##############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=10000000; glob_max_minutes=3; 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 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 = 2.176050419120134e-183 estimated_step_error = 2.176050419120134e-183 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.460322701565094e-175 estimated_step_error = 1.460322701565094e-175 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.800059559255625e-168 estimated_step_error = 9.800059559255625e-168 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 = 6.576708375401052e-160 estimated_step_error = 6.576708375401052e-160 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.413553922118905e-152 estimated_step_error = 4.413553922118905e-152 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.961885419727829e-144 estimated_step_error = 2.961885419727829e-144 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.987687014675067e-136 estimated_step_error = 1.987687014675067e-136 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.33391331174907e-128 estimated_step_error = 1.33391331174907e-128 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.951729110475022e-121 estimated_step_error = 8.951729110475022e-121 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.007388155520677e-113 estimated_step_error = 6.007388155520677e-113 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.031469063945828e-105 estimated_step_error = 4.031469063945828e-105 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.705445060834662e-97 estimated_step_error = 2.705445060834662e-97 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.815555820804895e-89 estimated_step_error = 1.815555820804895e-89 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.21834837617488e-81 estimated_step_error = 1.21834837617488e-81 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.175519336114875e-74 estimated_step_error = 8.175519336114875e-74 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.485587141141663e-66 estimated_step_error = 5.485587141141663e-66 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.680090513956986e-58 estimated_step_error = 3.680090513956986e-58 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.46801790833834e-50 estimated_step_error = 2.46801790833834e-50 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) = -0.5226872289306591 absolute error = 1.110223024625157e-16 relative error = 2.124067631988079e-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] = 0.5600000000000001 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) = -0.5311861979208834 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] = 0.5700000000000001 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) = -0.5396320487339692 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) = -0.5480239367918736 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) = -0.5563610229127838 absolute error = 1.110223024625157e-16 relative error = 1.99550827412868e-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) = -0.5646424733950354 absolute error = 1.110223024625157e-16 relative error = 1.966240722115181e-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) = -0.5728674601004813 absolute error = 1.110223024625157e-16 relative error = 1.938010276286984e-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) = -0.5810351605373051 absolute error = 1.110223024625157e-16 relative error = 1.910767368361135e-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) = -0.5891447579422695 absolute error = 1.110223024625157e-16 relative error = 1.884465591279941e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.85 Order of pole (ratio test) Not computed 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) = -0.8020957578842928 absolute error = 2.220446049250313e-16 relative error = 2.768305439125171e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.5971954413623921 y2[1] (numeric) = -0.597195441362392 absolute error = 1.110223024625157e-16 relative error = 1.859061452465856e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.15 Order of pole (ratio test) Not computed 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) = -0.796083798549056 absolute error = 2.220446049250313e-16 relative error = 2.789211453991783e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6051864057360397 y2[1] (numeric) = -0.6051864057360395 absolute error = 1.110223024625157e-16 relative error = 1.834514149859135e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.44 Order of pole (ratio test) Not computed 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) = -0.7899922314973652 absolute error = 2.220446049250313e-16 relative error = 2.810718840920298e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6131168519734339 y2[1] (numeric) = -0.6131168519734338 absolute error = 1.110223024625157e-16 relative error = 1.810785368322027e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.75 Order of pole (ratio test) Not computed 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) = -0.7838216658808493 absolute error = 1.110223024625157e-16 relative error = 1.416422986187172e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6209859870365598 y2[1] (numeric) = -0.6209859870365597 absolute error = 1.110223024625157e-16 relative error = 1.787839094281838e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.05 Order of pole (ratio test) Not computed 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) = -0.777572718750928 absolute error = 2.220446049250313e-16 relative error = 2.85561208065167e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6287930240184686 y2[1] (numeric) = -0.6287930240184686 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.36 Order of pole (ratio test) Not computed 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) = -0.7712460149971067 absolute error = 1.110223024625157e-16 relative error = 1.439518652980426e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6365371822219681 y2[1] (numeric) = -0.636537182221968 absolute error = 1.110223024625157e-16 relative error = 1.744160522955922e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.68 Order of pole (ratio test) Not computed 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) = -0.7648421872844885 absolute error = 2.220446049250313e-16 relative error = 2.903142747831198e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6442176872376912 y2[1] (numeric) = -0.6442176872376911 absolute error = 1.110223024625157e-16 relative error = 1.723366257430196e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16 Order of pole (ratio test) Not computed 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) = -0.7583618759905082 absolute error = 1.110223024625157e-16 relative error = 1.463975260063116e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6518337710215368 y2[1] (numeric) = -0.6518337710215367 absolute error = 1.110223024625157e-16 relative error = 1.703230292725159e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.33 Order of pole (ratio test) Not computed 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) = -0.7518057291408951 absolute error = 2.220446049250313e-16 relative error = 2.953483809956684e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6593846719714733 y2[1] (numeric) = -0.6593846719714732 absolute error = 1.110223024625157e-16 relative error = 1.683725861120999e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.66 Order of pole (ratio test) Not computed 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) = -0.7451744023448704 absolute error = 2.220446049250313e-16 relative error = 2.979766940817004e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.666869635003698 y2[1] (numeric) = -0.6668696350036979 absolute error = 1.110223024625157e-16 relative error = 1.664827675980479e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17 Order of pole (ratio test) Not computed 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) = -0.7384685587295879 absolute error = 2.220446049250313e-16 relative error = 3.006825440300696e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6742879116281453 y2[1] (numeric) = -0.6742879116281451 absolute error = 2.220446049250313e-16 relative error = 3.293023663866066e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.35 Order of pole (ratio test) Not computed 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) = -0.7316888688738209 absolute error = 1.110223024625157e-16 relative error = 1.517343056392202e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6816387600233343 y2[1] (numeric) = -0.6816387600233341 absolute error = 2.220446049250313e-16 relative error = 3.257511426102443e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.7 Order of pole (ratio test) Not computed 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) = -0.7248360107409052 absolute error = 2.220446049250313e-16 relative error = 3.063377117509162e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6889214451105515 y2[1] (numeric) = -0.6889214451105513 absolute error = 2.220446049250313e-16 relative error = 3.223075816567152e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.06 Order of pole (ratio test) Not computed 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) = -0.7179106696109434 absolute error = 2.220446049250313e-16 relative error = 3.092928052530042e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.6961352386273569 y2[1] (numeric) = -0.6961352386273567 absolute error = 2.220446049250313e-16 relative error = 3.189676266968757e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.42 Order of pole (ratio test) Not computed 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) = -0.7109135380122774 absolute error = 2.220446049250313e-16 relative error = 3.123370045053168e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7032794192004104 y2[1] (numeric) = -0.7032794192004101 absolute error = 2.220446049250313e-16 relative error = 3.157274318897085e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7900000000000003 y1[1] (analytic) = -0.703845315652236 y1[1] (numeric) = -0.7038453156522362 absolute error = 2.220446049250313e-16 relative error = 3.154735848732162e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.710353272417608 y2[1] (numeric) = -0.7103532724176078 absolute error = 2.220446049250313e-16 relative error = 3.125833490839386e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8000000000000003 y1[1] (analytic) = -0.6967067093471653 y1[1] (numeric) = -0.6967067093471655 absolute error = 2.220446049250313e-16 relative error = 3.187059948555593e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7173560908995229 y2[1] (numeric) = -0.7173560908995228 absolute error = 1.110223024625157e-16 relative error = 1.54765957759277e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8100000000000003 y1[1] (analytic) = -0.6894984329517468 y1[1] (numeric) = -0.6894984329517471 absolute error = 2.220446049250313e-16 relative error = 3.220378674023334e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7242871743701427 y2[1] (numeric) = -0.7242871743701426 absolute error = 1.110223024625157e-16 relative error = 1.532849212179731e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8200000000000003 