.609390982489847e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.610000000000001 y1[1] (analytic) = 0.0391936317729886 y1[1] (numeric) = 0.03919363177300737 absolute error = 1.877664690397296e-14 relative error = 4.790739223333067e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9992316344213905 y2[1] (numeric) = -0.999231634421437 absolute error = 4.651834473179406e-14 relative error = 4.655411531154207e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.620000000000001 y1[1] (analytic) = 0.04918382191417144 y1[1] (numeric) = 0.04918382191419068 absolute error = 1.924155279553474e-14 relative error = 3.912171125926803e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.998789743470524 y2[1] (numeric) = -0.998789743470571 absolute error = 4.707345624410664e-14 relative error = 4.713049623491239e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.630000000000001 y1[1] (analytic) = 0.05916909371414925 y1[1] (numeric) = 0.05916909371416895 absolute error = 1.970645868709653e-14 relative error = 3.33053245369957e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9982479743776324 y2[1] (numeric) = -0.99824797437768 absolute error = 4.762856775641922e-14 relative error = 4.771216068443687e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.640000000000001 y1[1] (analytic) = 0.06914844865406305 y1[1] (numeric) = 0.06914844865408323 absolute error = 2.017830347256222e-14 relative error = 2.918113690953582e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9976063813191736 y2[1] (numeric) = -0.9976063813192217 absolute error = 4.818367926873179e-14 relative error = 4.829928934999057e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.650000000000001 y1[1] (analytic) = 0.07912088880673497 y1[1] (numeric) = 0.07912088880675562 absolute error = 2.065014825802791e-14 relative error = 2.609948974217049e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9968650284539188 y2[1] (numeric) = -0.9968650284539674 absolute error = 4.862776847858186e-14 relative error = 4.878069456805077e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.660000000000001 y1[1] (analytic) = 0.08908541693646006 y1[1] (numeric) = 0.0890854169364812 absolute error = 2.113587083130142e-14 relative error = 2.372539923832486e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9960239899165366 y2[1] (numeric) = -0.9960239899165858 absolute error = 4.918287999089443e-14 relative error = 4.937921223666088e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.670000000000001 y1[1] (analytic) = 0.09904103659872912 y1[1] (numeric) = 0.09904103659875074 absolute error = 2.162159340457492e-14 relative error = 2.183094416931049e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9950833498101801 y2[1] (numeric) = -0.9950833498102297 absolute error = 4.96269692007445e-14 relative error = 4.987217323072608e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.680000000000001 y1[1] (analytic) = 0.1089867522398722 y1[1] (numeric) = 0.1089867522398943 absolute error = 2.212119376565624e-14 relative error = 2.029714007530846e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9940432021980758 y2[1] (numeric) = -0.994043202198126 absolute error = 5.018208071305708e-14 relative error = 5.048279652442878e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.690000000000001 y1[1] (analytic) = 0.1189215692966133 y1[1] (numeric) = 0.1189215692966359 absolute error = 2.260691633892975e-14 relative error = 1.900993778726863e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9929036510941184 y2[1] (numeric) = -0.9929036510941691 absolute error = 5.073719222536965e-14 relative error = 5.109981433693028e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.700000000000001 y1[1] (analytic) = 0.1288444942955257 y1[1] (numeric) = 0.1288444942955488 absolute error = 2.309263891220326e-14 relative error = 1.792287597422405e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9916648104524685 y2[1] (numeric) = -0.9916648104525196 absolute error = 5.118128143521972e-14 relative error = 5.161147284420343e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.710000000000001 y1[1] (analytic) = 0.1387545349523787 y1[1] (numeric) = 0.1387545349524023 absolute error = 2.359223927328458e-14 relative error = 1.700285996517632e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9903268041561579 y2[1] (numeric) = -0.9903268041562096 absolute error = 5.162537064506978e-14 relative error = 5.212963077280227e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.720000000000001 y1[1] (analytic) = 0.1486507002713647 y1[1] (numeric) = 0.1486507002713889 absolute error = 2.411959520998153e-14 relative error = 1.622568556081521e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9888897660047012 y2[1] (numeric) = -0.9888897660047534 absolute error = 5.218048215738236e-14 relative error = 5.276673290714821e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.730000000000001 y1[1] (analytic) = 0.1585320006441988 y1[1] (numeric) = 0.1585320006442235 absolute error = 2.464695114667848e-14 relative error = 1.554698801915384e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9873538397007163 y2[1] (numeric) = -0.9873538397007688 absolute error = 5.25135490647699e-14 relative error = 5.31861496388039e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.740000000000001 y1[1] (analytic) = 0.1683974479490781 y1[1] (numeric) = 0.1683974479491032 absolute error = 2.51465515077598e-14 relative error = 1.493285783960567e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9857191788355533 y2[1] (numeric) = -0.9857191788356063 absolute error = 5.306866057708248e-14 relative error = 5.383750434862533e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.750000000000001 y1[1] (analytic) = 0.1782460556494932 y1[1] (numeric) = 0.1782460556495188 absolute error = 2.564615186884112e-14 relative error = 1.438806136572932e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9839859468739367 y2[1] (numeric) = -0.9839859468739902 absolute error = 5.351274978693255e-14 relative error = 5.438365248704952e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.760000000000001 y1[1] (analytic) = 0.1880768388928812 y1[1] (numeric) = 0.1880768388929074 absolute error = 2.617350780553807e-14 relative error = 1.391639074731851e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9821543171376182 y2[1] (numeric) = -0.9821543171376722 absolute error = 5.395683899678261e-14 relative error = 5.493723140578757e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.770000000000001 y1[1] (analytic) = 0.1978888146091101 y1[1] (numeric) = 0.1978888146091368 absolute error = 2.670086374223501e-14 relative error = 1.349286153185426e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9802244727880453 y2[1] (numeric) = -0.9802244727880997 absolute error = 5.440092820663267e-14 relative error = 5.549843909926112e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.780000000000001 y1[1] (analytic) = 0.2076810016087849 y1[1] (numeric) = 0.2076810016088121 absolute error = 2.725597525454759e-14 relative error = 1.312396176993142e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9781966068080444 y2[1] (numeric) = -0.9781966068080993 absolute error = 5.484501741648273e-14 relative error = 5.606747869985732e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.790000000000001 y1[1] (analytic) = 0.2174524206813657 y1[1] (numeric) = 0.2174524206813935 absolute error = 2.781108676686017e-14 relative error = 1.278950433373741e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.976070921982524 y2[1] (numeric) = -0.9760709219825792 absolute error = 5.517808432387028e-14 relative error = 5.653081459674732e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.800000000000001 y1[1] (analytic) = 0.2272020946930882 y1[1] (numeric) = 0.2272020946931165 absolute error = 2.833844270355712e-14 relative error = 1.247279112538007e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9738476308781949 y2[1] (numeric) = -0.9738476308782505 absolute error = 5.562217353372034e-14 relative error = 5.711588935484852e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.810000000000001 y1[1] (analytic) = 0.2369290486846758 y1[1] (numeric) = 0.2369290486847047 absolute error = 2.88935542158697e-14 relative error = 1.219502394335933e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9715269558223151 y2[1] (numeric) = -0.9715269558223711 absolute error = 5.606626274357041e-14 relative error = 5.770942577307603e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.820000000000001 y1[1] (analytic) = 0.2466323099688351 y1[1] (numeric) = 0.2466323099688645 absolute error = 2.944866572818228e-14 relative error = 1.194031136143657e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9691091288804561 y2[1] (numeric) = -0.9691091288805126 absolute error = 5.651035195342047e-14 relative error = 5.831164960617276e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.830000000000001 y1[1] (analytic) = 0.2563109082275238 y1[1] (numeric) = 0.2563109082275538 absolute error = 3.003153281611048e-14 relative error = 1.171683757971467e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9665943918332973 y2[1] (numeric) = -0.9665943918333542 absolute error = 5.684341886080801e-14 relative error = 5.880793364939309e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.840000000000001 y1[1] (analytic) = 0.2659638756089814 y1[1] (numeric) = 0.265963875609012 absolute error = 3.058664432842306e-14 relative error = 1.150030027889629e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9639829961524479 y2[1] (numeric) = -0.963982996152505 absolute error = 5.717648576819556e-14 relative error = 5.931275343694285e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.850000000000001 y1[1] (analytic) = 0.275590246824514 y1[1] (numeric) = 0.2755902468245451 absolute error = 3.114175584073564e-14 relative error = 1.130002102743701e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9612752029752996 y2[1] (numeric) = -0.9612752029753572 absolute error = 5.762057497804562e-14 relative error = 5.994180937956247e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.860000000000001 y1[1] (analytic) = 0.2851890592450219 y1[1] (numeric) = 0.2851890592450536 absolute error = 3.169686735304822e-14 relative error = 1.111433497377459e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9584712830789138 y2[1] (numeric) = -0.9584712830789718 absolute error = 5.795364188543317e-14 relative error = 6.046466170511409e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.870000000000001 y1[1] (analytic) = 0.2947593529972621 y1[1] (numeric) = 0.2947593529972943 absolute error = 3.22519788653608e-14 relative error = 1.094179999291163e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9555715168529436 y2[1] (numeric) = -0.9555715168530019 absolute error = 5.828670879282072e-14 relative error = 6.099669963456087e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.880000000000001 y1[1] (analytic) = 0.3043001710598345 y1[1] (numeric) = 0.3043001710598673 absolute error = 3.280709037767338e-14 relative error = 1.078116067546427e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.952576194271595 y2[1] (numeric) = -0.9525761942716536 absolute error = 5.861977570020827e-14 relative error = 6.153814891944992e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.890000000000001 y1[1] (analytic) = 0.3138105593588835 y1[1] (numeric) = 0.3138105593589169 absolute error = 3.336220188998595e-14 relative error = 1.063131908567548e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9494856148646301 y2[1] (numeric) = -0.9494856148646891 absolute error = 5.895284260759581e-14 relative error = 6.208924251685564e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y1[1] (analytic) = 0.3232895668635046 y1[1] (numeric) = 0.3232895668635385 absolute error = 3.397282455352979e-14 relative error = 1.050848157060181e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9463000876874141 y2[1] (numeric) = -0.9463000876874734 absolute error = 5.928590951498336e-14 relative error = 6.265022088275124e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.910000000000001 y1[1] (analytic) = 0.3327362456808464 y1[1] (numeric) = 0.3327362456808809 absolute error = 3.452793606584237e-14 relative error = 1.037696869939467e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9430199312900102 y2[1] (numeric) = -0.9430199312900698 absolute error = 5.961897642237091e-14 relative error = 6.322133227959959e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.920000000000001 y1[1] (analytic) = 0.3421496511508994 y1[1] (numeric) = 0.3421496511509345 absolute error = 3.51385587293862e-14 relative error = 1.026993849363562e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9396454736853245 y2[1] (numeric) = -0.9396454736853844 absolute error = 5.995204332975845e-14 relative error = 6.38028330989818e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.930000000000001 y1[1] (analytic) = 0.3515288419409611 y1[1] (numeric) = 0.3515288419409968 absolute error = 3.574918139293004e-14 relative error = 1.016962966553228e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9361770523163055 y2[1] (numeric) = -0.9361770523163658 absolute error = 6.0285110237146e-14 relative error = 6.439498820013536e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.940000000000001 y1[1] (analytic) = 0.3608728801397684 y1[1] (numeric) = 0.3608728801398047 absolute error = 3.630429290524262e-14 relative error = 1.006013333315092e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9326150140222 y2[1] (numeric) = -0.9326150140222605 absolute error = 6.050715484207103e-14 relative error = 6.487902717876545e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.950000000000001 y1[1] (analytic) = 0.3701808313512881 y1[1] (numeric) = 0.3701808313513251 absolute error = 3.697042672001771e-14 relative error = 9.987126179673558e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9289597150038689 y2[1] (numeric) = -0.9289597150039296 absolute error = 6.072919944699606e-14 relative error = 6.537334016334943e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.960000000000001 y1[1] (analytic) = 0.3794517647881557 y1[1] (numeric) = 0.3794517647881933 absolute error = 3.752553823233029e-14 relative error = 9.889409330664318e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9252115207881677 y2[1] (numeric) = -0.9252115207882288 absolute error = 6.106226635438361e-14 relative error = 6.599816904826908e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.970000000000001 y1[1] (analytic) = 0.3886847533647532 y1[1] (numeric) = 0.3886847533647914 absolute error = 3.819167204710538e-14 relative error = 9.825873465961551e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9213708061913949 y2[1] (numeric) = -0.9213708061914562 absolute error = 6.128431095930864e-14 relative error = 6.651427476049003e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.980000000000001 y1[1] (analytic) = 0.3978788737899172 y1[1] (numeric) = 0.397878873789956 absolute error = 3.874678355941796e-14 relative error = 9.738336491792859e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9174379552818093 y2[1] (numeric) = -0.9174379552818709 absolute error = 6.161737786669619e-14 relative error = 6.716244680303115e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.990000000000001 y1[1] (analytic) = 0.4070332066592667 y1[1] (numeric) = 0.4070332066593061 absolute error = 3.941291737419306e-14 relative error = 9.682973459997373e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9134133613412246 y2[1] (numeric) = -0.9134133613412865 absolute error = 6.183942247162122e-14 relative error = 6.770146473532897e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.000000000000001 y1[1] (analytic) = 0.4161468365471436 y1[1] (numeric) = 0.4161468365471836 absolute error = 4.002354003773689e-14 relative error = 9.617648513159559e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9092974268256812 y2[1] (numeric) = -0.9092974268257432 absolute error = 6.206146707654625e-14 relative error = 6.825210898616551e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.010000000000001 y1[1] (analytic) = 0.4252188520981534 y1[1] (numeric) = 0.4252188520981942 absolute error = 4.08006961549745e-14 relative error = 9.595222778494417e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9050905633252004 y2[1] (numeric) = -0.9050905633252626 absolute error = 6.217248937900877e-14 relative error = 6.869200928423568e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.020000000000001 y1[1] (analytic) = 0.4342483461183013 y1[1] (numeric) = 0.4342483461183429 absolute error = 4.163336342344337e-14 relative error = 9.587454689372907e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9007931915226269 y2[1] (numeric) = -0.9007931915226891 absolute error = 6.217248937900877e-14 relative error = 6.901971502905954e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.030000000000001 y1[1] (analytic) = 0.4432344156657097 y1[1] (numeric) = 0.4432344156657522 absolute error = 4.246603069191224e-14 relative error = 9.580941639680885e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8964057411515596 y2[1] (numeric) = -0.8964057411516219 absolute error = 6.228351168147128e-14 relative error = 6.948138417928842e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.04 y1[1] (analytic) = 0.4521761621409124 y1[1] (numeric) = 0.4521761621409556 absolute error = 4.324318680914985e-14 relative error = 9.5633495150224e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8919286509533794 y2[1] (numeric) = -0.8919286509534418 absolute error = 6.23945339839338e-14 relative error = 6.995462464092896e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.05 y1[1] (analytic) = 0.4610726913767131 y1[1] (numeric) = 0.4610726913767572 absolute error = 4.407585407761871e-14 relative error = 9.559415446187669e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8873623686333753 y2[1] (numeric) = -0.8873623686334376 absolute error = 6.23945339839338e-14 relative error = 7.031460448342821e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.06 y1[1] (analytic) = 0.4699231137276022 y1[1] (numeric) = 0.4699231137276471 absolute error = 4.490852134608758e-14 relative error = 9.55656787976585e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8827073508159741 y2[1] (numeric) = -0.8827073508160364 absolute error = 6.228351168147128e-14 relative error = 7.055963862076876e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.07 y1[1] (analytic) = 0.4787265441587198 y1[1] (numeric) = 0.4787265441587655 absolute error = 4.574118861455645e-14 relative error = 9.554763397325039e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8779640629990781 y2[1] (numeric) = -0.8779640629991405 absolute error = 6.23945339839338e-14 relative error = 7.106729832516996e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.08 y1[1] (analytic) = 0.487482102334359 y1[1] (numeric) = 0.4874821023344055 absolute error = 4.651834473179406e-14 relative error = 9.542574898449831e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8731329795075167 y2[1] (numeric) = -0.8731329795075791 absolute error = 6.23945339839338e-14 relative error = 7.146051683802725e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.089999999999999 y1[1] (analytic) = 0.4961889127059985 y1[1] (numeric) = 0.4961889127060458 absolute error = 4.735101200026293e-14 relative error = 9.54294035754066e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8682145834456129 y2[1] (numeric) = -0.8682145834456751 absolute error = 6.228351168147128e-14 relative error = 7.173746314452789e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.099999999999999 y1[1] (analytic) = 0.5048461045998568 y1[1] (numeric) = 0.5048461045999049 absolute error = 4.807265696626928e-14 relative error = 9.522239852553061e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8632093666488742 y2[1] (numeric) = -0.8632093666489364 absolute error = 6.228351168147128e-14 relative error = 7.215342428832357e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.109999999999999 y1[1] (analytic) = 0.5134528123039588 y1[1] (numeric) = 0.5134528123040076 absolute error = 4.884981308350689e-14 relative error = 9.51398296258397e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8581178296348094 y2[1] (numeric) = -0.8581178296348716 absolute error = 6.217248937900877e-14 relative error = 7.245215893657356e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.119999999999999 y1[1] (analytic) = 0.5220081751547062 y1[1] (numeric) = 0.5220081751547559 absolute error = 4.973799150320701e-14 relative error = 9.528201639460204e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8529404815528769 y2[1] (numeric) = -0.852940481552939 absolute error = 6.206146707654625e-14 relative error = 7.276177930206357e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.129999999999999 y1[1] (analytic) = 0.5305113376229437 y1[1] (numeric) = 0.5305113376229942 absolute error = 5.051514762044462e-14 relative error = 9.521973243170879e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8476778401335705 y2[1] (numeric) = -0.8476778401336326 absolute error = 6.206146707654625e-14 relative error = 7.321350652125941e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.139999999999998 y1[1] (analytic) = 0.5389614493995101 y1[1] (numeric) = 0.5389614493995614 absolute error = 5.129230373768223e-14 relative error = 9.516878024361505e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8423304316366466 y2[1] (numeric) = -0.8423304316367085 absolute error = 6.195044477408373e-14 relative error = 7.354648775269121e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.149999999999998 y1[1] (analytic) = 0.5473576654802695 y1[1] (numeric) = 0.5473576654803216 absolute error = 5.206945985491984e-14 relative error = 9.512876705441294e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8368987907984987 y2[1] (numeric) = -0.8368987907985606 absolute error = 6.183942247162122e-14 relative error = 7.389116002022087e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.159999999999998 y1[1] (analytic) = 0.5556991462506109 y1[1] (numeric) = 0.5556991462506637 absolute error = 5.284661597215745e-14 relative error = 9.509932906811507e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8313834607786843 y2[1] (numeric) = -0.831383460778746 absolute error = 6.17284001691587e-14 relative error = 7.424780872035042e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.169999999999998 y1[1] (analytic) = 0.5639850575694082 y1[1] (numeric) = 0.5639850575694619 absolute error = 5.373479439185758e-14 relative error = 9.527698237864143e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8257849931056094 y2[1] (numeric) = -0.8257849931056709 absolute error = 6.150635556423367e-14 relative error = 7.448228785669837e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.179999999999997 y1[1] (analytic) = 0.5722145708524347 y1[1] (numeric) = 0.5722145708524892 absolute error = 5.451195050909519e-14 relative error = 9.526487664913549e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8201039476213756 y2[1] (numeric) = -0.820103947621437 absolute error = 6.139533326177116e-14 relative error = 7.486286761555264e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.189999999999997 y1[1] (analytic) = 0.5803868631552197 y1[1] (numeric) = 0.580386863155275 absolute error = 5.52891066263328e-14 relative error = 9.526250529820517e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8143408924257975 y2[1] (numeric) = -0.8143408924258586 absolute error = 6.106226635438361e-14 relative error = 7.498366706415591e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.199999999999997 y1[1] (analytic) = 0.5885011172553434 y1[1] (numeric) = 0.5885011172553994 absolute error = 5.606626274357041e-14 relative error = 9.526959439780289e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8084964038195919 y2[1] (numeric) = -0.8084964038196528 absolute error = 6.095124405192109e-14 relative error = 7.53883922847006e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.209999999999997 y1[1] (analytic) = 0.5965565217341574 y1[1] (numeric) = 0.5965565217342143 absolute error = 5.684341886080801e-14 relative error = 9.52858895843889e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.8025710662467491 y2[1] (numeric) = -0.8025710662468098 absolute error = 6.072919944699606e-14 relative error = 7.566831399865713e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.219999999999997 y1[1] (analytic) = 0.6045522710579269 y1[1] (numeric) = 0.6045522710579845 absolute error = 5.762057497804562e-14 relative error = 9.531115461234377e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.7965654722360886 y2[1] (numeric) = -0.7965654722361492 absolute error = 6.050715484207103e-14 relative error = 7.596005218782284e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.229999999999996 y1[1] (analytic) = 0.6124875656583824 y1[1] (numeric) = 0.6124875656584408 absolute error = 5.839773109528323e-14 relative error = 9.534517004032507e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.790480222342007 y2[1] (numeric) = -0.7904802223420672 absolute error = 6.017408793468348e-14 relative error = 7.612345791068854e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.239999999999996 y1[1] (analytic) = 0.6203616120126767 y1[1] (numeric) = 0.6203616120127358 absolute error = 5.906386491005833e-14 relative error = 9.520876818672557e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.7843159250844224 y2[1] (numeric) = -0.7843159250844823 absolute error = 5.995204332975845e-14 relative error = 7.643864087460078e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.249999999999996 y1[1] (analytic) = 0.628173622722736 y1[1] (numeric) = 0.6281736227227959 absolute error = 5.984102102729594e-14 relative error = 9.526191304869328e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.7780731968879238 y2[1] (numeric) = -0.7780731968879834 absolute error = 5.961897642237091e-14 relative error = 7.66238660589135e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.259999999999996 y1[1] (analytic) = 0.6359228165939993 y1[1] (numeric) = 0.6359228165940599 absolute error = 6.061817714453355e-14 relative error = 9.532316747054985e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.7717526620201285 y2[1] (numeric) = -0.7717526620201878 absolute error = 5.928590951498336e-14 relative error = 7.681983157634653e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.269999999999996 y1[1] (analytic) = 0.6436084187135371 y1[1] (numeric) = 0.6436084187135985 absolute error = 6.139533326177116e-14 relative error = 9.539237131871255e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.7653549525292563 y2[1] (numeric) = -0.7653549525293153 absolute error = 5.895284260759581e-14 relative error = 7.702679967350481e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.279999999999995 y1[1] (analytic) = 0.6512296605275422 y1[1] (numeric) = 0.6512296605276043 absolute error = 6.217248937900877e-14 relative error = 9.546937608561109e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.7588807081809249 y2[1] (numeric) = -0.7588807081809835 absolute error = 5.861977570020827e-14 relative error = 7.724504664339511e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.289999999999995 y1[1] (analytic) = 0.6587857799181841 y1[1] (numeric) = 0.6587857799182469 absolute error = 6.283862319378386e-14 relative error = 9.53855184937172e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.7523305763941739 y2[1] (numeric) = -0.7523305763942322 absolute error = 5.828670879282072e-14 relative error = 7.747486360607807e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.299999999999995 y1[1] (analytic) = 0.6662760212798204 y1[1] (numeric) = 0.6662760212798841 absolute error = 6.361577931102147e-14 relative error = 9.547961697439554e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.7457052121767236 y2[1] (numeric) = -0.7457052121767814 absolute error = 5.784261958297066e-14 relative error = 7.756767505235382e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.309999999999995 y1[1] (analytic) = 0.673699635594557 y1[1] (numeric) = 0.6736996355946213 absolute error = 6.428191312579656e-14 relative error = 9.541628008907284e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.7390052780594745 y2[1] (numeric) = -0.7390052780595319 absolute error = 5.739853037312059e-14 relative error = 7.766998704507387e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.319999999999995 y1[1] (analytic) = 0.6810558805071486 y1[1] (numeric) = 0.6810558805072137 absolute error = 6.505906924303417e-14 relative error = 9.552677115802584e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.7322314440302551 y2[1] (numeric) = -0.732231444030312 absolute error = 5.695444116327053e-14 relative error = 7.77820204630781e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.329999999999994 y1[1] (analytic) = 0.6883440203992341 y1[1] (numeric) = 0.6883440203993 absolute error = 6.583622536027178e-14 relative error = 9.56443630062876e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.7253843874668235 y2[1] (numeric) = -0.7253843874668801 absolute error = 5.651035195342047e-14 relative error = 7.79040091430215e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.339999999999994 y1[1] (analytic) = 0.6955633264628979 y1[1] (numeric) = 0.6955633264629645 absolute error = 6.661338147750939e-14 relative error = 9.576896731495896e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.7184647930691302 y2[1] (numeric) = -0.7184647930691863 absolute error = 5.606626274357041e-14 relative error = 7.80362006384017e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.349999999999994 y1[1] (analytic) = 0.7027130767735495 y1[1] (numeric) = 0.7027130767736168 absolute error = 6.727951529228449e-14 relative error = 9.574251215189129e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.7114733527908488 y2[1] (numeric) = -0.7114733527909043 absolute error = 5.551115123125783e-14 relative error = 7.802281141452166e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.359999999999994 y1[1] (analytic) = 0.7097925563621161 y1[1] (numeric) = 0.7097925563621841 absolute error = 6.794564910705958e-14 relative error = 9.572606601469575e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.7044107657701806 y2[1] (numeric) = -0.7044107657702356 absolute error = 5.506706202140776e-14 relative error = 7.817464567169011e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.369999999999993 y1[1] (analytic) = 0.7168010572865383 y1[1] (numeric) = 0.7168010572866069 absolute error = 6.861178292183467e-14 relative error = 9.571942204098535e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.6972777382599425 y2[1] (numeric) = -0.6972777382599971 absolute error = 5.451195050909519e-14 relative error = 7.817824593845463e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.379999999999993 y1[1] (analytic) = 0.723737878702564 y1[1] (numeric) = 0.7237378787026334 absolute error = 6.938893903907228e-14 relative error = 9.587578746529749e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.6900749835569413 y2[1] (numeric) = -0.6900749835569953 absolute error = 5.395683899678261e-14 relative error = 7.818982035642853e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.389999999999993 y1[1] (analytic) = 0.7306023269338324 y1[1] (numeric) = 0.7306023269339025 absolute error = 7.005507285384738e-14 relative error = 9.58867365613961e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.6828032219306449 y2[1] (numeric) = -0.6828032219306983 absolute error = 5.340172748447003e-14 relative error = 7.820954232388532e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.399999999999993 y1[1] (analytic) = 0.7373937155412407 y1[1] (numeric) = 0.7373937155413114 absolute error = 7.072120666862247e-14 relative error = 9.590698317345126e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.6754631805511563 y2[1] (numeric) = -0.6754631805512091 absolute error = 5.284661597215745e-14 relative error = 7.823759679844622e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.409999999999993 y1[1] (analytic) = 0.7441113653915875 y1[1] (numeric) = 0.7441113653916589 absolute error = 7.138734048339757e-14 relative error = 9.593636625322889e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.6680555934164966 y2[1] (numeric) = -0.6680555934165489 absolute error = 5.229150445984487e-14 relative error = 7.827418103397864e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.419999999999992 y1[1] (analytic) = 0.7507546047254859 y1[1] (numeric) = 0.750754604725558 absolute error = 7.205347429817266e-14 relative error = 9.597473507940598e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.6605812012792064 y2[1] (numeric) = -0.6605812012792581 absolute error = 5.173639294753229e-14 relative error = 7.83195053800282e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.429999999999992 y1[1] (analytic) = 0.7573227692245386 y1[1] (numeric) = 0.7573227692246113 absolute error = 7.271960811294775e-14 relative error = 9.602194872261542e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.6530407515722708 y2[1] (numeric) = -0.6530407515723219 absolute error = 5.10702591327572e-14 relative error = 7.820378591963775e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.439999999999992 y1[1] (analytic) = 0.7638152020777689 y1[1] (numeric) = 0.7638152020778423 absolute error = 7.338574192772285e-14 relative error = 9.607787554907944e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.6454349983343768 y2[1] (numeric) = -0.6454349983344272 absolute error = 5.040412531798211e-14 relative error = 7.809326337749898e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.449999999999992 y1[1] (analytic) = 0.7702312540473021 y1[1] (numeric) = 0.770231254047376 absolute error = 7.394085344003543e-14 relative error = 9.599825124143107e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.6377647021345101 y2[1] (numeric) = -0.6377647021345598 absolute error = 4.973799150320701e-14 relative error = 7.798799672785409e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.459999999999992 