y1[1] (analytic) = -0.6822212072876134 y1[1] (numeric) = -0.6822212072876136 absolute error = 2.220446049250313e-16 relative error = 3.254730321384174e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7311458297268961 y2[1] (numeric) = -0.7311458297268959 absolute error = 2.220446049250313e-16 relative error = 3.036940045298095e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8300000000000003 y1[1] (analytic) = -0.6748757600712669 y1[1] (numeric) = -0.6748757600712672 absolute error = 2.220446049250313e-16 relative error = 3.29015528579043e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7379313711099629 y2[1] (numeric) = -0.7379313711099628 absolute error = 1.110223024625157e-16 relative error = 1.504507150787219e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8400000000000003 y1[1] (analytic) = -0.6674628258413079 y1[1] (numeric) = -0.6674628258413081 absolute error = 2.220446049250313e-16 relative error = 3.326696204319001e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7446431199708595 y2[1] (numeric) = -0.7446431199708594 absolute error = 1.110223024625157e-16 relative error = 1.490946461264026e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8500000000000003 y1[1] (analytic) = -0.659983145884982 y1[1] (numeric) = -0.6599831458849822 absolute error = 2.220446049250313e-16 relative error = 3.364398110913698e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7512804051402929 y2[1] (numeric) = -0.7512804051402928 absolute error = 1.110223024625157e-16 relative error = 1.477774499413219e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8600000000000003 y1[1] (analytic) = -0.6524374681640516 y1[1] (numeric) = -0.6524374681640519 absolute error = 3.33066907387547e-16 relative error = 5.104962906633671e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7578425628952772 y2[1] (numeric) = -0.7578425628952771 absolute error = 1.110223024625157e-16 relative error = 1.464978451967171e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8700000000000003 y1[1] (analytic) = -0.644826547240001 y1[1] (numeric) = -0.6448265472400012 absolute error = 2.220446049250313e-16 relative error = 3.443478031036888e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7643289370255053 y2[1] (numeric) = -0.7643289370255052 absolute error = 1.110223024625157e-16 relative error = 1.452546110508059e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8800000000000003 y1[1] (analytic) = -0.63715114419858 y1[1] (numeric) = -0.6371511441985802 absolute error = 2.220446049250313e-16 relative error = 3.484959682593413e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7707388788989695 y2[1] (numeric) = -0.7707388788989694 absolute error = 1.110223024625157e-16 relative error = 1.440465837419741e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8900000000000003 y1[1] (analytic) = -0.6294120265736967 y1[1] (numeric) = -0.6294120265736969 absolute error = 2.220446049250313e-16 relative error = 3.527810012366081e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7770717475268241 y2[1] (numeric) = -0.777071747526824 absolute error = 1.110223024625157e-16 relative error = 1.428726534143917e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9000000000000004 y1[1] (analytic) = -0.6216099682706642 y1[1] (numeric) = -0.6216099682706645 absolute error = 3.33066907387547e-16 relative error = 5.358133305264524e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7833269096274836 y2[1] (numeric) = -0.7833269096274835 absolute error = 1.110223024625157e-16 relative error = 1.417317611561603e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.28 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9100000000000004 y1[1] (analytic) = -0.6137457494888112 y1[1] (numeric) = -0.6137457494888116 absolute error = 3.33066907387547e-16 relative error = 5.426789638298243e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7895037396899507 y2[1] (numeric) = -0.7895037396899506 absolute error = 1.110223024625157e-16 relative error = 1.406228962336717e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.99 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9200000000000004 y1[1] (analytic) = -0.6058201566434626 y1[1] (numeric) = -0.6058201566434629 absolute error = 3.33066907387547e-16 relative error = 5.497785171640692e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.7956016200363663 y2[1] (numeric) = -0.7956016200363661 absolute error = 1.110223024625157e-16 relative error = 1.395450935072768e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9300000000000004 y1[1] (analytic) = -0.5978339822872979 y1[1] (numeric) = -0.5978339822872983 absolute error = 4.440892098500626e-16 relative error = 7.428303224767993e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.8016199408837774 y2[1] (numeric) = -0.8016199408837773 absolute error = 1.110223024625157e-16 relative error = 1.384974310146461e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9400000000000004 y1[1] (analytic) = -0.589788025031098 y1[1] (numeric) = -0.5897880250310983 absolute error = 3.33066907387547e-16 relative error = 5.647230754981592e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.8075581004051146 y2[1] (numeric) = -0.8075581004051144 absolute error = 1.110223024625157e-16 relative error = 1.374790277093635e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9500000000000004 y1[1] (analytic) = -0.5816830894638831 y1[1] (numeric) = -0.5816830894638836 absolute error = 4.440892098500626e-16 relative error = 7.634555961724176e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.813415504789374 y2[1] (numeric) = -0.8134155047893739 absolute error = 1.110223024625157e-16 relative error = 1.364890413433462e-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] = 0.9600000000000004 y1[1] (analytic) = -0.5735199860724564 y1[1] (numeric) = -0.5735199860724568 absolute error = 4.440892098500626e-16 relative error = 7.743221171615074e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.8191915683009985 y2[1] (numeric) = -0.8191915683009984 absolute error = 1.110223024625157e-16 relative error = 1.355266664826344e-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] = 0.9700000000000004 y1[1] (analytic) = -0.5652995311603539 y1[1] (numeric) = -0.5652995311603545 absolute error = 5.551115123125783e-16 relative error = 9.81977662661663e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.8248857133384503 y2[1] (numeric) = -0.8248857133384502 absolute error = 1.110223024625157e-16 relative error = 1.345911326469577e-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] = 0.9800000000000004 y1[1] (analytic) = -0.557022546766217 y1[1] (numeric) = -0.5570225467662174 absolute error = 4.440892098500626e-16 relative error = 7.972553578454112e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.8304973704919707 y2[1] (numeric) = -0.8304973704919706 absolute error = 1.110223024625157e-16 relative error = 1.336817025642696e-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] = 0.9900000000000004 y1[1] (analytic) = -0.5486898605815872 y1[1] (numeric) = -0.5486898605815878 absolute error = 5.551115123125783e-16 relative error = 1.011703609256027e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8360259786005207 y2[1] (numeric) = -0.8360259786005206 absolute error = 1.110223024625157e-16 relative error = 1.327976705321565e-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] = 1 y1[1] (analytic) = -0.5403023058681393 y1[1] (numeric) = -0.5403023058681399 absolute error = 5.551115123125783e-16 relative error = 1.027409112053749e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8414709848078967 y2[1] (numeric) = -0.8414709848078966 absolute error = 1.110223024625157e-16 relative error = 1.319383608786718e-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] = 1.01 y1[1] (analytic) = -0.531860721374355 y1[1] (numeric) = -0.5318607213743556 absolute error = 5.551115123125783e-16 relative error = 1.043715939161933e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8468318446180154 y2[1] (numeric) = -0.8468318446180153 absolute error = 1.110223024625157e-16 relative error = 1.31103126515743e-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] = 1.02 y1[1] (analytic) = -0.5233659512516492 y1[1] (numeric) = -0.5233659512516496 absolute error = 4.440892098500626e-16 relative error = 8.48525221765013e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.8521080219493632 y2[1] (numeric) = -0.8521080219493631 absolute error = 1.110223024625157e-16 relative error = 1.302913475788322e-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] = 1.03 y1[1] (analytic) = -0.5148188449699549 y1[1] (numeric) = -0.5148188449699554 absolute error = 5.551115123125783e-16 relative error = 1.078265719556119e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8572989891886036 y2[1] (numeric) = -0.8572989891886035 absolute error = 1.110223024625157e-16 relative error = 1.295024301470289e-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] = 1.04 y1[1] (analytic) = -0.506220257232778 y1[1] (numeric) = -0.5062202572327785 absolute error = 5.551115123125783e-16 relative error = 1.096580992920081e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8624042272433387 y2[1] (numeric) = -0.8624042272433385 absolute error = 1.110223024625157e-16 relative error = 1.287358050381973e-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] = 1.05 y1[1] (analytic) = -0.4975710478917266 y1[1] (numeric) = -0.4975710478917271 absolute error = 5.551115123125783e-16 relative error = 1.11564271005047e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8674232255940172 y2[1] (numeric) = -0.8674232255940171 absolute error = 1.110223024625157e-16 relative error = 1.279909266742159e-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] = 1.06 y1[1] (analytic) = -0.4888720818605271 y1[1] (numeric) = -0.4888720818605277 absolute error = 6.106226635438361e-16 relative error = 1.249043842348199e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8723554823449865 y2[1] (numeric) = -0.8723554823449864 absolute error = 1.110223024625157e-16 relative error = 1.272672720117212e-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] = 1.070000000000001 y1[1] (analytic) = -0.4801242290285337 y1[1] (numeric) = -0.4801242290285343 absolute error = 6.106226635438361e-16 relative error = 1.27180139352548e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8772005042746819 y2[1] (numeric) = -0.8772005042746818 absolute error = 1.110223024625157e-16 relative error = 1.265643395341126e-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] = 1.080000000000001 y1[1] (analytic) = -0.4713283641737396 y1[1] (numeric) = -0.4713283641737402 absolute error = 6.106226635438361e-16 relative error = 1.295535575530842e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8819578068849477 y2[1] (numeric) = -0.8819578068849476 absolute error = 1.110223024625157e-16 relative error = 1.258816483008905e-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] = 1.090000000000001 y1[1] (analytic) = -0.4624853668753004 y1[1] (numeric) = -0.4624853668753011 absolute error = 6.661338147750939e-16 relative error = 1.440334900270916e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8866269144494875 y2[1] (numeric) = -0.8866269144494874 absolute error = 1.110223024625157e-16 relative error = 1.252187370506908e-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] = 1.100000000000001 y1[1] (analytic) = -0.4535961214255769 y1[1] (numeric) = -0.4535961214255776 absolute error = 6.661338147750939e-16 relative error = 1.46856153152621e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8912073600614355 y2[1] (numeric) = -0.8912073600614355 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] = 1.110000000000001 y1[1] (analytic) = -0.4446615167417063 y1[1] (numeric) = -0.4446615167417071 absolute error = 7.216449660063518e-16 relative error = 1.622908524430592e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8956986856800478 y2[1] (numeric) = -0.8956986856800478 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] = 1.120000000000001 y1[1] (analytic) = -0.4356824462767117 y1[1] (numeric) = -0.4356824462767124 absolute error = 7.216449660063518e-16 relative error = 1.65635538492184e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9001004421765052 y2[1] (numeric) = -0.9001004421765052 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] = 1.130000000000001 y1[1] (analytic) = -0.4266598079301568 y1[1] (numeric) = -0.4266598079301575 absolute error = 7.216449660063518e-16 relative error = 1.691382578329204e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9044121893788262 y2[1] (numeric) = -0.9044121893788262 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] = 1.140000000000001 y1[1] (analytic) = -0.4175945039583576 y1[1] (numeric) = -0.4175945039583583 absolute error = 7.216449660063518e-16 relative error = 1.728099769431626e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9086334961158835 y2[1] (numeric) = -0.9086334961158835 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] = 1.150000000000001 y1[1] (analytic) = -0.4084874408841568 y1[1] (numeric) = -0.4084874408841575 absolute error = 7.216449660063518e-16 relative error = 1.766627058213532e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9127639402605213 y2[1] (numeric) = -0.9127639402605213 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] = 1.160000000000001 y1[1] (analytic) = -0.3993395294062726 y1[1] (numeric) = -0.3993395294062734 absolute error = 7.771561172376096e-16 relative error = 1.946103653683032e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9168031087717672 y2[1] (numeric) = -0.9168031087717672 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] = 1.170000000000001 y1[1] (analytic) = -0.3901516843082297 y1[1] (numeric) = -0.3901516843082304 absolute error = 7.771561172376096e-16 relative error = 1.991933262099252e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9207505977361359 y2[1] (numeric) = -0.9207505977361359 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] = 1.180000000000001 y1[1] (analytic) = -0.3809248243668812 y1[1] (numeric) = -0.380924824366882 absolute error = 8.326672684688674e-16 relative error = 2.185909699775561e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9246060124080205 y2[1] (numeric) = -0.9246060124080205 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] = 1.190000000000001 y1[1] (analytic) = -0.3716598722605324 y1[1] (numeric) = -0.3716598722605332 absolute error = 8.326672684688674e-16 relative error = 2.240401320175804e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.928368967249167 y2[1] (numeric) = -0.9283689672491668 absolute error = 1.110223024625157e-16 relative error = 1.195885540977138e-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] = 1.200000000000001 y1[1] (analytic) = -0.362357754476673 y1[1] (numeric) = -0.3623577544766738 absolute error = 8.326672684688674e-16 relative error = 2.297914859505154e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9320390859672266 y2[1] (numeric) = -0.9320390859672265 absolute error = 1.110223024625157e-16 relative error = 1.191176466030949e-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] = 1.210000000000001 y1[1] (analytic) = -0.3530194012193297 y1[1] (numeric) = -0.3530194012193306 absolute error = 8.881784197001252e-16 relative error = 2.515947895873017e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9356160015533862 y2[1] (numeric) = -0.9356160015533861 absolute error = 1.110223024625157e-16 relative error = 1.186622527598794e-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] = 1.220000000000001 y1[1] (analytic) = -0.3436457463160464 y1[1] (numeric) = -0.3436457463160473 absolute error = 8.326672684688674e-16 relative error = 2.423039648810535e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9390993563190678 y2[1] (numeric) = -0.9390993563190677 absolute error = 1.110223024625157e-16 relative error = 1.182221047383987e-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] = 1.230000000000001 y1[1] (analytic) = -0.334237727124502 y1[1] (numeric) = -0.3342377271245028 absolute error = 8.326672684688674e-16 relative error = 2.491242612353879e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9424888019316977 y2[1] (numeric) = -0.9424888019316976 absolute error = 1.110223024625157e-16 relative error = 1.177969459530634e-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] = 1.240000000000001 y1[1] (analytic) = -0.3247962844387756 y1[1] (numeric) = -0.3247962844387765 absolute error = 8.326672684688674e-16 relative error = 2.563660079756319e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9457839994495392 y2[1] (numeric) = -0.9457839994495391 absolute error = 1.110223024625157e-16 relative error = 1.173865306741628e-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] = 1.250000000000001 y1[1] (analytic) = -0.315322362395268 y1[1] (numeric) = -0.3153223623952689 absolute error = 8.881784197001252e-16 relative error = 2.81673146475657e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9489846193555864 y2[1] (numeric) = -0.9489846193555863 absolute error = 1.110223024625157e-16 relative error = 1.169906236603771e-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] = 1.260000000000001 y1[1] (analytic) = -0.3058169083782887 y1[1] (numeric) = -0.3058169083782896 absolute error = 8.881784197001252e-16 relative error = 2.904281599111153e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.952090341590516 y2[1] (numeric) = -0.9520903415905159 absolute error = 1.110223024625157e-16 relative error = 1.166089998109288e-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] = 1.270000000000001 y1[1] (analytic) = -0.2962808729253181 y1[1] (numeric) = -0.296280872925319 absolute error = 8.881784197001252e-16 relative error = 2.99775821142529e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9551008555846925 y2[1] (numeric) = -0.9551008555846924 absolute error = 1.110223024625157e-16 relative error = 1.162414438363686e-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] = 1.280000000000001 y1[1] (analytic) = -0.2867152096319548 y1[1] (numeric) = -0.2867152096319557 absolute error = 8.881784197001252e-16 relative error = 3.097772248776915e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9580158602892251 y2[1] (numeric) = -0.9580158602892251 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] = 1.290000000000001 y1[1] (analytic) = -0.277120875056557 y1[1] (numeric) = -0.2771208750565579 absolute error = 8.881784197001252e-16 relative error = 3.205021705848969e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9608350642060729 y2[1] (numeric) = -0.9608350642060728 absolute error = 1.110223024625157e-16 relative error = 1.155477215584884e-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] = 1.300000000000001 y1[1] (analytic) = -0.2674988286245867 y1[1] (numeric) = -0.2674988286245876 absolute error = 8.881784197001252e-16 relative error = 3.320307697296921e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9635581854171932 y2[1] (numeric) = -0.9635581854171931 absolute error = 1.110223024625157e-16 relative error = 1.152211710125696e-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] = 1.310000000000001 y1[1] (analytic) = -0.257850032532669 y1[1] (numeric) = -0.2578500325326699 absolute error = 8.881784197001252e-16 relative error = 3.444554227805246e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9661849516127342 y2[1] (numeric) = -0.9661849516127341 absolute error = 1.110223024625157e-16 relative error = 1.149079193142056e-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] = 1.320000000000001 y1[1] (analytic) = -0.2481754516523723 y1[1] (numeric) = -0.2481754516523731 absolute error = 8.881784197001252e-16 relative error = 3.578832691898257e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9687151001182654 y2[1] (numeric) = -0.9687151001182653 absolute error = 1.110223024625157e-16 relative error = 1.146077958823616e-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] = 1.330000000000001 y1[1] (analytic) = -0.2384760534337225 y1[1] (numeric) = -0.2384760534337234 absolute error = 8.881784197001252e-16 relative error = 3.724392478454734e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9711483779210447 y2[1] (numeric) = -0.9711483779210446 absolute error = 1.110223024625157e-16 relative error = 1.143206383150051e-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] = 1.340000000000001 y1[1] (analytic) = -0.2287528078084587 y1[1] (numeric) = -0.2287528078084596 absolute error = 8.881784197001252e-16 relative error = 3.882699531469019e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9734845416953195 y2[1] (numeric) = -0.9734845416953194 absolute error = 1.110223024625157e-16 relative error = 1.140462921672806e-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] = 1.350000000000001 y1[1] (analytic) = -0.2190066870930409 y1[1] (numeric) = -0.2190066870930417 absolute error = 8.881784197001252e-16 relative error = 4.055485389461187e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9757233578266592 y2[1] (numeric) = -0.9757233578266591 absolute error = 1.110223024625157e-16 relative error = 1.137846107423403e-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] = 1.360000000000001 y1[1] (analytic) = -0.2092386658914186 y1[1] (numeric) = -0.2092386658914195 absolute error = 8.881784197001252e-16 relative error = 4.24481018322413e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9778646024353164 y2[1] (numeric) = -0.9778646024353163 absolute error = 1.110223024625157e-16 relative error = 1.135354548942879e-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] = 1.370000000000001 y1[1] (analytic) = -0.1994497209975722 y1[1] (numeric) = -0.1994497209975731 absolute error = 9.159339953157541e-16 relative error = 4.592305222261521e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9799080613986144 y2[1] (numeric) = -0.9799080613986143 absolute error = 1.110223024625157e-16 relative error = 1.13298692842729e-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] = 1.380000000000001 y1[1] (analytic) = -0.1896408312978336 y1[1] (numeric) = -0.1896408312978345 absolute error = 9.159339953157541e-16 relative error = 4.829835373782278e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9818535303723599 y2[1] (numeric) = -0.9818535303723598 absolute error = 1.110223024625157e-16 relative error = 1.130741999984574e-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] = 1.390000000000001 y1[1] (analytic) = -0.1798129776729987 y1[1] (numeric) = -0.1798129776729996 