y1[1] (analytic) = 0.7765702835332877 y1[1] (numeric) = 0.7765702835333623 absolute error = 7.460698725481052e-14 relative error = 9.607242105036393e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.6300306299958988 y2[1] (numeric) = -0.6300306299959478 absolute error = 4.907185768843192e-14 relative error = 7.788805075834385e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.469999999999991 y1[1] (analytic) = 0.7828316566380599 y1[1] (numeric) = 0.782831656638135 absolute error = 7.51620987671231e-14 relative error = 9.601310592102701e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.6222335553193116 y2[1] (numeric) = -0.62223355531936 absolute error = 4.840572387365683e-14 relative error = 7.779349644494254e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.479999999999991 y1[1] (analytic) = 0.7890147472295257 y1[1] (numeric) = 0.7890147472296015 absolute error = 7.582823258189819e-14 relative error = 9.610496235736343e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.6143742578057187 y2[1] (numeric) = -0.6143742578057664 absolute error = 4.762856775641922e-14 relative error = 7.752370342879929e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.489999999999991 y1[1] (analytic) = 0.7951189370037787 y1[1] (numeric) = 0.7951189370038551 absolute error = 7.638334409421077e-14 relative error = 9.606530613148731e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.6064535233783221 y2[1] (numeric) = -0.606453523378369 absolute error = 4.685141163918161e-14 relative error = 7.725474390550194e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.499999999999991 y1[1] (analytic) = 0.8011436155469281 y1[1] (numeric) = 0.8011436155470052 absolute error = 7.704947790898586e-14 relative error = 9.617436426349775e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.598472144103964 y2[1] (numeric) = -0.5984721441040101 absolute error = 4.6074255521944e-14 relative error = 7.698646624719124e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.50999999999999 y1[1] (analytic) = 0.8070881803961404 y1[1] (numeric) = 0.8070881803962181 absolute error = 7.771561172376096e-14 relative error = 9.629135156658602e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.5904309181139206 y2[1] (numeric) = -0.5904309181139659 absolute error = 4.529709940470639e-14 relative error = 7.671871173244784e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.51999999999999 y1[1] (analytic) = 0.8129520370998843 y1[1] (numeric) = 0.8129520370999626 absolute error = 7.827072323607354e-14 relative error = 9.627963233267193e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.5823306495240899 y2[1] (numeric) = -0.5823306495241344 absolute error = 4.451994328746878e-14 relative error = 7.645131391221247e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.52999999999999 y1[1] (analytic) = 0.818734599277376 y1[1] (numeric) = 0.8187345992774548 absolute error = 7.882583474838611e-14 relative error = 9.62776396868517e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.5741721483545806 y2[1] (numeric) = -0.5741721483546244 absolute error = 4.374278717023117e-14 relative error = 7.618409791486048e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.53999999999999 y1[1] (analytic) = 0.8244352886772165 y1[1] (numeric) = 0.8244352886772959 absolute error = 7.938094626069869e-14 relative error = 9.628523590743334e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.5659562304487112 y2[1] (numeric) = -0.5659562304487541 absolute error = 4.285460875053104e-14 relative error = 7.572071203554789e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.54999999999999 y1[1] (analytic) = 0.8300535352352164 y1[1] (numeric) = 0.8300535352352963 absolute error = 7.993605777301127e-14 relative error = 9.630229181586389e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.5576837173914255 y2[1] (numeric) = -0.5576837173914675 absolute error = 4.196643033083092e-14 relative error = 7.525131005640539e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.559999999999989 y1[1] (analytic) = 0.8355887771314018 y1[1] (numeric) = 0.8355887771314823 absolute error = 8.049116928532385e-14 relative error = 9.632868641636398e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.5493554364271356 y2[1] (numeric) = -0.5493554364271767 absolute error = 4.107825191113079e-14 relative error = 7.477536251992522e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.569999999999989 y1[1] (analytic) = 0.8410404608461957 y1[1] (numeric) = 0.8410404608462767 absolute error = 8.104628079763643e-14 relative error = 9.636430655915575e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.5409722203769975 y2[1] (numeric) = -0.5409722203770377 absolute error = 4.019007349143067e-14 relative error = 7.429230555207188e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.579999999999989 y1[1] (analytic) = 0.8464080412157696 y1[1] (numeric) = 0.8464080412158512 absolute error = 8.160139230994901e-14 relative error = 9.640904662571236e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.5325349075556305 y2[1] (numeric) = -0.5325349075556698 absolute error = 3.930189507173054e-14 relative error = 7.380153772853833e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.589999999999989 y1[1] (analytic) = 0.8516909814865598 y1[1] (numeric) = 0.8516909814866418 absolute error = 8.204548151979907e-14 relative error = 9.633245308831981e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.5240443416872855 y2[1] (numeric) = -0.5240443416873239 absolute error = 3.841371665203042e-14 relative error = 7.330241660151947e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.599999999999989 y1[1] (analytic) = 0.8568887533689413 y1[1] (numeric) = 0.8568887533690238 absolute error = 8.248957072964913e-14 relative error = 9.626637110749017e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.515501371821474 y2[1] (numeric) = -0.5155013718215115 absolute error = 3.741451592986778e-14 relative error = 7.257888722520217e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.609999999999988 y1[1] (analytic) = 0.8620008370900576 y1[1] (numeric) = 0.8620008370901405 absolute error = 8.293365993949919e-14 relative error = 9.621064895884166e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.5069068522480634 y2[1] (numeric) = -0.5069068522480998 absolute error = 3.641531520770513e-14 relative error = 7.183827767608216e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.619999999999988 y1[1] (analytic) = 0.8670267214457965 y1[1] (numeric) = 0.8670267214458799 absolute error = 8.337774914934926e-14 relative error = 9.616514357286938e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.4982616424118489 y2[1] (numeric) = -0.4982616424118844 absolute error = 3.547162563677375e-14 relative error = 7.11907612736802e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.629999999999988 y1[1] (analytic) = 0.8719659038519106 y1[1] (numeric) = 0.8719659038519946 absolute error = 8.393286066166183e-14 relative error = 9.625704433038986e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.48956660682661 y2[1] (numeric) = -0.4895666068266444 absolute error = 3.447242491461111e-14 relative error = 7.041416721222619e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.639999999999988 y1[1] (analytic) = 0.8768178903942755 y1[1] (numeric) = 0.8768178903943599 absolute error = 8.43769498715119e-14 relative error = 9.623087165063481e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.4808226149886591 y2[1] (numeric) = -0.4808226149886926 absolute error = 3.347322419244847e-14 relative error = 6.961657615301223e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.649999999999987 y1[1] (analytic) = 0.88158219587828 y1[1] (numeric) = 0.8815821958783648 absolute error = 8.482103908136196e-14 relative error = 9.62145554639504e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.4720305412898936 y2[1] (numeric) = -0.4720305412899261 absolute error = 3.241851231905457e-14 relative error = 6.867884486979628e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.659999999999987 y1[1] (analytic) = 0.886258343877346 y1[1] (numeric) = 0.8862583438774313 absolute error = 8.526512829121202e-14 relative error = 9.620798368812008e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.4631912649303566 y2[1] (numeric) = -0.463191264930388 absolute error = 3.141931159689193e-14 relative error = 6.783226277295191e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.669999999999987 y1[1] (analytic) = 0.8908458667805706 y1[1] (numeric) = 0.8908458667806562 absolute error = 8.559819519859957e-14 relative error = 9.608642571126588e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.4543056698303179 y2[1] (numeric) = -0.4543056698303483 absolute error = 3.030908857226677e-14 relative error = 6.671518888062116e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.679999999999987 y1[1] (analytic) = 0.8953443058394861 y1[1] (numeric) = 0.8953443058395721 absolute error = 8.604228440844963e-14 relative error = 9.609966115524162e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.4453746445418831 y2[1] (numeric) = -0.4453746445419123 absolute error = 2.919886554764162e-14 relative error = 6.556023317779096e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.689999999999987 y1[1] (analytic) = 0.8997532112139355 y1[1] (numeric) = 0.8997532112140219 absolute error = 8.637535131583718e-14 relative error = 9.599893641868825e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.4363990821601383 y2[1] (numeric) = -0.4363990821601664 absolute error = 2.814415367424772e-14 relative error = 6.449178017271841e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.699999999999986 y1[1] (analytic) = 0.9040721420170553 y1[1] (numeric) = 0.904072142017142 absolute error = 8.670841822322473e-14 relative error = 9.590873802368415e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.4273798802338422 y2[1] (numeric) = -0.4273798802338692 absolute error = 2.703393064962256e-14 relative error = 6.325503819887558e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.709999999999986 y1[1] (analytic) = 0.9083006663593644 y1[1] (numeric) = 0.9083006663594515 absolute error = 8.715250743307479e-14 relative error = 9.595116535849085e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.4183179406756715 y2[1] (numeric) = -0.4183179406756974 absolute error = 2.592370762499741e-14 relative error = 6.197130245746851e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.719999999999986 y1[1] (analytic) = 0.9124383613919522 y1[1] (numeric) = 0.9124383613920397 absolute error = 8.748557434046234e-14 relative error = 9.588107870322381e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.4092141696720303 y2[1] (numeric) = -0.409214169672055 absolute error = 2.475797344914099e-14 relative error = 6.050126140300463e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.729999999999986 y1[1] (analytic) = 0.9164848133487636 y1[1] (numeric) = 0.9164848133488515 absolute error = 8.781864124784988e-14 relative error = 9.58211636120488e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.4000694775924326 y2[1] (numeric) = -0.4000694775924561 absolute error = 2.359223927328458e-14 relative error = 5.897035538741842e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.739999999999986 y1[1] (analytic) = 0.920439617587975 y1[1] (numeric) = 0.9204396175880631 absolute error = 8.815170815523743e-14 relative error = 9.577131022047946e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.3908847788984657 y2[1] (numeric) = -0.3908847788984881 absolute error = 2.242650509742816e-14 relative error = 5.737369759095573e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.749999999999985 y1[1] (analytic) = 0.9243023786324579 y1[1] (numeric) = 0.9243023786325464 absolute error = 8.848477506262498e-14 relative error = 9.573141550662426e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.3816609920523453 y2[1] (numeric) = -0.3816609920523664 absolute error = 2.114974861910923e-14 relative error = 5.541501243126392e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.759999999999985 y1[1] (analytic) = 0.9280727102093271 y1[1] (numeric) = 0.9280727102094158 absolute error = 8.870681966755001e-14 relative error = 9.558175635564389e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.3723990394250693 y2[1] (numeric) = -0.3723990394250893 absolute error = 1.998401444325282e-14 relative error = 5.36629054524557e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.769999999999985 y1[1] (analytic) = 0.9317502352885667 y1[1] (numeric) = 0.9317502352886557 absolute error = 8.903988657493755e-14 relative error = 9.556196843606008e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.3630998472041824 y2[1] (numeric) = -0.3630998472042011 absolute error = 1.876276911616515e-14 relative error = 5.167385571940011e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.779999999999985 y1[1] (analytic) = 0.9353345861207334 y1[1] (numeric) = 0.9353345861208227 absolute error = 8.926193117986259e-14 relative error = 9.543315569038587e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.3537643453011572 y2[1] (numeric) = -0.3537643453011747 absolute error = 1.748601263784622e-14 relative error = 4.94284199922988e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.789999999999984 y1[1] (analytic) = 0.9388254042737308 y1[1] (numeric) = 0.9388254042738204 absolute error = 8.959499808725013e-14 relative error = 9.543307805625502e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.3443934672584046 y2[1] (numeric) = -0.3443934672584208 absolute error = 1.626476731075854e-14 relative error = 4.722728174908961e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.799999999999984 y1[1] (analytic) = 0.9422223406686528 y1[1] (numeric) = 0.9422223406687427 absolute error = 8.981704269217516e-14 relative error = 9.532467955327406e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.3349881501559197 y2[1] (numeric) = -0.3349881501559347 absolute error = 1.498801083243961e-14 relative error = 4.474191348399479e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.809999999999984 y1[1] (analytic) = 0.9455250556146907 y1[1] (numeric) = 0.9455250556147807 absolute error = 9.00390872971002e-14 relative error = 9.522654821512406e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.3255493345175751 y2[1] (numeric) = -0.3255493345175888 absolute error = 1.371125435412068e-14 relative error = 4.21172857700327e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.819999999999984 y1[1] (analytic) = 0.948733218843102 y1[1] (numeric) = 0.9487332188431922 absolute error = 9.015010959956271e-14 relative error = 9.502155907378574e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.316077964217069 y2[1] (numeric) = -0.3160779642170814 absolute error = 1.243449787580175e-14 relative error = 3.933997077778654e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.829999999999984 y1[1] (analytic) = 0.9518465095402373 y1[1] (numeric) = 0.9518465095403277 absolute error = 9.037215420448774e-14 relative error = 9.494404118594654e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.3065749863835386 y2[1] (numeric) = -0.3065749863835496 absolute error = 1.104671909502031e-14 relative error = 3.603268233110311e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.839999999999983 y1[1] (analytic) = 0.9548646163796215 y1[1] (numeric) = 0.954864616379712 absolute error = 9.048317650695026e-14 relative error = 9.476021517062608e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.2970413513068481 y2[1] (numeric) = -0.2970413513068578 absolute error = 9.71445146547012e-15 relative error = 3.270403741004715e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.849999999999983 y1[1] (analytic) = 0.9577872375530855 y1[1] (numeric) = 0.9577872375531762 absolute error = 9.070522111187529e-14 relative error = 9.470289178586799e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.2874780123425605 y2[1] (numeric) = -0.2874780123425689 absolute error = 8.382183835919932e-15 relative error = 2.915765198046406e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.859999999999983 y1[1] (analytic) = 0.9606140808009476 y1[1] (numeric) = 0.9606140808010384 absolute error = 9.081624341433781e-14 relative error = 9.453977953208473e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.277885925816603 y2[1] (numeric) = -0.27788592581661 absolute error = 6.994405055138486e-15 relative error = 2.517005866556409e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.869999999999983 y1[1] (analytic) = 0.9633448634412386 y1[1] (numeric) = 0.9633448634413295 absolute error = 9.092726571680032e-14 relative error = 9.438703538833643e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.2682660509296346 y2[1] (numeric) = -0.2682660509296402 absolute error = 5.551115123125783e-15 relative error = 2.069257404688088e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.879999999999983 y1[1] (analytic) = 0.9659793123979703 y1[1] (numeric) = 0.9659793123980612 absolute error = 9.092726571680032e-14 relative error = 