absolute error = 9.436895709313831e-16 relative error = 5.248172757850339e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9837008148112767 y2[1] (numeric) = -0.9837008148112766 absolute error = 1.110223024625157e-16 relative error = 1.128618587998378e-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] = 1.400000000000001 y1[1] (analytic) = -0.1699671429002401 y1[1] (numeric) = -0.1699671429002411 absolute error = 9.436895709313831e-16 relative error = 5.552188233729789e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9854497299884604 y2[1] (numeric) = -0.9854497299884603 absolute error = 1.110223024625157e-16 relative error = 1.126615585594769e-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] = 1.410000000000001 y1[1] (analytic) = -0.1601043115548304 y1[1] (numeric) = -0.1601043115548313 absolute error = 9.436895709313831e-16 relative error = 5.894217099882414e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9871001010138505 y2[1] (numeric) = -0.9871001010138504 absolute error = 1.110223024625157e-16 relative error = 1.124731953208035e-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] = 1.420000000000001 y1[1] (analytic) = -0.150225469911685 y1[1] (numeric) = -0.1502254699116859 absolute error = 9.436895709313831e-16 relative error = 6.281821394775215e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.98865176285172 y2[1] (numeric) = -0.9886517628517199 absolute error = 1.110223024625157e-16 relative error = 1.122966717242045e-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] = 1.430000000000001 y1[1] (analytic) = -0.1403316058467358 y1[1] (numeric) = -0.1403316058467368 absolute error = 9.71445146547012e-16 relative error = 6.922497185758585e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9901045603371779 y2[1] (numeric) = -0.9901045603371779 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] = 1.440000000000001 y1[1] (analytic) = -0.1304237087381447 y1[1] (numeric) = -0.1304237087381457 absolute error = 9.992007221626409e-16 relative error = 7.661189302389524e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9914583481916865 y2[1] (numeric) = -0.9914583481916865 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] = 1.450000000000001 y1[1] (analytic) = -0.1205027693673657 y1[1] (numeric) = -0.1205027693673667 absolute error = 9.992007221626409e-16 relative error = 8.291931607948937e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9927129910375886 y2[1] (numeric) = -0.9927129910375886 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] = 1.460000000000001 y1[1] (analytic) = -0.1105697798200687 y1[1] (numeric) = -0.1105697798200697 absolute error = 1.013078509970455e-15 relative error = 9.162345367957214e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.993868363411645 y2[1] (numeric) = -0.993868363411645 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] = 1.470000000000001 y1[1] (analytic) = -0.1006257333869308 y1[1] (numeric) = -0.1006257333869319 absolute error = 1.013078509970455e-15 relative error = 1.006778759141976e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9949243497775809 y2[1] (numeric) = -0.994924349777581 absolute error = 1.110223024625157e-16 relative error = 1.115886876096008e-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] = 1.480000000000001 y1[1] (analytic) = -0.09067162446430879 y1[1] (numeric) = -0.09067162446430981 absolute error = 1.013078509970455e-15 relative error = 1.117304907633187e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9958808445376401 y2[1] (numeric) = -0.9958808445376403 absolute error = 1.110223024625157e-16 relative error = 1.114815121422084e-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] = 1.490000000000001 y1[1] (analytic) = -0.08070844845479974 y1[1] (numeric) = -0.08070844845480077 absolute error = 1.02695629777827e-15 relative error = 1.272427258161715e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9967377520431434 y2[1] (numeric) = -0.9967377520431436 absolute error = 2.220446049250313e-16 relative error = 2.227713402746886e-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] = 1.500000000000001 y1[1] (analytic) = -0.07073720166770202 y1[1] (numeric) = -0.07073720166770306 absolute error = 1.040834085586084e-15 relative error = 1.471409754764613e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9974949866040544 y2[1] (numeric) = -0.9974949866040547 absolute error = 2.220446049250313e-16 relative error = 2.226022264843419e-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] = 1.510000000000001 y1[1] (analytic) = -0.06075888121938501 y1[1] (numeric) = -0.06075888121938605 absolute error = 1.040834085586084e-15 relative error = 1.713056700020355e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9981524724975481 y2[1] (numeric) = -0.9981524724975483 absolute error = 2.220446049250313e-16 relative error = 2.224555977599672e-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] = 1.520000000000001 y1[1] (analytic) = -0.05077448493357829 y1[1] (numeric) = -0.05077448493357934 absolute error = 1.047772979489991e-15 relative error = 2.063581700258816e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.998710143975583 y2[1] (numeric) = -0.9987101439755832 absolute error = 2.220446049250313e-16 relative error = 2.223313803954513e-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] = 1.530000000000001 y1[1] (analytic) = -0.04078501124159015 y1[1] (numeric) = -0.0407850112415912 absolute error = 1.054711873393899e-15 relative error = 2.586028154182206e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.999167945271476 y2[1] (numeric) = -0.9991679452714762 absolute error = 2.220446049250313e-16 relative error = 2.222295120413429e-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] = 1.540000000000001 y1[1] (analytic) = -0.03079145908246523 y1[1] (numeric) = -0.0307914590824663 absolute error = 1.06512021424976e-15 relative error = 3.459141742511033e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9995258306054791 y2[1] (numeric) = -0.9995258306054793 absolute error = 2.220446049250313e-16 relative error = 2.221499416283461e-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] = 1.550000000000001 y1[1] (analytic) = -0.02079482780309154 y1[1] (numeric) = -0.02079482780309261 absolute error = 1.072059108153667e-15 relative error = 5.155412289561182e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.999783764189357 y2[1] (numeric) = -0.9997837641893572 absolute error = 2.220446049250313e-16 relative error = 2.220926293047669e-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] = 1.560000000000001 y1[1] (analytic) = -0.0107961170582665 y1[1] (numeric) = -0.01079611705826758 absolute error = 1.077263278581597e-15 relative error = 9.978247482568235e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9999417202299663 y2[1] (numeric) = -0.9999417202299665 absolute error = 2.220446049250313e-16 relative error = 2.22057546387769e-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] = 1.570000000000001 y1[1] (analytic) = -0.0007963267107323752 y1[1] (numeric) = -0.0007963267107334582 absolute error = 1.08300955009577e-15 relative error = 1.360006559493321e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = -0.9999996829318346 y2[1] (numeric) = -0.9999996829318348 absolute error = 2.220446049250313e-16 relative error = 2.220446753283291e-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] = 1.580000000000001 y1[1] (analytic) = 0.009203543268809225 y1[1] (numeric) = 0.009203543268808135 absolute error = 1.089406342913435e-15 relative error = 1.183681448649705e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = -0.9999576464987401 y2[1] (numeric) = -0.9999576464987403 absolute error = 2.220446049250313e-16 relative error = 2.220540096898105e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008874 Order of pole (three term test) = -0.8949 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.008862 Order of pole (three term test) = -0.8909 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) = 0.01920249290169244 absolute error = 1.092875789865388e-15 relative error = 5.691322452039568e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9998156151342908 y2[1] (numeric) = -0.9998156151342911 absolute error = 2.220446049250313e-16 relative error = 2.220855541401074e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01851 Order of pole (three term test) = -0.9018 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.01849 Order of pole (three term test) = -0.8974 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) = 0.0291995223012886 absolute error = 1.099814683769296e-15 relative error = 3.766550262093563e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9995736030415051 y2[1] (numeric) = -0.9995736030415053 absolute error = 2.220446049250313e-16 relative error = 2.22139324457342e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02814 Order of pole (three term test) = -0.9135 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02811 Order of pole (three term test) = -0.9087 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) = 0.03919363177298749 absolute error = 1.110223024625157e-15 relative error = 2.832661772850298e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9992316344213905 y2[1] (numeric) = -0.9992316344213907 absolute error = 2.220446049250313e-16 relative error = 2.222153475491268e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03776 Order of pole (three term test) = -0.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03771 Order of pole (three term test) = -0.9245 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) = 0.04918382191417033 absolute error = 1.110223024625157e-15 relative error = 2.257293112687661e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.998789743470524 y2[1] (numeric) = -0.9987897434705242 absolute error = 2.220446049250313e-16 relative error = 2.223136614854358e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04737 Order of pole (three term test) = -0.9513 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0473 Order of pole (three term test) = -0.945 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) = 0.05916909371414813 absolute error = 1.117161918529064e-15 relative error = 1.888083538893066e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9982479743776324 y2[1] (numeric) = -0.9982479743776326 absolute error = 2.220446049250313e-16 relative error = 2.224343155451602e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05696 Order of pole (three term test) = -0.9775 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05688 Order of pole (three term test) = -0.9701 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) = 0.06914844865406193 absolute error = 1.124100812432971e-15 relative error = 1.6256341744652e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9976063813191736 y2[1] (numeric) = -0.9976063813191738 absolute error = 2.220446049250313e-16 relative error = 2.225773702764542e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06652 Order of pole (three term test) = -1.008 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06643 Order of pole (three term test) = -0.9997 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) = 0.07912088880673385 absolute error = 