9.412962011689494e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.2586193496611275 y2[1] (numeric) = -0.2586193496611317 absolute error = 4.163336342344337e-15 relative error = 1.609831726744195e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.889999999999982 y1[1] (analytic) = 0.9685171642284423 y1[1] (numeric) = 0.9685171642285333 absolute error = 9.103828801926284e-14 relative error = 9.399759899122429e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.2489467866731698 y2[1] (numeric) = -0.2489467866731725 absolute error = 2.747801985947262e-15 relative error = 1.103770818923933e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.899999999999982 y1[1] (analytic) = 0.9709581651495862 y1[1] (numeric) = 0.9709581651496774 absolute error = 9.114931032172535e-14 relative error = 9.387563089052642e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.2392493292139997 y2[1] (numeric) = -0.239249329214001 absolute error = 1.304512053934559e-15 relative error = 5.452521259809766e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.909999999999982 y1[1] (analytic) = 0.9733020710633444 y1[1] (numeric) = 0.9733020710634356 absolute error = 9.114931032172535e-14 relative error = 9.36495596091187e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.2295279470212819 y2[1] (numeric) = -0.2295279470212818 absolute error = 1.387778780781446e-16 relative error = 6.04623009438049e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.919999999999982 y1[1] (analytic) = 0.9755486475810786 y1[1] (numeric) = 0.9755486475811699 absolute error = 9.126033262418787e-14 relative error = 9.354770041501509e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.2197836122251347 y2[1] (numeric) = -0.2197836122251331 absolute error = 1.582067810090848e-15 relative error = 7.198297425698243e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.929999999999982 y1[1] (analytic) = 0.9776976700470092 y1[1] (numeric) = 0.9776976700471005 absolute error = 9.126033262418787e-14 relative error = 9.334207845642092e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.2100172992509174 y2[1] (numeric) = -0.2100172992509143 absolute error = 3.05311331771918e-15 relative error = 1.453743729020858e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.939999999999981 y1[1] (analytic) = 0.9797489235606806 y1[1] (numeric) = 0.9797489235607718 absolute error = 9.126033262418787e-14 relative error = 9.314665260618241e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.2002299847217888 y2[1] (numeric) = -0.2002299847217843 absolute error = 4.524158825347513e-15 relative error = 2.259481181918704e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.949999999999981 y1[1] (analytic) = 0.9817022029984505 y1[1] (numeric) = 0.9817022029985417 absolute error = 9.126033262418787e-14 relative error = 9.296131998629314e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.1904226473610458 y2[1] (numeric) = -0.1904226473610398 absolute error = 6.022959908591474e-15 relative error = 3.162943059588811e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.959999999999981 y1[1] (analytic) = 0.983557313034003 y1[1] (numeric) = 0.9835573130340942 absolute error = 9.126033262418787e-14 relative error = 9.2785983505806e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.1805962678942517 y2[1] (numeric) = -0.1805962678942442 absolute error = 7.521760991835436e-15 relative error = 4.164959264961007e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.969999999999981 y1[1] (analytic) = 0.9853140681578805 y1[1] (numeric) = 0.9853140681579716 absolute error = 9.114931032172535e-14 relative error = 9.250787466389871e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.1707518289511646 y2[1] (numeric) = -0.1707518289511555 absolute error = 9.048317650695026e-15 relative error = 5.299104382233507e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.97999999999998 y1[1] (analytic) = 0.9869722926960345 y1[1] (numeric) = 0.9869722926961255 absolute error = 9.103828801926284e-14 relative error = 9.223996326237358e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.1608903149674751 y2[1] (numeric) = -0.1608903149674645 absolute error = 1.057487430955462e-14 relative error = 6.572722734548932e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.98999999999998 y1[1] (analytic) = 0.988531820827393 y1[1] (numeric) = 0.988531820827484 absolute error = 9.103828801926284e-14 relative error = 9.209444359926071e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.1510127120863636 y2[1] (numeric) = -0.1510127120863515 absolute error = 1.212918654402984e-14 relative error = 8.031897696859585e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.99999999999998 y1[1] (analytic) = 0.9899924966004426 y1[1] (numeric) = 0.9899924966005336 absolute error = 9.092726571680032e-14 relative error = 9.184641906785909e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.141120008059887 y2[1] (numeric) = -0.1411200080598733 absolute error = 1.368349877850505e-14 relative error = 9.696356290383854e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.00999999999998 y1[1] (analytic) = 0.9913541739488232 y1[1] (numeric) = 0.991354173948914 absolute error = 9.081624341433781e-14 relative error = 9.160827260412183e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.131213192150204 y2[1] (numeric) = -0.1312131921501888 absolute error = 1.52655665885959e-14 relative error = 1.163417057266689e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.01999999999998 y1[1] (analytic) = 0.9926167167059347 y1[1] (numeric) = 0.9926167167060252 absolute error = 9.059419880941277e-14 relative error = 9.126805672793394e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.12129325503065 y2[1] (numeric) = -0.1212932550306332 absolute error = 1.686151218649456e-14 relative error = 1.390144256762981e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.029999999999979 y1[1] (analytic) = 0.9937799986185533 y1[1] (numeric) = 0.9937799986186437 absolute error = 9.048317650695026e-14 relative error = 9.104950455103775e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.1113611886866703 y2[1] (numeric) = -0.1113611886866518 absolute error = 1.847133557220104e-14 relative error = 1.658686997691146e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.039999999999979 y1[1] (analytic) = 0.9948439033594574 y1[1] (numeric) = 0.9948439033595476 absolute error = 9.026113190202523e-14 relative error = 9.072893908001569e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.1014179863166226 y2[1] (numeric) = -0.1014179863166025 absolute error = 2.009503674571533e-14 relative error = 1.981407586123776e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.049999999999979 y1[1] (analytic) = 0.9958083245390593 y1[1] (numeric) = 0.9958083245391494 absolute error = 9.00390872971002e-14 relative error = 9.041809058864574e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.09146464223245798 y2[1] (numeric) = -0.09146464223243626 absolute error = 2.171873791922962e-14 relative error = 2.374550141904159e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.059999999999979 y1[1] (analytic) = 0.9966731657160448 y1[1] (numeric) = 0.9966731657161347 absolute error = 8.992806499463768e-14 relative error = 9.022823939483735e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.08150215176029037 y2[1] (numeric) = -0.08150215176026701 absolute error = 2.335631688055173e-14 relative error = 2.865730091304343e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.069999999999979 y1[1] (analytic) = 0.997438340407017 y1[1] (numeric) = 0.9974383404071067 absolute error = 8.970602038971265e-14 relative error = 8.993640684907601e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.07153151114086496 y2[1] (numeric) = -0.07153151114083994 absolute error = 2.502165141748947e-14 relative error = 3.497990049198743e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.079999999999978 y1[1] (analytic) = 0.9981037720951443 y1[1] (numeric) = 0.9981037720952337 absolute error = 8.93729534823251e-14 relative error = 8.954274693774588e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.06155371742993487 y2[1] (numeric) = -0.06155371742990817 absolute error = 2.669392484833111e-14 relative error = 4.336687687257259e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.089999999999978 y1[1] (analytic) = 0.9986693942378124 y1[1] (numeric) = 0.9986693942379016 absolute error = 8.915090887740007e-14 relative error = 8.92696916434896e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.05156976839855636 y2[1] (numeric) = -0.051569768398528 absolute error = 2.836619827917275e-14 relative error = 5.500547929543703e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.099999999999978 y1[1] (analytic) = 0.9991351502732786 y1[1] (numeric) = 0.9991351502733674 absolute error = 8.881784197001252e-14 relative error = 8.889472254651385e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.04158066243331267 y2[1] (numeric) = -0.04158066243328262 absolute error = 3.005928839172611e-14 relative error = 7.229150915990189e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.109999999999978 y1[1] (analytic) = 0.9995009936263272 y1[1] (numeric) = 0.9995009936264158 absolute error = 8.859579736508749e-14 relative error = 8.864002930467307e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.03158739843647609 y2[1] (numeric) = -0.03158739843644433 absolute error = 3.176625629208729e-14 relative error = 1.005662316761252e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.119999999999977 y1[1] (analytic) = 0.9997668877129279 y1[1] (numeric) = 0.9997668877130161 absolute error = 8.826273045769994e-14 relative error = 8.828331038209341e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.0215909757261186 y2[1] (numeric) = -0.02159097572608513 absolute error = 3.347322419244847e-14 relative error = 1.550334019965384e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.129999999999977 y1[1] (analytic) = 0.9999328059438936 y1[1] (numeric) = 0.9999328059439815 absolute error = 8.79296635503124e-14 relative error = 8.793557229809115e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.01159239393618092 y2[1] (numeric) = -0.01159239393614572 absolute error = 3.519753932756942e-14 relative error = 3.036261493643231e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.139999999999977 y1[1] (analytic) = 0.9999987317275395 y1[1] (numeric) = 0.999998731727627 absolute error = 8.748557434046234e-14 relative error = 8.748568529614768e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.001592652916509921 y2[1] (numeric) = -0.001592652916472989 absolute error = 3.693139544180823e-14 relative error = 2.318860252536271e-09 % Correct digits = 11 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.149999999999977 y1[1] (analytic) = 0.9999646584713422 y1[1] (numeric) = 0.9999646584714292 absolute error = 8.704148513061227e-14 relative error = 8.704456141847415e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.008407247367125526 y2[1] (numeric) = 0.008407247367164201 absolute error = 3.867565989690291e-14 relative error = 4.600276191245969e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.159999999999977 y1[1] (analytic) = 0.9998305895825987 y1[1] (numeric) = 0.9998305895826854 absolute error = 8.670841822322473e-14 relative error = 8.67231100214918e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.01840630693303028 y2[1] (numeric) = 0.0184063069330707 absolute error = 4.042946533111547e-14 relative error = 2.1965006602473e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.169999999999976 y1[1] (analytic) = 0.9995965384680865 y1[1] (numeric) = 0.9995965384681728 absolute error = 8.626432901337466e-14 relative error = 8.629914739958733e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.02840352588358026 y2[1] (numeric) = 0.02840352588362245 absolute error = 4.21919443827079e-14 relative error = 1.485447424930387e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.179999999999976 y1[1] (analytic) = 0.9992625285327218 y1[1] (numeric) = 0.9992625285328076 absolute error = 8.58202398035246e-14 relative error = 8.58835764906943e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.03839790450521142 y2[1] (numeric) = 0.03839790450525538 absolute error = 4.395789288125229e-14 relative error = 1.144799265680924e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.189999999999976 y1[1] (analytic) = 0.9988285931772198 y1[1] (numeric) = 0.9988285931773052 absolute error = 8.537615059367454e-14 relative error = 8.547627808901387e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.0483884433683902 y2[1] (numeric) = 0.04838844336843594 absolute error = 4.574118861455645e-14 relative error = 9.452915909346431e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.199999999999976 y1[1] (analytic) = 0.9982947757947545 y1[1] (numeric) = 0.9982947757948394 absolute error = 8.493206138382448e-14 relative error = 8.507713697711083e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.0583741434275557 y2[1] (numeric) = 0.05837414342760324 absolute error = 4.753836213566842e-14 relative error = 8.14373613801548e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.209999999999976 y1[1] (analytic) = 0.9976611297666192 y1[1] (numeric) = 0.9976611297667036 absolute error = 8.43769498715119e-14 relative error = 8.457475925843679e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.06835400612102341 y2[1] (numeric) = 0.06835400612107276 absolute error = 4.934941344458821e-14 relative error = 7.219681222079825e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.219999999999975 y1[1] (analytic) = 0.9969277184568889 y1[1] (numeric) = 0.9969277184569727 absolute error = 8.382183835919932e-14 relative error = 8.4080156271454e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.07832703347084051 y2[1] (numeric) = 0.07832703347089166 absolute error = 5.115352585960409e-14 relative error = 6.530762572368768e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.229999999999975 y1[1] (analytic) = 0.9960946152060831 y1[1] (numeric) = 0.9960946152061664 absolute error = 8.326672684688674e-14 relative error = 8.35931904216344e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.08829222818258282 y2[1] (numeric) = 0.0882922281826358 absolute error = 5.297151606242778e-14 relative error = 5.999567249892707e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.239999999999975 y1[1] (analytic) = 0.9951619033238328 y1[1] (numeric) = 0.9951619033239155 absolute error = 8.271161533457416e-14 relative error = 8.311372758374093e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.09824859374508349 y2[1] (numeric) = 0.09824859374513829 absolute error = 5.480338405305929e-14 relative error = 5.578032413904319e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.249999999999975 y1[1] (analytic) = 0.9941296760805489 y1[1] (numeric) = 0.9941296760806311 absolute error = 8.215650382226158e-14 relative error = 8.264163700068933e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1081951345300832 y2[1] (numeric) = 0.1081951345301398 absolute error = 5.66352520436908e-14 relative error = 5.234547032976201e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.259999999999974 y1[1] (analytic) = 0.9929980366980957 y1[1] (numeric) = 0.9929980366981772 absolute error = 8.149037000748649e-14 relative error = 8.206498602802601e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1181308558917922 y2[1] (numeric) = 0.1181308558918507 absolute error = 5.848099782213012e-14 relative error = 4.950526886531548e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.269999999999974 y1[1] (analytic) = 0.9917670983394682 y1[1] (numeric) = 0.9917670983395491 absolute error = 8.093525849517391e-14 relative error = 8.160712190461363e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1280547642663541 y2[1] (numeric) = 0.1280547642664145 absolute error = 6.034062138837726e-14 relative error = 4.712094995768269e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.279999999999974 y1[1] (analytic) = 0.9904369840974767 y1[1] (numeric) = 0.9904369840975569 absolute error = 8.01581023779363e-14 relative error = 8.093205692533723e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1379658672712013 y2[1] (numeric) = 0.1379658672712635 absolute error = 6.22002449546244e-14 relative error = 4.50837922341738e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.289999999999974 y1[1] (analytic) = 0.9890078269824367 y1[1] (numeric) = 0.9890078269825163 absolute error = 7.960299086562372e-14 relative error = 8.048772587422339e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1478631738042926 y2[1] (numeric) = 0.1478631738043567 absolute error = 6.405986852087153e-14 relative error = 4.332374780867298e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.299999999999974 y1[1] (analytic) = 0.9874797699088691 y1[1] (numeric) = 0.9874797699089479 absolute error = 7.882583474838611e-14 relative error = 7.982526543876505e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1577456941432223 y2[1] (numeric) = 0.1577456941432883 absolute error = 6.591949208711867e-14 relative error = 4.178845733010516e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.309999999999973 y1[1] (analytic) = 0.9858529656812075 y1[1] (numeric) = 0.9858529656812857 absolute error = 7.815970093361102e-14 relative error = 7.928129615109896e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.167612440044192 y2[1] (numeric) = 0.1676124400442598 absolute error = 6.780687122898144e-14 relative error = 4.045455767549458e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.319999999999973 y1[1] (analytic) = 0.9841275769785193 y1[1] (numeric) = 0.9841275769785967 absolute error = 7.738254481637341e-14 relative error = 7.863060300977873e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1774624248408339 y2[1] (numeric) = 0.1774624248409036 absolute error = 6.96942503708442e-14 relative error = 3.927268008050323e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.329999999999973 y1[1] (analytic) = 0.9823037763382367 y1[1] (numeric) = 0.9823037763383133 absolute error = 7.66053886991358e-14 relative error = 7.798543642446333e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1872946635428766 y2[1] (numeric) = 0.1872946635429481 absolute error = 7.155387393709134e-14 relative error = 3.820390425630616e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.339999999999973 y1[1] (analytic) = 0.9803817461389042 y1[1] (numeric) = 0.98038174613898 absolute error = 7.582823258189819e-14 relative error = 7.734561856188882e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.1971081729346433 y2[1] (numeric) = 0.1971081729347167 absolute error = 7.344125307895411e-14 relative error = 3.725936473639051e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.349999999999973 y1[1] (analytic) = 0.9783616785819398 y1[1] (numeric) = 0.9783616785820148 absolute error = 7.505107646466058e-14 relative error = 7.67109731581488e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2069019716733728 y2[1] (numeric) = 0.2069019716734482 absolute error = 7.53563877964325e-14 relative error = 3.642129999389004e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.359999999999972 y1[1] (analytic) = 0.9762437756724158 y1[1] (numeric) = 0.9762437756724901 absolute error = 7.427392034742297e-14 relative error = 7.608132538029724e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2166750803873528 y2[1] (numeric) = 0.21667508038743 absolute error = 7.724376693829527e-14 relative error = 3.564958499159461e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.369999999999972 y1[1] (analytic) = 0.9740282491988584 y1[1] (numeric) = 0.9740282491989319 absolute error = 7.349676423018536e-14 relative error = 7.54565016883614e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2264265217738559 y2[1] (numeric) = 0.2264265217739351 absolute error = 7.918665723138929e-14 relative error = 3.497234184892756e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.379999999999972 y1[1] (analytic) = 0.9717153207120687 y1[1] (numeric) = 0.9717153207121413 absolute error = 7.260858581048524e-14 relative error = 7.472207575905873e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2361553206968698 y2[1] (numeric) = 0.2361553206969509 absolute error = 8.107403637325206e-14 relative error = 3.433081081298994e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.389999999999972 y1[1] (analytic) = 0.9693052215029678 y1[1] (numeric) = 0.9693052215030395 absolute error = 7.172040739078511e-14 relative error = 7.399156199693031e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2458605042846095 y2[1] (numeric) = 0.2458605042846925 absolute error = 8.298917109073045e-14 relative error = 3.37545761293411e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.399999999999971 y1[1] (analytic) = 0.9667981925794683 y1[1] (numeric) = 0.9667981925795391 absolute error = 7.083222897108499e-14 relative error = 7.326475112877578e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2555411020268037 y2[1] (numeric) = 0.2555411020268887 absolute error = 8.493206138382448e-14 relative error = 3.323616463660548e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.409999999999971 y1[1] (analytic) = 0.9641944846423733 y1[1] (numeric) = 0.9641944846424433 absolute error = 6.994405055138486e-14 relative error = 7.254143397981333e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2651961458717456 y2[1] (numeric) = 0.2651961458718324 absolute error = 8.68749516769185e-14 relative error = 3.275875348465021e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.419999999999971 y1[1] (analytic) = 0.9614943580603068 y1[1] (numeric) = 0.9614943580603759 absolute error = 6.905587213168474e-14 relative error = 7.182140129349924e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2748246703230963 y2[1] (numeric) = 0.274824670323185 absolute error = 8.876233081878127e-14 relative error = 3.22978030736572e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.429999999999971 y1[1] (analytic) = 0.9586980828436769 y1[1] (numeric) = 0.958698082843745 absolute error = 6.816769371198461e-14 relative error = 7.11044435488872e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2844257125364344 y2[1] (numeric) = 0.2844257125365252 absolute error = 9.070522111187529e-14 relative error = 3.189065443591219e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.439999999999971 y1[1] (analytic) = 0.955805938617675 y1[1] (numeric) = 0.9558059386177422 absolute error = 6.716849298982197e-14 relative error = 7.027419508081708e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.2939983124155396 y2[1] (numeric) = 0.2939983124156322 absolute error = 9.264811140496931e-14 relative error = 3.151314395098286e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.44999999999997 y1[1] (analytic) = 0.9528182145943137 y1[1] (numeric) = 0.9528182145943799 absolute error = 6.616929226765933e-14 relative error = 6.944587252231798e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.303541512708401 y2[1] (numeric) = 0.3035415127084956 absolute error = 9.459100169806334e-14 relative error = 3.11624597420165e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.45999999999997 y1[1] (analytic) = 0.9497352095435054 y1[1] (numeric) = 0.9497352095435706 absolute error = 6.517009154549669e-14 relative error = 6.861922237969991e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3130543591029419 y2[1] (numeric) = 0.3130543591030385 absolute error = 9.653389199115736e-14 relative error = 3.083614368692245e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.46999999999997 y1[1] (analytic) = 0.9465572317631863 y1[1] (numeric) = 0.9465572317632504 absolute error = 6.405986852087153e-14 relative error = 6.767669864139637e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3225359003224504 y2[1] (numeric) = 0.3225359003225489 absolute error = 9.847678228425139e-14 relative error = 3.053203757653046e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.47999999999997 y1[1] (analytic) = 0.9432845990484858 y1[1] (numeric) = 0.9432845990485489 absolute error = 6.306066779870889e-14 relative error = 6.685221815591999e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3319851882207056 y2[1] (numeric) = 0.331985188220806 absolute error = 1.004196725773454e-13 relative error = 3.024823881919269e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.48999999999997 y1[1] (analytic) = 0.9399176386599484 y1[1] (numeric) = 0.9399176386600104 absolute error = 6.206146707654625e-14 relative error = 6.602862264083906e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3414012778767921 y2[1] (numeric) = 0.3414012778768945 absolute error = 1.023625628704394e-13 relative error = 2.998306377382129e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.499999999999969 y1[1] (analytic) = 0.9364566872908071 y1[1] (numeric) = 0.9364566872908681 absolute error = 6.095124405192109e-14 relative error = 6.508709359346302e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3507832276895911 y2[1] (numeric) = 0.3507832276896954 absolute error = 1.043054531635335e-13 relative error = 2.973501722147149e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.509999999999969 y1[1] (analytic) = 0.9329020910333147 y1[1] (numeric) = 0.9329020910333745 absolute error = 5.984102102729594e-14 relative error = 6.414501757736865e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3601300994719396 y2[1] (numeric) = 0.3601300994720458 absolute error = 1.062483434566275e-13 relative error = 2.950276680911146e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.519999999999969 y1[1] (analytic) = 0.9292542053441347 y1[1] (numeric) = 0.9292542053441935 absolute error = 5.873079800267078e-14 relative error = 6.320207932868138e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3694409585444482 y2[1] (numeric) = 0.3694409585445564 absolute error = 1.082467449009528e-13 relative error = 2.930014726234784e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.529999999999969 y1[1] (analytic) = 0.9255133950087963 y1[1] (numeric) = 0.9255133950088539 absolute error = 5.762057497804562e-14 relative error = 6.225795897583739e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3787148738289688 y2[1] (numeric) = 0.378714873829079 absolute error = 1.101896351940468e-13 relative error = 2.909567138992525e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.539999999999969 y1[1] (analytic) = 0.9216800341052156 y1[1] (numeric) = 0.921680034105272 absolute error = 5.639932965095795e-14 relative error = 6.119187523218021e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3879509179417013 y2[1] (numeric) = 0.3879509179418134 absolute error = 1.121325254871408e-13 relative error = 2.890379176883179e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.549999999999968 y1[1] (analytic) = 0.9177545059662885 y1[1] (numeric) = 0.9177545059663437 absolute error = 5.517808432387028e-14 relative error = 6.012292390302588e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3971481672859308 y2[1] (numeric) = 0.397148167286045 absolute error = 1.141309269314661e-13 relative error = 2.873761893739179e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.559999999999968 y1[1] (analytic) = 0.9137372031415577 y1[1] (numeric) = 0.9137372031416116 absolute error = 5.384581669432009e-14 relative error = 5.892921565324314e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4063057021443875 y2[1] (numeric) = 0.4063057021445036 absolute error = 1.160738172245601e-13 relative error = 2.856809949059276e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.569999999999968 y1[1] (analytic) = 0.9096285273579579 y1[1] (numeric) = 0.9096285273580105 absolute error = 5.262457136723242e-14 relative error = 5.785281550050106e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4154226067712168 y2[1] (numeric) = 0.4154226067713348 absolute error = 1.180167075176541e-13 relative error = 2.840883129469378e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.579999999999968 y1[1] (analytic) = 0.9054288894796434 y1[1] (numeric) = 0.9054288894796948 absolute error = 5.140332604014475e-14 relative error = 5.677235025015229e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4244979694835532 y2[1] (numeric) = 0.4244979694836732 absolute error = 1.200151089619794e-13 relative error = 2.827224570897018e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.589999999999967 y1[1] (analytic) = 0.9011387094669026 y1[1] (numeric) = 0.9011387094669527 absolute error = 5.018208071305708e-14 relative error = 5.568740992465399e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4335308827526885 y2[1] (numeric) = 0.4335308827528104 absolute error = 1.219579992550734e-13 relative error = 2.813132907180812e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.599999999999967 y1[1] (analytic) = 0.8967584163341615 y1[1] (numeric) = 0.8967584163342104 absolute error = 4.884981308350689e-14 relative error = 5.447377152388369e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.442520443294823 y2[1] (numeric) = 0.4425204432949469 absolute error = 1.239008895481675e-13 relative error = 2.799890749129081e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.609999999999967 y1[1] (analytic) = 0.8922884481070832 y1[1] (numeric) = 0.8922884481071307 absolute error = 4.75175454539567e-14 relative error = 5.325357013728159e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4514657521613938 y2[1] (numeric) = 0.4514657521615197 absolute error = 1.258437798412615e-13 relative error = 2.787449086420929e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.619999999999967 y1[1] (analytic) = 0.8877292517787654 y1[1] (numeric) = 0.8877292517788116 absolute error = 4.618527782440651e-14 relative error = 5.202631064805391e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4603659148289687 y2[1] (numeric) = 0.4603659148290966 absolute error = 1.278421812855868e-13 relative error = 2.776968866886716e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.629999999999967 y1[1] (analytic) = 0.8830812832650416 y1[1] (numeric) = 0.8830812832650864 absolute error = 4.474198789239381e-14 relative error = 5.066576400189117e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4692200412886977 y2[1] (numeric) = 0.4692200412888275 absolute error = 1.297850715786808e-13 relative error = 2.765974599512636e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.639999999999966 y1[1] (analytic) = 0.8783450073588901 y1[1] (numeric) = 0.8783450073589334 absolute error = 4.329869796038111e-14 relative error = 4.92957751198207e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4780272461353132 y2[1] (numeric) = 0.4780272461354449 absolute error = 1.317279618717748e-13 relative error = 2.755658028632266e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.649999999999966 y1[1] (analytic) = 0.8735208976839544 y1[1] (numeric) = 0.8735208976839962 absolute error = 4.18554080283684e-14 relative error = 4.791574894125998e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4867866486556699 y2[1] (numeric) = 0.4867866486558036 absolute error = 1.336708521648688e-13 relative error = 2.745984355446473e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.659999999999966 y1[1] (analytic) = 0.8686094366471818 y1[1] (numeric) = 0.8686094366472222 absolute error = 4.04121180963557e-14 relative error = 4.6525073745855e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4954973729168152 y2[1] (numeric) = 0.4954973729169508 absolute error = 1.356137424579629e-13 relative error = 2.736921523108255e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.669999999999966 y1[1] (analytic) = 0.8636111153905833 y1[1] (numeric) = 0.8636111153906223 absolute error = 3.896882816434299e-14 relative error = 4.512312019828352e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5041585478535819 y2[1] (numeric) = 0.5041585478537195 absolute error = 1.375566327510569e-13 relative error = 2.728439958752939e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.679999999999966 y1[1] (analytic) = 0.8585264337421193 y1[1] (numeric) = 0.8585264337421569 absolute error = 3.752553823233029e-14 relative error = 4.370924034192529e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.512769307355694 y2[1] (numeric) = 0.5127693073558335 absolute error = 1.394440118929197e-13 relative error = 2.719429768759368e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.689999999999965 y1[1] (analytic) = 0.8533559001657175 y1[1] (numeric) = 0.8533559001657535 absolute error = 3.597122599785507e-14 relative error = 4.215266571763274e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.521328790354377 y2[1] (numeric) = 0.5213287903545183 absolute error = 1.413313910347824e-13 relative error = 2.710983810019612e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.699999999999965 y1[1] (analytic) = 0.8481000317104267 y1[1] (numeric) = 0.848100031710461 absolute error = 3.430589146091734e-14 relative error = 4.045028909117015e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5298361409084636 y2[1] (numeric) = 0.5298361409086069 absolute error = 1.432187701766452e-13 relative error = 2.703076651794279e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.709999999999965 y1[1] (analytic) = 0.8427593539587124 y1[1] (numeric) = 0.8427593539587452 absolute error = 3.286260152890463e-14 relative error = 3.899405135586855e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.538290508289988 y2[1] (numeric) = 0.5382905082901333 absolute error = 1.452171716209705e-13 relative error = 2.697747208701273e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.719999999999965 y1[1] (analytic) = 0.8373344009738994 y1[1] (numeric) = 0.8373344009739306 absolute error = 3.11972669919669e-14 relative error = 3.725783504855588e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5466910470692574 y2[1] (numeric) = 0.5466910470694045 absolute error = 1.471045507628332e-13 relative error = 2.690816898345828e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.729999999999964 y1[1] (analytic) = 0.8318257152467654 y1[1] (numeric) = 0.831825715246795 absolute error = 2.964295475749168e-14 relative error = 3.563601631226073e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5550369171993943 