1.124100812432971e-15 relative error = 1.42073835290041e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9968650284539188 y2[1] (numeric) = -0.996865028453919 absolute error = 2.220446049250313e-16 relative error = 2.227428975710081e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07606 Order of pole (three term test) = -1.044 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07595 Order of pole (three term test) = -1.034 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) = 0.08908541693645894 absolute error = 1.124100812432971e-15 relative error = 1.261823597048137e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9960239899165366 y2[1] (numeric) = -0.9960239899165368 absolute error = 2.220446049250313e-16 relative error = 2.229309807524193e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08556 Order of pole (three term test) = -1.085 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08544 Order of pole (three term test) = -1.073 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) = 0.09904103659872798 absolute error = 1.137978600240785e-15 relative error = 1.148997061542657e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9950833498101801 y2[1] (numeric) = -0.9950833498101803 absolute error = 2.220446049250313e-16 relative error = 2.231417146788639e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09503 Order of pole (three term test) = -1.13 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0949 Order of pole (three term test) = -1.116 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) = 0.1089867522398711 absolute error = 1.137978600240785e-15 relative error = 1.044143968742342e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = -0.9940432021980758 y2[1] (numeric) = -0.9940432021980761 absolute error = 2.220446049250313e-16 relative error = 2.233752058603043e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1045 Order of pole (three term test) = -1.18 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1043 Order of pole (three term test) = -1.164 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) = 0.1189215692966122 absolute error = 1.1518563880486e-15 relative error = 9.685849210210538e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9929036510941184 y2[1] (numeric) = -0.9929036510941186 absolute error = 2.220446049250313e-16 relative error = 2.236315725905045e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1139 Order of pole (three term test) = -1.235 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1137 Order of pole (three term test) = -1.217 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) = 0.1288444942955246 absolute error = 1.165734175856414e-15 relative error = 9.047605660065023e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9916648104524685 y2[1] (numeric) = -0.9916648104524687 absolute error = 2.220446049250313e-16 relative error = 2.23910945094158e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1232 Order of pole (three term test) = -1.294 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.123 Order of pole (three term test) = -1.274 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) = 0.1387545349523775 absolute error = 1.165734175856414e-15 relative error = 8.401413159263594e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9903268041561579 y2[1] (numeric) = -0.9903268041561581 absolute error = 2.220446049250313e-16 relative error = 2.242134656894721e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1325 Order of pole (three term test) = -1.358 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1323 Order of pole (three term test) = -1.335 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) = 0.1486507002713636 absolute error = 1.165734175856414e-15 relative error = 7.842103493144291e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9888897660047012 y2[1] (numeric) = -0.9888897660047016 absolute error = 3.33066907387547e-16 relative error = 3.368089334498822e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1417 Order of pole (three term test) = -1.427 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1416 Order of pole (three term test) = -1.401 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) = 0.1585320006441977 absolute error = 1.165734175856414e-15 relative error = 7.353305144194381e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9873538397007163 y2[1] (numeric) = -0.9873538397007166 absolute error = 2.220446049250313e-16 relative error = 2.248885819822575e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1509 Order of pole (three term test) = -1.5 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1507 Order of pole (three term test) = -1.472 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) = 0.1683974479490769 absolute error = 1.193489751472043e-15 relative error = 7.087338709746623e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9857191788355533 y2[1] (numeric) = -0.9857191788355536 absolute error = 3.33066907387547e-16 relative error = 3.378922867068535e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1601 Order of pole (three term test) = -1.578 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1598 Order of pole (three term test) = -1.546 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) = 0.178246055649492 absolute error = 1.221245327087672e-15 relative error = 6.851457793204439e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9839859468739367 y2[1] (numeric) = -0.983985946873937 absolute error = 3.33066907387547e-16 relative error = 3.384874636123414e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1691 Order of pole (three term test) = -1.661 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1689 Order of pole (three term test) = -1.625 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) = 0.18807683889288 absolute error = 1.221245327087672e-15 relative error = 6.493331843923802e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9821543171376182 y2[1] (numeric) = -0.9821543171376186 absolute error = 3.33066907387547e-16 relative error = 3.391187123814047e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1781 Order of pole (three term test) = -1.748 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1779 Order of pole (three term test) = -1.709 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) = 0.1978888146091089 absolute error = 1.221245327087672e-15 relative error = 6.171371178810681e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9802244727880453 y2[1] (numeric) = -0.9802244727880456 absolute error = 3.33066907387547e-16 relative error = 3.39786361832211e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.187 Order of pole (three term test) = -1.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1868 Order of pole (three term test) = -1.797 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) = 0.2076810016087837 absolute error = 1.193489751472043e-15 relative error = 5.746744970540236e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9781966068080444 y2[1] (numeric) = -0.9781966068080448 absolute error = 3.33066907387547e-16 relative error = 3.404907613351659e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1959 Order of pole (three term test) = -1.936 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1956 Order of pole (three term test) = -1.889 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) = 0.2174524206813645 absolute error = 1.193489751472043e-15 relative error = 5.488509843819447e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.976070921982524 y2[1] (numeric) = -0.9760709219825243 absolute error = 3.33066907387547e-16 relative error = 3.412322812680925e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2047 Order of pole (three term test) = -2.036 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2044 Order of pole (three term test) = -1.985 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) = 0.227202094693087 absolute error = 1.221245327087672e-15 relative error = 5.375149946295034e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9738476308781949 y2[1] (numeric) = -0.9738476308781953 absolute error = 3.33066907387547e-16 relative error = 3.42011313502087e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2133 Order of pole (three term test) = -2.141 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.213 Order of pole (three term test) = -2.086 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) = 0.2369290486846745 absolute error = 1.221245327087672e-15 relative error = 5.154476978941505e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9715269558223151 y2[1] (numeric) = -0.9715269558223154 absolute error = 3.33066907387547e-16 relative error = 3.428282719192635e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2219 Order of pole (three term test) = -2.25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2216 Order of pole (three term test) = -2.19 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) = 0.2466323099688339 absolute error = 1.221245327087672e-15 relative error = 4.95168425921969e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9691091288804561 y2[1] (numeric) = -0.9691091288804564 absolute error = 3.33066907387547e-16 relative error = 3.436835929636901e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2305 Order of pole (three term test) = -2.363 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2301 Order of pole (three term test) = -2.299 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) = 0.2563109082275226 absolute error = 1.221245327087672e-15 relative error = 4.764702897481012e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9665943918332973 y2[1] (numeric) = -0.9665943918332977 absolute error = 3.33066907387547e-16 relative error = 3.445777362269126e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2389 Order of pole (three term test) = -2.481 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2385 Order of pole (three term test) = -2.412 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) = 0.2659638756089802 absolute error = 1.221245327087672e-15 relative error = 4.591771436219932e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9639829961524479 y2[1] (numeric) = -0.9639829961524482 absolute error = 3.33066907387547e-16 relative error = 3.4551118506957e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2472 Order of pole (three term test) = -2.603 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2469 Order of pole (three term test) = -2.529 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) = 0.2755902468245128 absolute error = 1.221245327087672e-15 relative error = 4.431380795073338e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9612752029752996 y2[1] (numeric) = -0.9612752029753 absolute error = 4.440892098500626e-16 relative error = 4.619792630409439e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2554 Order of pole (three term test) = -2.729 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2551 Order of pole (three term test) = -2.65 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) = 0.2851890592450207 absolute error = 1.221245327087672e-15 relative error = 4.28223063788163e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9584712830789138 y2[1] (numeric) = -0.9584712830789143 absolute