y2[1] (numeric) = 0.5550369171995433 absolute error = 1.48991929904696e-13 relative error = 2.684360720661242e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.739999999999964 y1[1] (analytic) = 0.8262338476412924 y1[1] (numeric) = 0.8262338476413205 absolute error = 2.808864252301646e-14 relative error = 3.399599593166399e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5633272841003404 y2[1] (numeric) = 0.5633272841004913 absolute error = 1.508793090465588e-13 relative error = 2.678359690806029e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.749999999999964 y1[1] (analytic) = 0.8205593573395813 y1[1] (numeric) = 0.8205593573396077 absolute error = 2.642330798607873e-14 relative error = 3.220158023881223e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5715613187423143 y2[1] (numeric) = 0.5715613187424671 absolute error = 1.527666881884215e-13 relative error = 2.672796131910663e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.759999999999964 y1[1] (analytic) = 0.8148028117859334 y1[1] (numeric) = 0.8148028117859581 absolute error = 2.475797344914099e-14 relative error = 3.038523320123919e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5797381977287135 y2[1] (numeric) = 0.5797381977288681 absolute error = 1.546540673302843e-13 relative error = 2.66765357080463e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.769999999999964 y1[1] (analytic) = 0.808964786630107 y1[1] (numeric) = 0.8089647866301301 absolute error = 2.309263891220326e-14 relative error = 2.854591360941671e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5878571033784533 y2[1] (numeric) = 0.5878571033786099 absolute error = 1.565414464721471e-13 relative error = 2.662916643730136e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.779999999999963 y1[1] (analytic) = 0.8030458656697526 y1[1] (numeric) = 0.803045865669774 absolute error = 2.142730437526552e-14 relative error = 2.668254117390272e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5959172238077346 y2[1] (numeric) = 0.595917223807893 absolute error = 1.584288256140098e-13 relative error = 2.658571010948409e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.789999999999963 y1[1] (analytic) = 0.7970466407920339 y1[1] (numeric) = 0.7970466407920536 absolute error = 1.965094753586527e-14 relative error = 2.465470215938419e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6039177530112312 y2[1] (numeric) = 0.6039177530113915 absolute error = 1.603162047558726e-13 relative error = 2.654603279279507e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.799999999999963 y1[1] (analytic) = 0.7909677119144394 y1[1] (numeric) = 0.7909677119144572 absolute error = 1.787459069646502e-14 relative error = 2.259838224394999e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6118578909426898 y2[1] (numeric) = 0.6118578909428519 absolute error = 1.620925615952729e-13 relative error = 2.649186420486246e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.809999999999963 y1[1] (analytic) = 0.7848096869247909 y1[1] (numeric) = 0.784809686924807 absolute error = 1.609823385706477e-14 relative error = 2.051227721225551e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.619736843594934 y2[1] (numeric) = 0.619736843595098 absolute error = 1.639799407371356e-13 relative error = 2.645960820820821e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.819999999999963 y1[1] (analytic) = 0.778573181620456 y1[1] (numeric) = 0.7785731816204702 absolute error = 1.4210854715202e-14 relative error = 1.825243284854064e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6275538230792643 y2[1] (numeric) = 0.6275538230794301 absolute error = 1.657562975765359e-13 relative error = 2.641308067620516e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.829999999999962 y1[1] (analytic) = 0.7722588196467677 y1[1] (numeric) = 0.7722588196467801 absolute error = 1.243449787580175e-14 relative error = 1.610146437885852e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6353080477042465 y2[1] (numeric) = 0.6353080477044141 absolute error = 1.675326544159361e-13 relative error = 2.637030256760217e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.839999999999962 y1[1] (analytic) = 0.7658672324346617 y1[1] (numeric) = 0.7658672324346723 absolute error = 1.054711873393899e-14 relative error = 1.377147146041242e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6429987420538799 y2[1] (numeric) = 0.6429987420540493 absolute error = 1.694200335577989e-13 relative error = 2.634842379576575e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.849999999999962 y1[1] (analytic) = 0.7593990591375327 y1[1] (numeric) = 0.7593990591375415 absolute error = 8.770761894538737e-15 relative error = 1.154960858721618e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6506251370651384 y2[1] (numeric) = 0.6506251370653096 absolute error = 1.711963903971991e-13 relative error = 2.631260008942131e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.859999999999962 y1[1] (analytic) = 0.7528549465673204 y1[1] (numeric) = 0.7528549465673273 absolute error = 6.883382752675971e-15 relative error = 9.143039816715155e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.6581864701048762 y2[1] (numeric) = 0.6581864701050492 absolute error = 1.729727472365994e-13 relative error = 2.628020402926813e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.869999999999961 y1[1] (analytic) = 0.7462355491298286 y1[1] (numeric) = 0.7462355491298335 absolute error = 4.884981308350689e-15 relative error = 6.546165368357182e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.6656819850460903 y2[1] (numeric) = 0.6656819850462652 absolute error = 1.748601263784622e-13 relative error = 2.626781711185338e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.879999999999961 y1[1] (analytic) = 0.7395415287592845 y1[1] (numeric) = 0.7395415287592876 absolute error = 3.108624468950438e-15 relative error = 4.203448147348428e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.673110932343533 y2[1] (numeric) = 0.6731109323437097 absolute error = 1.766364832178624e-13 relative error = 2.624180870200354e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.889999999999961 y1[1] (analytic) = 0.7327735548521471 y1[1] (numeric) = 0.7327735548521482 absolute error = 1.110223024625157e-15 relative error = 1.515097013632224e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.6804725691086654 y2[1] (numeric) = 0.6804725691088438 absolute error = 1.784128400572627e-13 relative error = 2.621896137429336e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.899999999999961 y1[1] (analytic) = 0.7259323042001671 y1[1] (numeric) = 0.7259323042001663 absolute error = 7.771561172376096e-16 relative error = 1.070562795926104e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.6877661591839453 y2[1] (numeric) = 0.6877661591841255 absolute error = 1.801891968966629e-13 relative error = 2.619919495755108e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.909999999999961 y1[1] (analytic) = 0.7190184609227086 y1[1] (numeric) = 0.7190184609227058 absolute error = 2.775557561562891e-15 relative error = 3.860203475166755e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.6949909732164435 y2[1] (numeric) = 0.6949909732166255 absolute error = 1.819655537360632e-13 relative error = 2.6182434124852e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.91999999999996 y1[1] (analytic) = 0.7120327163983379 y1[1] (numeric) = 0.7120327163983332 absolute error = 4.662936703425657e-15 relative error = 6.548767487836943e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.7021462887307773 y2[1] (numeric) = 0.702146288730961 absolute error = 1.836308882730009e-13 relative error = 2.615279625061297e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.92999999999996 y1[1] (analytic) = 0.7049757691956861 y1[1] (numeric) = 0.7049757691956793 absolute error = 6.772360450213455e-15 relative error = 9.60651521106904e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.7092313902013579 y2[1] (numeric) = 0.7092313902015434 absolute error = 1.854072451124011e-13 relative error = 2.614199648717778e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.93999999999996 y1[1] (analytic) = 0.6978483250035924 y1[1] (numeric) = 0.6978483250035836 absolute error = 8.770761894538737e-15 relative error = 1.256829253619486e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7162455691239427 y2[1] (numeric) = 0.7162455691241297 absolute error = 1.870725796493389e-13 relative error = 2.611849730228026e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.94999999999996 y1[1] (analytic) = 0.6906510965605368 y1[1] (numeric) = 0.6906510965605259 absolute error = 1.088018564132653e-14 relative error = 1.575351967948822e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7231881240864843 y2[1] (numeric) = 0.7231881240866731 absolute error = 1.888489364887391e-13 relative error = 2.611339016763986e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.95999999999996 y1[1] (analytic) = 0.6833848035833657 y1[1] (numeric) = 0.6833848035833529 absolute error = 1.287858708565182e-14 relative error = 1.884529333710998e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.730058360839272 y2[1] (numeric) = 0.7300583608394625 absolute error = 1.905142710256769e-13 relative error = 2.609575908515896e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.969999999999959 y1[1] (analytic) = 0.6760501726953219 y1[1] (numeric) = 0.6760501726953069 absolute error = 1.498801083243961e-14 relative error = 2.216996820322435e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7368555923643557 y2[1] (numeric) = 0.7368555923645479 absolute error = 1.921796055626146e-13 relative error = 2.60810405124247e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.979999999999959 y1[1] (analytic) = 0.6686479373533817 y1[1] (numeric) = 0.6686479373533646 absolute error = 1.709743457922741e-14 relative error = 2.557015975686976e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7435791389442473 y2[1] (numeric) = 0.7435791389444412 absolute error = 1.938449400995523e-13 relative error = 2.606917407268557e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.989999999999959 y1[1] (analytic) = 0.6611788377749109 y1[1] (numeric) = 0.6611788377748917 absolute error = 1.920685832601521e-14 relative error = 2.904941481589572e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7502283282298917 y2[1] (numeric) = 0.7502283282300872 absolute error = 1.955102746364901e-13 relative error = 2.606010294196463e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.999999999999959 y1[1] (analytic) = 0.6536436208636431 y1[1] (numeric) = 0.6536436208636219 absolute error = 2.120525977034049e-14 relative error = 3.24416227642863e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7568024953079012 y2[1] (numeric) = 0.7568024953080985 absolute error = 1.972866314758903e-13 relative error = 2.606844357663293e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.009999999999959 y1[1] (analytic) = 0.6460430401349899 y1[1] (numeric) = 0.6460430401349669 absolute error = 2.298161660974074e-14 relative error = 3.557288784496271e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7633009827670469 y2[1] (numeric) = 0.7633009827672456 absolute error = 1.986188991054405e-13 relative error = 2.602104590320661e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.019999999999959 y1[1] (analytic) = 0.6383778556406909 y1[1] (numeric) = 0.6383778556406658 absolute error = 2.509104035652854e-14 relative error = 3.930437143899138e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7697231407639977 y2[1] (numeric) = 0.769723140764198 absolute error = 2.002842336423782e-13 relative error = 2.602029522505765e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.029999999999959 y1[1] (analytic) = 0.6306488338928077 y1[1] (numeric) = 0.6306488338927804 absolute error = 2.731148640577885e-14 relative error = 4.33069640947295e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.776068327088306 y2[1] (numeric) = 0.7760683270885078 absolute error = 2.018385458768535e-13 relative error = 2.600783189208635e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.039999999999958 y1[1] (analytic) = 0.6228567477870741 y1[1] (numeric) = 0.6228567477870446 absolute error = 2.953193245502916e-14 relative error = 4.741368309800308e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7823359072266267 y2[1] (numeric) = 0.7823359072268302 absolute error = 2.035038804137912e-13 relative error = 2.601234054758019e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.049999999999958 y1[1] (analytic) = 0.6150023765256074 y1[1] (numeric) = 0.6150023765255757 absolute error = 3.175237850427948e-14 relative error = 5.162968423579315e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7885252544261693 y2[1] (numeric) = 0.7885252544263743 absolute error = 2.050581926482664e-13 relative error = 2.60052790316136e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.059999999999958 y1[1] (analytic) = 0.6070865055389884 y1[1] (numeric) = 0.6070865055389544 absolute error = 3.397282455352979e-14 relative error = 5.596043437560479e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7946357497573715 y2[1] (numeric) = 0.794635749757578 absolute error = 2.065014825802791e-13 relative error = 2.598693585624997e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.069999999999958 y1[1] (analytic) = 0.5991099264077191 y1[1] (numeric) = 0.5991099264076829 absolute error = 3.61932706027801e-14 relative error = 6.041173582249927e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8006667821757921 y2[1] (numeric) = 0.8006667821760002 absolute error = 2.080557948147543e-13 relative error = 2.598531616977638e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.079999999999957 y1[1] (analytic) = 0.5910734367830658 y1[1] (numeric) = 0.5910734367830273 absolute error = 3.852473895449293e-14 relative error = 6.517758464018436e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8066177485832153 y2[1] (numeric) = 0.8066177485834249 absolute error = 2.096101070492296e-13 relative error = 2.598629988211882e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.089999999999957 y1[1] (analytic) = 0.5829778403072937 y1[1] (numeric) = 0.5829778403072529 absolute error = 4.085620730620576e-14 relative error = 7.008192161244076e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8124880538879594 y2[1] (numeric) = 0.8124880538881706 absolute error = 2.111644192837048e-13 relative error = 2.598984911510144e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.099999999999957 y1[1] (analytic) = 0.574823946533304 y1[1] (numeric) = 0.574823946533261 absolute error = 4.307665335545607e-14 relative error = 7.493886365598777e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8182771110643858 y2[1] (numeric) = 0.8182771110645984 absolute error = 2.126077092157175e-13 relative error = 2.59823605403266e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.109999999999957 y1[1] (analytic) = 0.5666125708436796 y1[1] (numeric) = 0.5666125708436341 absolute error = 4.54081217071689e-14 relative error = 8.013962987011872e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8239843412116011 y2[1] (numeric) = 0.8239843412118152 absolute error = 2.140509991477302e-13 relative error = 2.597755666484946e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.119999999999957 y1[1] (analytic) = 0.5583445343691462 y1[1] (numeric) = 0.5583445343690985 absolute error = 4.773959005888173e-14 relative error = 8.550202808525923e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8296091736113466 y2[1] (numeric) = 0.8296091736115622 absolute error = 2.156053113822054e-13 relative error = 2.598878101162508e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.129999999999956 y1[1] (analytic) = 0.5500206639064614 y1[1] (numeric) = 0.5500206639064115 absolute error = 4.996003610813204e-14 relative error = 9.083301662395076e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8351510457850696 y2[1] (numeric) = 0.8351510457852866 absolute error = 2.170486013142181e-13 relative error = 2.598914321063745e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.139999999999956 y1[1] (analytic) = 0.5416417918357351 y1[1] (numeric) = 0.5416417918356828 absolute error = 5.229150445984487e-14 relative error = 9.654259558262341e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8406094035501709 y2[1] (numeric) = 0.8406094035503895 absolute error = 2.186029135486933e-13 relative error = 2.600529004618091e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.149999999999956 y1[1] (analytic) = 0.533208756037192 y1[1] (numeric) = 0.5332087560371372 absolute error = 5.473399511402022e-14 relative error = 1.026502181262051e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8459837010754229 y2[1] (numeric) = 0.8459837010756428 absolute error = 2.199351811782435e-13 relative error = 2.599756719883134e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.159999999999956 y1[1] (analytic) = 