error = 4.440892098500626e-16 relative error = 4.63330741035357e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2636 Order of pole (three term test) = -2.859 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2632 Order of pole (three term test) = -2.774 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) = 0.2947593529972609 absolute error = 1.221245327087672e-15 relative error = 4.14319448957067e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9555715168529436 y2[1] (numeric) = -0.9555715168529441 absolute error = 4.440892098500626e-16 relative error = 4.647367591204637e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2716 Order of pole (three term test) = -2.993 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2712 Order of pole (three term test) = -2.903 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) = 0.3043001710598333 absolute error = 1.221245327087672e-15 relative error = 4.013291622000235e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.952576194271595 y2[1] (numeric) = -0.9525761942715955 absolute error = 4.440892098500626e-16 relative error = 4.661980978746206e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2795 Order of pole (three term test) = -3.131 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2791 Order of pole (three term test) = -3.035 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) = 0.3138105593588823 absolute error = 1.221245327087672e-15 relative error = 3.891664224373718e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9494856148646301 y2[1] (numeric) = -0.9494856148646306 absolute error = 4.440892098500626e-16 relative error = 4.677155745149201e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2873 Order of pole (three term test) = -3.273 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2869 Order of pole (three term test) = -3.172 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) = 0.3232895668635034 absolute error = 1.165734175856414e-15 relative error = 3.60585151932415e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9463000876874141 y2[1] (numeric) = -0.9463000876874146 absolute error = 4.440892098500626e-16 relative error = 4.692900440655523e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.295 Order of pole (three term test) = -3.419 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2946 Order of pole (three term test) = -3.312 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) = 0.3327362456808452 absolute error = 1.221245327087672e-15 relative error = 3.670310472454705e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9430199312900102 y2[1] (numeric) = -0.9430199312900106 absolute error = 4.440892098500626e-16 relative error = 4.709224005929206e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3025 Order of pole (three term test) = -3.569 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3021 Order of pole (three term test) = -3.455 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) = 0.3421496511508982 absolute error = 1.221245327087672e-15 relative error = 3.569330914059773e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9396454736853245 y2[1] (numeric) = -0.939645473685325 absolute error = 5.551115123125783e-16 relative error = 5.907669731387203e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.31 Order of pole (three term test) = -3.723 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3095 Order of pole (three term test) = -3.602 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) = 0.3515288419409598 absolute error = 1.221245327087672e-15 relative error = 3.474097090709784e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9361770523163055 y2[1] (numeric) = -0.9361770523163061 absolute error = 5.551115123125783e-16 relative error = 5.929556924506019e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3173 Order of pole (three term test) = -3.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3168 Order of pole (three term test) = -3.753 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) = 0.3608728801397671 absolute error = 1.27675647831893e-15 relative error = 3.537967380160111e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9326150140222 y2[1] (numeric) = -0.9326150140222006 absolute error = 5.551115123125783e-16 relative error = 5.952204328327105e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3245 Order of pole (three term test) = -4.041 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.324 Order of pole (three term test) = -3.908 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) = 0.3701808313512869 absolute error = 1.221245327087672e-15 relative error = 3.299050689982256e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9289597150038689 y2[1] (numeric) = -0.9289597150038694 absolute error = 5.551115123125783e-16 relative error = 5.975625243450588e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3315 Order of pole (three term test) = -4.205 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3311 Order of pole (three term test) = -4.065 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) = 0.3794517647881545 absolute error = 1.27675647831893e-15 relative error = 3.364739861024842e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9252115207881677 y2[1] (numeric) = -0.9252115207881684 absolute error = 6.661338147750939e-16 relative error = 7.199800259811172e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3385 Order of pole (three term test) = -4.373 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.338 Order of pole (three term test) = -4.226 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) = 0.388684753364752 absolute error = 1.221245327087672e-15 relative error = 3.141994422255147e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9213708061913949 y2[1] (numeric) = -0.9213708061913956 absolute error = 6.661338147750939e-16 relative error = 7.229812473966307e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3453 Order of pole (three term test) = -4.545 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3448 Order of pole (three term test) = -4.391 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) = 0.3978788737899159 absolute error = 1.27675647831893e-15 relative error = 3.208907439989051e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9174379552818093 y2[1] (numeric) = -0.91743795528181 absolute error = 7.771561172376096e-16 relative error = 8.470939236418344e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3519 Order of pole (three term test) = -4.719 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3514 Order of pole (three term test) = -4.558 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) = 0.4070332066592655 absolute error = 1.221245327087672e-15 relative error = 3.000357973520313e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9134133613412246 y2[1] (numeric) = -0.9134133613412254 absolute error = 7.771561172376096e-16 relative error = 8.508263072662528e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3584 Order of pole (three term test) = -4.898 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3579 Order of pole (three term test) = -4.729 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) = 0.4161468365471424 absolute error = 1.221245327087672e-15 relative error = 2.93465003175465e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9092974268256812 y2[1] (numeric) = -0.9092974268256819 absolute error = 7.771561172376096e-16 relative error = 8.546775722775646e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3648 Order of pole (three term test) = -5.079 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3643 Order of pole (three term test) = -4.903 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) = 0.4252188520981524 absolute error = 1.054711873393899e-15 relative error = 2.480397725052979e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9050905633252004 y2[1] (numeric) = -0.9050905633252012 absolute error = 7.771561172376096e-16 relative error = 8.58650116052946e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.371 Order of pole (three term test) = -5.263 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3705 Order of pole (three term test) = -5.08 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) = 0.4342483461183004 absolute error = 8.326672684688674e-16 relative error = 1.917490937874582e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.9007931915226269 y2[1] (numeric) = -0.9007931915226276 absolute error = 6.661338147750939e-16 relative error = 7.394969467399236e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3771 Order of pole (three term test) = -5.451 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3766 Order of pole (three term test) = -5.259 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) = 0.4432344156657091 absolute error = 6.106226635438361e-16 relative error = 1.377651739039082e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8964057411515596 y2[1] (numeric) = -0.8964057411515602 absolute error = 6.661338147750939e-16 relative error = 7.431164083346355e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.383 Order of pole (three term test) = -5.641 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3825 Order of pole (three term test) = -5.442 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) = 0.4521761621409119 absolute error = 4.440892098500626e-16 relative error = 9.821154829291297e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.8919286509533794 y2[1] (numeric) = -0.8919286509533799 absolute error = 5.551115123125783e-16 relative error = 6.22372105346343e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3888 Order of pole (three term test) = -5.835 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3883 Order of pole (three term test) = -5.628 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) = 0.4610726913767129 absolute error = 2.220446049250313e-16 relative error = 4.815826421253233e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.8873623686333753 y2[1] (numeric) = -0.8873623686333757 absolute error = 4.440892098500626e-16 relative error = 5.004598183873894e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3944 Order of pole (three term test) = -6.031 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3939 Order of pole (three term test) = -5.816 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) = 0.4699231137276022 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.8827073508159741 y2[1] (numeric) = -0.8827073508159743 absolute error = 2.220446049250313e-16 relative error = 2.515495137995321e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3999 Order of pole (three term test) = -6.23 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3993 Order of pole (three term test) = -6.007 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) = 0.47872654415872 absolute error = 2.220446049250313e-16 relative error = 4.63823465889565e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.8779640629990781 y2[1] (numeric) = -0.8779640629990784 absolute error = 2.220446049250313e-16 relative error = 2.529085349650176e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4052 Order of pole (three term test) = -6.432 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4046 Order of