0.5247223998073841 y1[1] (numeric) = 0.524722399807327 absolute error = 5.706546346573305e-14 relative error = 1.087536257012865e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8512734009355513 y2[1] (numeric) = 0.8512734009357726 absolute error = 2.213784711102562e-13 relative error = 2.60055665861239e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.169999999999956 y1[1] (analytic) = 0.5161835717748627 y1[1] (numeric) = 0.5161835717748033 absolute error = 5.939693181744587e-14 relative error = 1.150693959771201e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8564779741649782 y2[1] (numeric) = 0.856477974165201 absolute error = 2.228217610422689e-13 relative error = 2.601605269061456e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.179999999999955 y1[1] (analytic) = 0.5075931258153156 y1[1] (numeric) = 0.5075931258152536 absolute error = 6.195044477408373e-14 relative error = 1.220474463175138e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.861596900310718 y2[1] (numeric) = 0.8615969003109422 absolute error = 2.241540286718191e-13 relative error = 2.601611363631674e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.189999999999955 y1[1] (analytic) = 0.4989519209661796 y1[1] (numeric) = 0.4989519209661152 absolute error = 6.433742427702782e-14 relative error = 1.289451379452426e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8666296674844217 y2[1] (numeric) = 0.8666296674846472 absolute error = 2.254862963013693e-13 relative error = 2.601876034960718e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.199999999999955 y1[1] (analytic) = 0.4902608213407389 y1[1] (numeric) = 0.4902608213406721 absolute error = 6.677991493120317e-14 relative error = 1.362130360500295e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.871575772413566 y2[1] (numeric) = 0.8715757724137928 absolute error = 2.268185639309195e-13 relative error = 2.602396384915725e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.209999999999955 y1[1] (analytic) = 0.4815206960417135 y1[1] (numeric) = 0.4815206960416442 absolute error = 6.927791673660977e-14 relative error = 1.438731861498396e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8764347204917796 y2[1] (numeric) = 0.8764347204920078 absolute error = 2.281508315604697e-13 relative error = 2.603169708206575e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.219999999999954 y1[1] (analytic) = 0.4727324190743498 y1[1] (numeric) = 0.472732419074278 absolute error = 7.177591854201637e-14 relative error = 1.518320209190639e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8812060258283039 y2[1] (numeric) = 0.8812060258285334 absolute error = 2.294830991900199e-13 relative error = 2.60419348556217e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.229999999999954 y1[1] (analytic) = 0.4638968692590211 y1[1] (numeric) = 0.4638968692589468 absolute error = 7.427392034742297e-14 relative error = 1.601086906795904e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8858892112965813 y2[1] (numeric) = 0.885889211296812 absolute error = 2.307043445171075e-13 relative error = 2.604212147244126e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.239999999999954 y1[1] (analytic) = 0.4550149301433458 y1[1] (numeric) = 0.4550149301432691 absolute error = 7.671641100159832e-14 relative error = 1.68601964285941e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8904838085819675 y2[1] (numeric) = 0.8904838085821994 absolute error = 2.319255898441952e-13 relative error = 2.604489689863315e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.249999999999954 y1[1] (analytic) = 0.4460874899138341 y1[1] (numeric) = 0.4460874899137549 absolute error = 7.921441280700492e-14 relative error = 1.775759567306089e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.894989358228563 y2[1] (numeric) = 0.8949893582287961 absolute error = 2.331468351712829e-13 relative error = 2.605023546120664e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.259999999999954 y1[1] (analytic) = 0.4371154413070694 y1[1] (numeric) = 0.4371154413069877 absolute error = 8.171241461241152e-14 relative error = 1.869355481199058e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.8994054096851575 y2[1] (numeric) = 0.8994054096853918 absolute error = 2.343680804983705e-13 relative error = 2.605811327957351e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.269999999999953 y1[1] (analytic) = 0.4280996815204356 y1[1] (numeric) = 0.4280996815203513 absolute error = 8.426592756904938e-14 relative error = 1.968371648158465e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9037315213502856 y2[1] (numeric) = 0.903731521350521 absolute error = 2.354783035229957e-13 relative error = 2.605622333181012e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.279999999999953 y1[1] (analytic) = 0.4190411121223983 y1[1] (numeric) = 0.4190411121223115 absolute error = 8.681944052568724e-14 relative error = 2.071859729608775e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9079672606163857 y2[1] (numeric) = 0.9079672606166224 absolute error = 2.366995488500834e-13 relative error = 2.606917221766308e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.289999999999953 y1[1] (analytic) = 0.4099406389623485 y1[1] (numeric) = 0.4099406389622591 absolute error = 8.93729534823251e-14 relative error = 2.180143781513051e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.912112203913061 y2[1] (numeric) = 0.9121122039132988 absolute error = 2.378097718747085e-13 relative error = 2.607242517471849e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.299999999999953 y1[1] (analytic) = 0.4007991720800186 y1[1] (numeric) = 0.4007991720799266 absolute error = 9.198197759019422e-14 relative error = 2.294964261349079e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.916165936749436 y2[1] (numeric) = 0.9161659367496749 absolute error = 2.389199948993337e-13 relative error = 2.607824470608716e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.309999999999953 y1[1] (analytic) = 0.3916176256144788 y1[1] (numeric) = 0.3916176256143843 absolute error = 9.453549054683208e-14 relative error = 2.413974355686838e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9201280537556052 y2[1] (numeric) = 0.9201280537558452 absolute error = 2.399191956214963e-13 relative error = 2.607454415091893e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.319999999999952 y1[1] (analytic) = 0.3823969177127246 y1[1] (numeric) = 0.3823969177126274 absolute error = 9.720002580593246e-14 relative error = 2.54186216738687e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9239981587231696 y2[1] (numeric) = 0.9239981587234106 absolute error = 2.410294186461215e-13 relative error = 2.60854868995831e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.329999999999952 y1[1] (analytic) = 0.3731379704378621 y1[1] (numeric) = 0.3731379704377623 absolute error = 9.975353876257032e-14 relative error = 2.673368744690165e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9277758646448576 y2[1] (numeric) = 0.9277758646450996 absolute error = 2.420286193682841e-13 relative error = 2.608697085054374e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.339999999999952 y1[1] (analytic) = 0.3638417096769031 y1[1] (numeric) = 0.3638417096768007 absolute error = 1.024180740216707e-13 relative error = 2.814907452821159e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9314607937532251 y2[1] (numeric) = 0.9314607937534681 absolute error = 2.430278200904468e-13 relative error = 2.609104126768356e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.349999999999952 y1[1] (analytic) = 0.3545090650481768 y1[1] (numeric) = 0.3545090650480718 absolute error = 1.050270981295398e-13 relative error = 2.962606840963768e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9350525775584321 y2[1] (numeric) = 0.9350525775586761 absolute error = 2.440270208126094e-13 relative error = 2.6097679068465e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.359999999999951 y1[1] (analytic) = 0.3451409698083689 y1[1] (numeric) = 0.3451409698082613 absolute error = 1.076916333886402e-13 relative error = 3.120221671986184e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.938550856885091 y2[1] (numeric) = 0.938550856885336 absolute error = 2.45026221534772e-13 relative error = 2.610686674433149e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.369999999999951 y1[1] (analytic) = 0.3357383607591968 y1[1] (numeric) = 0.3357383607590864 absolute error = 1.103561686477406e-13 relative error = 3.286969305449485e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9419552819081846 y2[1] (numeric) = 0.9419552819084306 absolute error = 2.460254222569347e-13 relative error = 2.611858832178783e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.379999999999951 y1[1] (analytic) = 0.3263021781537297 y1[1] (numeric) = 0.3263021781536167 absolute error = 1.130207039068409e-13 relative error = 3.46368217786134e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9452655121880474 y2[1] (numeric) = 0.9452655121882944 absolute error = 2.469136006766348e-13 relative error = 2.612108423432196e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.389999999999951 y1[1] (analytic) = 0.3168333656023649 y1[1] (numeric) = 0.3168333656022491 absolute error = 1.157407503171726e-13 relative error = 3.653048033534151e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9484812167044101 y2[1] (numeric) = 0.948481216704658 absolute error = 2.479128013987975e-13 relative error = 2.613787147627388e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.399999999999951 y1[1] (analytic) = 0.3073328699784666 y1[1] (numeric) = 0.3073328699783482 absolute error = 1.184052855762729e-13 relative error = 3.852672367409612e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9516020738895008 y2[1] (numeric) = 0.9516020738897496 absolute error = 2.488009798184976e-13 relative error = 2.614548524485332e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.40999999999995 y1[1] (analytic) = 0.2978016413236805 y1[1] (numeric) = 0.2978016413235594 absolute error = 1.211253319866046e-13 relative error = 4.067315796119253e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9546277716602015 y2[1] (numeric) = 0.9546277716604512 absolute error = 2.496891582381977e-13 relative error = 2.615565623069619e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.41999999999995 y1[1] (analytic) = 0.2882406327529292 y1[1] (numeric) = 0.2882406327528054 absolute error = 1.23789867245705e-13 relative error = 4.294670951260842e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9575580074492568 y2[1] (numeric) = 0.9575580074495073 absolute error = 2.504663143554353e-13 relative error = 2.615677717766964e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.42999999999995 y1[1] (analytic) = 0.2786508003591023 y1[1] (numeric) = 0.2786508003589758 absolute error = 1.265099136560366e-13 relative error = 4.540087934181455e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9603924882355295 y2[1] (numeric) = 0.9603924882357807 absolute error = 2.512434704726729e-13 relative error = 2.616049933233726e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.43999999999995 y1[1] (analytic) = 0.2690331031174478 y1[1] (numeric) = 0.2690331031173185 absolute error = 1.292854712175995e-13 relative error = 4.805559974571576e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.963130930573303 y2[1] (numeric) = 0.963130930573555 absolute error = 2.520206265899105e-13 relative error = 2.616680853971697e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.44999999999995 y1[1] (analytic) = 0.259388502789675 y1[1] (numeric) = 0.259388502789543 absolute error = 1.320055176279311e-13 relative error = 5.089104420906724e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9657730606206257 y2[1] (numeric) = 0.9657730606208784 absolute error = 2.526867604046856e-13 relative error = 2.616419640472306e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.459999999999949 y1[1] (analytic) = 0.2497179638277796 y1[1] (numeric) = 0.2497179638276449 absolute error = 1.347533196138784e-13 relative error = 5.396220502054561e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9683186141666945 y2[1] (numeric) = 0.968318614166948 absolute error = 2.534639165219232e-13 relative error = 2.617567325606423e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.469999999999949 y1[1] (analytic) = 0.2400224532775991 y1[1] (numeric) = 0.2400224532774616 absolute error = 1.375011215998256e-13 relative error = 5.728677451721489e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9707673366582761 y2[1] (numeric) = 0.9707673366585303 absolute error = 2.542410726391608e-13 relative error = 2.618970200566785e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.479999999999949 y1[1] (analytic) = 0.2303029406821088 y1[1] (numeric) = 0.2303029406819685 absolute error = 1.402489235857729e-13 relative error = 6.089758262329832e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.973118983225162 y2[1] (numeric) = 0.9731189832254169 absolute error = 2.549072064539359e-13 relative error = 2.619486525780322e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.489999999999949 y1[1] (analytic) = 0.2205603979844688 y1[1] (numeric) = 0.2205603979843258 absolute error = 1.430244811473358e-13 relative error = 6.484594807332871e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9753733187046552 y2[1] (numeric) = 0.9753733187049107 absolute error = 2.55573340268711e-13 relative error = 2.620261753808534e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.499999999999948 y1[1] (analytic) = 0.2107957994308301 y1[1] (numeric) = 0.2107957994306843 absolute error = 1.458000387088987e-13 relative error = 6.916648201841474e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9775301176650862 y2[1] (numeric) = 0.9775301176653425 absolute error = 2.562394740834861e-13 relative error = 2.621294929465047e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.509999999999948 y1[1] (analytic) = 0.2010101214729108 y1[1] (numeric) = 0.2010101214727623 absolute error = 1.485755962704616e-13 relative error = 7.39144850924755e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9795891644283565 y2[1] (numeric) = 0.9795891644286133 absolute error = 2.567945855957987e-13 relative error = 2.6214518792238e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.519999999999948 y1[1] (analytic) = 0.1912043426703522 y1[1] (numeric) = 0.1912043426702008 absolute error = 1.513511538320245e-13 relative error = 7.915675539491432e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9815502530915056 y2[1] (numeric) = 0.9815502530917629 absolute error = 2.573496971081113e-13 relative error = 2.6218698054181e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.529999999999948 y1[1] (analytic) = 0.1813794435928629 y1[1] (numeric) = 0.1813794435927088 absolute error = 1.541267113935874e-13 relative error = 8.497474043395515e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9834131875473012 y2[1] (numeric) = 0.9834131875475591 absolute error = 2.579048086204239e-13 relative error = 2.62254779462187e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.539999999999948 y1[1] (analytic) = 0.1715364067221634 y1[1] (numeric) = 0.1715364067220065 absolute error = 1.569300245307659e-13 relative error = 9.148496667820761e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9851777815038505 y2[1] (numeric) = 0.9851777815041088 absolute error = 2.583488978302739e-13 relative error = 2.622358143683574e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.549999999999947 y1[1] (analytic) = 0.1616762163537382 y1[1] (numeric) = 0.1616762163535785 absolute error = 1.597333376679444e-13 relative error = 9.879829035487637e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9868438585032281 y2[1] (numeric) = 0.986843858503487 absolute error = 2.589040093425865e-13 relative error = 2.623555966951783e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.559999999999947 y1[1] (analytic) = 0.1517998584984074 y1[1] (numeric) = 0.1517998584982448 absolute error = 1.625088952295073e-13 relative error = 1.070547079799895e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9884112519391225 y2[1] (numeric) = 0.9884112519393818 absolute error = 2.593480985524366e-13 relative error = 2.623888569091382e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.569999999999947 y1[1] (analytic) = 0.1419083207837261 y1[1] (numeric) = 0.1419083207835608 absolute error = 1.653399639423014e-13 relative error = 1.165118176504153e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9898798050734964 y2[1] (numeric) = 0.9898798050737561 absolute error = 2.596811654598241e-13 relative error = 2.623360574979539e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.579999999999947 y1[1] (analytic) = 0.1320025923552231 y1[1] (numeric) = 0.1320025923550549 absolute error = 1.681710326550956e-13 relative error = 1.273997954544272e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9912493710522599 y2[1] (numeric) = 0.99124937105252 absolute error = 2.601252546696742e-13 relative error = 2.62421608796118e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.589999999999947 y1[1] (analytic) = 0.1220836637774863 y1[1] (numeric) = 0.1220836637773153 absolute error = 1.709743457922741e-13 relative error = 1.400468666339319e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9925198129199566 y2[1] (numeric) = 0.9925198129202171 absolute error = 2.604583215770617e-13 relative error = 2.62421281859153e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.599999999999946 y1[1] (analytic) = 0.1121525269351078 y1[1] (numeric) = 0.112152526934934 absolute error = 1.737915367172604e-13 relative error = 1.549599830397199e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9936910036334584 y2[1] (numeric) = 0.9936910036337192 absolute error = 2.607913884844493e-13 relative error = 2.624471667056041e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.609999999999946 y1[1] (analytic) = 0.102210174933496 y1[1] (numeric) = 0.1022101749333194 absolute error = 1.766087276422468e-13 relative error = 1.727897714265326e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.99476282607467 y2[1] (numeric) = 0.9947628260749311 absolute error = 2.610134330893743e-13 relative error = 2.623876026000411e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.619999999999946 y1[1] (analytic) = 0.09225760199956561 y1[1] (numeric) = 0.09225760199938618 absolute error = 1.794259185672331e-13 relative error = 1.944836140094753e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9957351730622404 y2[1] (numeric) = 0.9957351730625017 absolute error = 2.613464999967618e-13 relative error = 2.624658715158452e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.629999999999946 y1[1] (analytic) = 0.08229580338231637 y1[1] (numeric) = 0.08229580338213412 absolute error = 1.822569872800273e-13 relative error = 2.214657124535593e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9966079473622811 y2[1] (numeric) = 0.9966079473625427 absolute error = 2.615685446016869e-13 relative error = 2.624588187300527e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.639999999999946 y1[1] (analytic) = 0.07232577525330852 y1[1] (numeric) = 0.07232577525312343 absolute error = 1.850880559928214e-13 relative error = 2.559088448683509e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9973810616980894 y2[1] (numeric) = 0.9973810616983512 absolute error = 2.617905892066119e-13 relative error = 2.624780029018205e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.649999999999945 y1[1] (analytic) = 0.06234851460704662 y1[1] (numeric) = 0.0623485146068587 absolute error = 1.879191247056156e-13 relative error = 3.01401125415708e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.998054438758876 y2[1] (numeric) = 0.998054438759138 absolute error = 2.620126338115369e-13 relative error = 2.625233891423408e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.659999999999945 y1[1] (analytic) = 0.05236501916128092 y1[1] (numeric) = 0.05236501916109017 absolute error = 1.907501934184097e-13 relative error = 3.642702637631264e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.998628011207496 y2[1] (numeric) = 0.9986280112077582 absolute error = 2.62234678416462e-13 relative error = 2.625949557527228e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.669999999999945 y1[1] (analytic) = 0.04237628725723648 y1[1] (numeric) = 0.04237628725704289 absolute error = 1.935882010251078e-13 relative error = 4.56831434641668e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9991017216871825 y2[1] (numeric) = 0.9991017216874448 absolute error = 2.623457007189245e-13 relative error = 2.625815720504429e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.679999999999945 y1[1] (analytic) = 0.03238331775977977 y1[1] (numeric) = 0.03238331775958334 absolute error = 1.964262086318058e-13 relative error = 6.065660414689445e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9994755228272822 y2[1] (numeric) = 0.9994755228275447 absolute error = 2.62456723021387e-13 relative error = 2.625944478149484e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.689999999999944 y1[1] (analytic) = 0.02238710995753308 y1[1] (numeric) = 0.02238710995733382 absolute error = 1.992642162385039e-13 relative error = 8.90084591608722e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9997493772479927 y2[1] (numeric) = 0.9997493772482553 absolute error = 2.625677453238495e-13 relative error = 2.626335672712485e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.699999999999944 y1[1] (analytic) = 0.01238866346294651 y1[1] (numeric) = 0.0123886634627444 absolute error = 2.021056932921539e-13 relative error = 1.63137608747413e-09 % Correct digits = 11 h = 0.01 y2[1] (analytic) = 0.9999232575641002 y2[1] (numeric) = 0.9999232575643628 absolute error = 2.62678767626312e-13 relative error = 2.626989277819383e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.709999999999944 y1[1] (analytic) = 0.002388978112337493 y1[1] (numeric) = 0.002388978112132548 absolute error = 2.049454356223279e-13 relative error = 8.578790846342215e-09 % Correct digits = 11 h = 0.01 y2[1] (analytic) = 0.9999971463877179 y2[1] (numeric) = 0.9999971463879805 absolute error = 2.62678767626312e-13 relative error = 2.626795172118086e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.719999999999944 y1[1] (analytic) = -0.007610946134091949 y1[1] (numeric) = -0.007610946134299735 absolute error = 2.077860453142399e-13 relative error = 2.730094808889757e-09 % Correct digits = 11 h = 0.01 y2[1] (analytic) = 0.9999710363300249 y2[1] (numeric) = 0.9999710363302876 absolute error = 2.62678767626312e-13 relative error = 2.626863759878131e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.729999999999944 y1[1] (analytic) = -0.01761010929225042 y1[1] (numeric) = -0.01761010929246104 absolute error = 2.106231855592e-13 relative error = 1.196035652384553e-09 % Correct digits = 11 h = 0.01 y2[1] (analytic) = 0.9998449300020054 y2[1] (numeric) = 0.999844930002268 absolute error = 2.62678767626312e-13 relative error = 2.627195075398194e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.739999999999943 y1[1] (analytic) = -0.0276075114541547 y1[1] (numeric) = -0.02760751145436816 absolute error = 2.134611931658981e-13 relative error = 7.73199690672496e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.999618840014187 y2[1] (numeric) = 0.9996188400144496 absolute error = 2.625677453238495e-13 relative error = 2.626678638030902e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.749999999999943 y1[1] (analytic) = -0.03760215288791975 y1[1] (numeric) = -0.03760215288813605 absolute error = 2.162992007725961e-13 relative error = 5.752308954684492e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9992927889753801 y2[1] (numeric) = 0.9992927889756426 absolute error = 2.62456723021387e-13 relative error = 2.626424666693489e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.759999999999943 y1[1] (analytic) = -0.04759303413773103 y1[1] (numeric) = -0.04759303413795017 absolute error = 2.191372083792942e-13 relative error = 4.604396680092424e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9988668094904168 y2[1] (numeric) = 0.9988668094906792 absolute error = 2.623457007189245e-13 relative error = 2.626433256429484e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.769999999999943 y1[1] (analytic) = -0.05757915612378928 y1[1] (numeric) = -0.05757915612401125 absolute error = 2.219682770920883e-13 relative error = 3.855010945538683e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9983409441568909 y2[1] (numeric) = 0.998340944157153 absolute error = 2.621236561139995e-13 relative error = 2.625592565827955e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.779999999999943 y1[1] (analytic) = -0.0675595202422176 y1[1] (numeric) = -0.06755952024244241 absolute error = 2.248062846987864e-13 relative error = 3.327529323666009e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9977152455608972 y2[1] (numeric) = 0.9977152455611592 absolute error = 2.620126338115369e-13 relative error = 2.626126392047244e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.789999999999942 y1[1] (analytic) = -0.07753312846492112 y1[1] (numeric) = -0.07753312846514876 absolute error = 2.276373534115805e-13 relative error = 2.936001138075734e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.996989776271774 y2[1] (numeric) = 0.9969897762720358 absolute error = 2.617905892066119e-13 relative error = 2.625810168140072e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.799999999999942 y1[1] (analytic) = -0.08749898343938889 y1[1] (numeric) = -0.08749898343961934 absolute error = 2.304545443365669e-13 relative error = 2.633796820007677e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9961646088358458 y2[1] (numeric) = 0.9961646088361072 absolute error = 2.614575222992244e-13 relative error = 2.624641750772226e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.809999999999942 y1[1] (analytic) = -0.09745608858842827 y1[1] (numeric) = -0.09745608858866156 absolute error = 2.33285613049361e-13 relative error = 2.393751036269896e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9952398257691683 y2[1] (numeric) = 0.9952398257694295 absolute error = 2.612354776942993e-13 relative error = 2.624849517978285e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.819999999999942 y1[1] (analytic) = -0.107403448209822 y1[1] (numeric) = -0.1074034482100581 absolute error = 2.361028039743474e-13 relative error = 2.198279551631341e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9942155195492777 y2[1] (numeric) = 0.9942155195495386 absolute error = 2.609024107869118e-13 relative error = 2.62420376323627e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.829999999999941 y1[1] (analytic) = -0.1173400675758972 y1[1] (numeric) = -0.1173400675761362 absolute error = 2.389338726871415e-13 relative error = 2.036251364288636e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9930917926059423 y2[1] (numeric) = 0.9930917926062028 absolute error = 2.605693438795242e-13 relative error = 2.623819326869796e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.839999999999941 y1[1] (analytic) = -0.127264953032998 y1[1] (numeric) = -0.1272649530332397 absolute error = 2.417233080365122e-13 relative error = 1.89937058299025e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9918687573109201 y2[1] (numeric) = 0.9918687573111802 absolute error = 2.601252546696742e-13 relative error = 2.62257735967918e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.849999999999941 y1[1] (analytic) = -0.1371771121008492 y1[1] (numeric) = -0.1371771121010938 absolute error = 2.445266211736907e-13 relative error = 1.782561372147278e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9905465359667213 y2[1] (numeric) = 0.9905465359669811 absolute error = 2.597921877622866e-13 relative error = 2.622715625457648e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.859999999999941 y1[1] (analytic) = -0.1470755535718042 y1[1] (numeric) = -0.1470755535720516 absolute error = 2.473576898864849e-13 relative error = 1.681840957788553e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9891252607943786 y2[1] (numeric) = 0.9891252607946379 absolute error = 2.593480985524366e-13 relative error = 2.6219944918215e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.869999999999941 y1[1] (analytic) = -0.1569592876099646 y1[1] (numeric) = -0.1569592876102148 absolute error = 2.501610030236634e-13 relative error = 1.593795479279315e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9876050739202247 y2[1] (numeric) = 0.9876050739204836 absolute error = 2.589040093425865e-13 relative error = 2.621533811231714e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.87999999999994 y1[1] (analytic) = -0.166827325850163 y1[1] (numeric) = -0.166827325850416 absolute error = 2.529365605852263e-13 relative error = 1.516157855412745e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9859861273616802 y2[1] (numeric) = 0.9859861273619387 absolute error = 2.584599201327364e-13 relative error = 2.621334245587494e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.88999999999994 y1[1] (analytic) = -0.1766786814967987 y1[1] (numeric) = -0.1766786814970544 absolute error = 2.557121181467892e-13 relative error = 1.447328653238917e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.984268583012052 y2[1] (numeric) = 0.9842685830123099 absolute error = 2.579048086204239e-13 relative error = 2.620268624557591e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.89999999999994 y1[1] (analytic) = -0.1865123694225164 y1[1] (numeric) = -0.1865123694227749 absolute error = 2.584876757083521e-13 relative error = 1.385900980769732e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9824526126243437 y2[1] (numeric) = 0.982452612624601 absolute error = 2.573496971081113e-13 relative error = 2.619461679893898e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.90999999999994 y1[1] (analytic) = -0.1963274062667184 y1[1] (numeric) = -0.1963274062669796 absolute error = 2.61263233269915e-13 relative error = 1.33075273716487e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9805383977940807 y2[1] (numeric) = 0.9805383977943375 absolute error = 2.567945855957987e-13 relative error = 2.618914120788232e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.91999999999994 y1[1] (analytic) = -0.2061228105338992 y1[1] (numeric) = -0.2061228105341633 absolute error = 2.640387908314779e-13 relative error = 1.280978025418752e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.978526129941151 y2[1] (numeric) = 0.9785261299414071 absolute error = 2.561284517810236e-13 relative error = 2.61749220530705e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.929999999999939 y1[1] (analytic) = -0.2158976026917952 y1[1] (numeric) = -0.215897602692062 absolute error = 2.668143483930407e-13 relative error = 1.235837476036878e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9764160102906628 y2[1] (numeric) = 0.9764160102909183 absolute error = 2.554623179662485e-13 relative error = 2.616326599255594e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.939999999999939 y1[1] (analytic) = -0.225650805269336 y1[1] (numeric) = -0.2256508052696056 absolute error = 2.69562150378988e-13 relative error = 1.194598663440352e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9742082498528229 y2[1] (numeric) = 0.9742082498530776 absolute error = 2.546851618490109e-13 relative error = 2.61427843469286e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.949999999999939 y1[1] (analytic) = -0.2353814429543916 y1[1] (numeric) = -0.2353814429546639 absolute error = 2.723099523649353e-13 relative error = 1.156887938773062e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9719030694018352 y2[1] (numeric) = 0.9719030694020893 absolute error = 2.540190280342358e-13 relative error = 2.61362512406277e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.959999999999939 y1[1] (analytic) = -0.2450885426913023 y1[1] (numeric) = -0.2450885426915774 absolute error = 2.750577543508825e-13 relative error = 1.122279121375851e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9695006994538239 y2[1] (numeric) = 0.9695006994540771 absolute error = 2.532418719169982e-13 relative error = 2.612085499883229e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.969999999999938 y1[1] (analytic) = -0.2547711337781837 y1[1] (numeric) = -0.2547711337784615 absolute error = 2.778333119124454e-13 relative error = 1.090521158312781e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9670013802437817 y2[1] (numeric) = 0.9670013802440341 absolute error = 2.524647157997606e-13 relative error = 2.610799952903005e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.979999999999938 y1[1] (analytic) = -0.2644282479639958 y1[1] (numeric) = -0.2644282479642763 absolute error = 2.805533583227771e-13 relative error = 1.060981042997255e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9644053617015469 y2[1] (numeric) = 0.9644053617017986 absolute error = 2.51687559682523e-13 relative error = 2.609769394463532e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.989999999999938 y1[1] (analytic) = -0.2740589195453677 y1[1] (numeric) = -0.2740589195456509 absolute error = 2.832734047331087e-13 relative error = 1.033622278023378e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9617129034268105 y2[1] (numeric) = 0.9617129034270613 absolute error = 2.507993812628229e-13 relative error = 2.607840451855906e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.999999999999938 y1[1] (analytic) = -0.2836621854631666 y1[1] (numeric) = -0.2836621854634526 absolute error = 2.859934511434403e-13 relative error = 1.008218457728044e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9589242746631561 y2[1] (numeric) = 0.958924274663406 absolute error = 2.499112028431227e-13 relative error = 2.606162023908611e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; Iterations = 451 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 %