pole (three term test) = -6.2 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) = 0.4874821023343594 absolute error = 3.885780586188048e-16 relative error = 7.971124616843534e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.8731329795075167 y2[1] (numeric) = -0.8731329795075168 absolute error = 1.110223024625157e-16 relative error = 1.271539445516499e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4103 Order of pole (three term test) = -6.636 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4097 Order of pole (three term test) = -6.396 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) = 0.4961889127059991 absolute error = 6.106226635438361e-16 relative error = 1.230625368498796e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8682145834456129 y2[1] (numeric) = -0.8682145834456129 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4153 Order of pole (three term test) = -6.843 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4147 Order of pole (three term test) = -6.595 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) = 0.5048461045998576 absolute error = 7.771561172376096e-16 relative error = 1.539392123969317e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8632093666488742 y2[1] (numeric) = -0.863209366648874 absolute error = 1.110223024625157e-16 relative error = 1.286157295692042e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4201 Order of pole (three term test) = -7.053 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4195 Order of pole (three term test) = -6.796 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) = 0.5134528123039597 absolute error = 8.881784197001252e-16 relative error = 1.729815084106176e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8581178296348094 y2[1] (numeric) = -0.8581178296348091 absolute error = 3.33066907387547e-16 relative error = 3.881365657316441e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4247 Order of pole (three term test) = -7.265 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4241 Order of pole (three term test) = -6.999 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) = 0.5220081751547073 absolute error = 1.110223024625157e-15 relative error = 2.126830723093796e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8529404815528769 y2[1] (numeric) = -0.8529404815528765 absolute error = 4.440892098500626e-16 relative error = 5.206567391918681e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4292 Order of pole (three term test) = -7.479 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4286 Order of pole (three term test) = -7.204 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) = 0.5305113376229449 absolute error = 1.221245327087672e-15 relative error = 2.302015509338015e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8476778401335705 y2[1] (numeric) = -0.8476778401335699 absolute error = 5.551115123125783e-16 relative error = 6.548614179003525e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4335 Order of pole (three term test) = -7.695 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4329 Order of pole (three term test) = -7.411 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) = 0.5389614493995115 absolute error = 1.443289932012704e-15 relative error = 2.677909400794363e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8423304316366466 y2[1] (numeric) = -0.8423304316366459 absolute error = 6.661338147750939e-16 relative error = 7.90822448953669e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4376 Order of pole (three term test) = -7.913 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.437 Order of pole (three term test) = -7.62 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) = 0.5473576654802712 absolute error = 1.665334536937735e-15 relative error = 3.042497880205104e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8368987907984987 y2[1] (numeric) = -0.8368987907984979 absolute error = 7.771561172376096e-16 relative error = 9.286142192846429e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4415 Order of pole (three term test) = -8.133 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4409 Order of pole (three term test) = -7.832 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) = 0.5556991462506127 absolute error = 1.77635683940025e-15 relative error = 3.196616103129919e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8313834607786843 y2[1] (numeric) = -0.8313834607786834 absolute error = 8.881784197001252e-16 relative error = 1.068313794537416e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4453 Order of pole (three term test) = -8.356 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4447 Order of pole (three term test) = -8.045 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) = 0.5639850575694102 absolute error = 1.998401444325282e-15 relative error = 3.54335884879245e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8257849931056094 y2[1] (numeric) = -0.8257849931056083 absolute error = 1.110223024625157e-15 relative error = 1.344445629182281e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4489 Order of pole (three term test) = -8.58 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4483 Order of pole (three term test) = -8.26 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) = 0.5722145708524368 absolute error = 2.109423746787797e-15 relative error = 3.686420888663084e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8201039476213756 y2[1] (numeric) = -0.8201039476213744 absolute error = 1.221245327087672e-15 relative error = 1.489134798862711e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4523 Order of pole (three term test) = -8.806 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4517 Order of pole (three term test) = -8.476 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) = 0.580386863155222 absolute error = 2.331468351712829e-15 relative error = 4.017093596912266e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8143408924257975 y2[1] (numeric) = -0.8143408924257961 absolute error = 1.443289932012704e-15 relative error = 1.772341221516413e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4555 Order of pole (three term test) = -9.033 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4549 Order of pole (three term test) = -8.694 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) = 0.5885011172553458 absolute error = 2.442490654175344e-15 relative error = 4.150358567825077e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8084964038195919 y2[1] (numeric) = -0.8084964038195903 absolute error = 1.554312234475219e-15 relative error = 1.922472662997829e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.83 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4586 Order of pole (three term test) = -9.262 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.1 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4579 Order of pole (three term test) = -8.914 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) = 0.5965565217341601 absolute error = 2.664535259100376e-15 relative error = 4.466526074268229e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.8025710662467491 y2[1] (numeric) = -0.8025710662467473 absolute error = 1.77635683940025e-15 relative error = 2.213332767785218e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.12 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4615 Order of pole (three term test) = -9.493 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4608 Order of pole (three term test) = -9.135 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) = 0.6045522710579296 absolute error = 2.775557561562891e-15 relative error = 4.591096079592667e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7965654722360886 y2[1] (numeric) = -0.7965654722360868 absolute error = 1.887379141862766e-15 relative error = 2.369396123289887e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4641 Order of pole (three term test) = -9.725 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4635 Order of pole (three term test) = -9.358 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) = 0.6124875656583854 absolute error = 2.997602166487923e-15 relative error = 4.894143709294253e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.790480222342007 y2[1] (numeric) = -0.7904802223420049 absolute error = 2.109423746787797e-15 relative error = 2.668534502404211e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4666 Order of pole (three term test) = -9.958 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.466 Order of pole (three term test) = -9.581 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) = 0.6203616120126798 absolute error = 3.108624468950438e-15 relative error = 5.010987799301346e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7843159250844224 y2[1] (numeric) = -0.7843159250844202 absolute error = 2.220446049250313e-15 relative error = 2.831060773133362e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4689 Order of pole (three term test) = -10.19 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.24 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4683 Order of pole (three term test) = -9.806 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) = 0.6281736227227392 absolute error = 3.219646771412954e-15 relative error = 5.125409050857338e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7780731968879238 y2[1] (numeric) = -0.7780731968879214 absolute error = 2.331468351712829e-15 relative error = 2.996464035823433e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.34 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4711 Order of pole (three term test) = -10.43 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4704 Order of pole (three term test) = -10.03 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) = 0.6359228165940027 absolute error = 3.441691376337985e-15 relative error = 5.412121230012903e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7717526620201285 y2[1] (numeric) = -0.771752662020126 absolute error = 2.442490654175344e-15 relative error = 3.164861975055475e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.473 Order of pole (three term test) = -10.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.83 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4723 Order of pole (three term test) = -10.26 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) = 0.6436084187135407 absolute error = 3.552713678800501e-15 relative error = 5.519992553704885e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7653549525292563 y2[1] (numeric) = -0.7653549525292537 absolute error = 2.664535259100376e-15 relative error = 3.481437273378748e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.98 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4747 Order of pole (three term test) = -10.9 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.14 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4741 Order of pole (three term test) = -10.49 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) = 0.6512296605275458 absolute error = 3.663735981263017e-15 relative error = 5.625873947902082e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7588807081809249 y2[1] (numeric) = -0.7588807081809221 absolute error = 2.775557561562891e-15 relative error = 3.657435920615299e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4763 Order of pole (three term test) = -11.14 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.45 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4756 Order of pole (three term test) = -10.71 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) = 0.6587857799181879 absolute error = 3.774758283725532e-15 relative error = 5.729872135664991e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7523305763941739 y2[1] (numeric) = -0.7523305763941709 absolute error = 2.997602166487923e-15 relative error = 3.984421556884015e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4776 Order of pole (three term test) = -11.38 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.477 Order of pole (three term test) = -10.94 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) = 0.6662760212798243 absolute error = 3.885780586188048e-15 relative error = 5.832088296865348e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7457052121767236 y2[1] (numeric) = -0.7457052121767204 absolute error = 3.219646771412954e-15 relative error = 4.317586519228907e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.98 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4788 Order of pole (three term test) = -11.62 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.08 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4781 Order of pole (three term test) = -11.17 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) = 0.673699635594561 absolute error = 3.996802888650564e-15 relative error = 5.932618451134063e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7390052780594745 y2[1] (numeric) = -0.739005278059471 absolute error = 3.441691376337985e-15 relative error = 4.657194581039246e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.32 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4798 Order of pole (three term test) = -11.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.41 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4791 Order of pole (three term test) = -11.4 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) = 0.6810558805071527 absolute error = 4.107825191113079e-15 relative error = 6.031553810319037e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7322314440302551 y2[1] (numeric) = -0.7322314440302514 absolute error = 3.663735981263017e-15 relative error = 5.003521784174615e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4806 Order of pole (three term test) = -12.1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4799 Order of pole (three term test) = -11.64 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) = 0.6883440203992384 absolute error = 4.218847493575595e-15 relative error = 6.128981103269694e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7253843874668235 y2[1] (numeric) = -0.7253843874668197 absolute error = 3.885780586188048e-15 relative error = 5.356857210227411e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4812 Order of pole (three term test) = -12.34 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.08 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4805 Order of pole (three term test) = -11.87 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) = 0.6955633264629022 absolute error = 4.329869796038111e-15 relative error = 6.224982875472332e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7184647930691302 y2[1] (numeric) = -0.7184647930691263 absolute error = 3.996802888650564e-15 relative error = 5.562976679173191e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -12.58 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4809 Order of pole (three term test) = -12.1 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) = 0.702713076773554 absolute error = 4.440892098500626e-15 relative error = 6.319637765801406e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7114733527908488 y2[1] (numeric) = -0.7114733527908446 absolute error = 4.218847493575595e-15 relative error = 5.929733667503646e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.78 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4811 Order of pole (three term test) = -12.33 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) = 0.7097925563621207 absolute error = 4.551914400963142e-15 relative error = 6.413020762422427e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.7044107657701806 y2[1] (numeric) = -0.7044107657701763 absolute error = 4.329869796038111e-15 relative error = 6.146796736282086e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.07 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.14 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4811 Order of pole (three term test) = -12.56 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) = 0.716801057286543 absolute error = 4.662936703425657e-15 relative error = 6.505203439678616e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.6972777382599425 y2[1] (numeric) = -0.697277738259938 absolute error = 4.551914400963142e-15 relative error = 6.528122369606192e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -13.31 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.48 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4809 Order of pole (three term test) = -12.79 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) = 0.7237378787025688 absolute error = 4.773959005888173e-15 relative error = 6.596254177612467e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.6900749835569413 y2[1] (numeric) = -0.6900749835569365 absolute error = 4.773959005888173e-15 relative error = 6.918029373099643e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.07 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4813 Order of pole (three term test) = -13.55 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.12 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4806 Order of pole (three term test) = -13.02 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) = 0.7306023269338373 absolute error = 4.884981308350689e-15 relative error = 6.686238365612406e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.6828032219306449 y2[1] (numeric) = -0.6828032219306399 absolute error = 4.996003610813204e-15 relative error = 7.316901049012139e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4807 Order of pole (three term test) = -13.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.48 Order of pole (three term test) = -13.25 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) = 0.7373937155412457 absolute error = 4.996003610813204e-15 relative error = 6.775218591531094e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.6754631805511563 y2[1] (numeric) = -0.6754631805511511 absolute error = 5.218048215738236e-15 relative error = 7.725140860350783e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.32 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4799 Order of pole (three term test) = -14.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4792 Order of pole (three term test) = -13.48 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) = 0.7441113653915926 absolute error = 5.10702591327572e-15 relative error = 6.863254817493824e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.6680555934164966 y2[1] (numeric) = -0.6680555934164912 absolute error = 5.329070518200751e-15 relative error = 7.976986602188905e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.96 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.479 Order of pole (three term test) = -14.27 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.06 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4783 Order of pole (three term test) = -13.72 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) = 0.7507546047254912 absolute error = 5.218048215738236e-15 relative error = 6.950404543500894e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.6605812012792064 y2[1] (numeric) = -0.6605812012792008 absolute error = 5.551115123125783e-15 relative error = 8.403380405582424e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4779 Order of pole (three term test) = -14.51 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4772 Order of pole (three term test) = -13.95 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) = 0.7573227692245439 absolute error = 5.329070518200751e-15 relative error = 7.036722959825252e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.6530407515722708 y2[1] (numeric) = -0.653040751572265 absolute error = 5.773159728050814e-15 relative error = 8.840427973524266e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.25 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4765 Order of pole (three term test) = -14.75 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4758 Order of pole (three term test) = -14.17 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) = 0.7638152020777743 absolute error = 5.440092820663267e-15 relative error = 7.122263089114816e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.6454349983343768 y2[1] (numeric) = -0.6454349983343708 absolute error = 5.995204332975845e-15 relative error = 9.288626040495473e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.475 Order of pole (three term test) = -14.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.06 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4743 Order of pole (three term test) = -14.4 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) = 0.7702312540473075 absolute error = 5.440092820663267e-15 relative error = 7.062934400645829e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.6377647021345101 y2[1] (numeric) = -0.6377647021345039 absolute error = 6.217248937900877e-15 relative error = 9.748499590981761e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4733 Order of pole (three term test) = -15.22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4726 Order of pole (three term test) = -14.63 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) = 0.7765702835332933 absolute error = 5.551115123125783e-15 relative error = 7.148245613866364e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.6300306299958988 y2[1] (numeric) = -0.6300306299958923 absolute error = 6.439293542825908e-15 relative error = 1.022060394566503e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.23 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4714 Order of pole (three term test) = -15.46 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.41 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4707 Order of pole (three term test) = -14.86 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) = 0.7828316566380654 absolute error = 5.551115123125783e-15 relative error = 7.091071338332867e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.6222335553193116 y2[1] (numeric) = -0.6222335553193049 absolute error = 6.661338147750939e-15 relative error = 1.070552703370769e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4693 Order of pole (three term test) = -15.7 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.1 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4686 Order of pole (three term test) = -15.08 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) = 0.7890147472295314 absolute error = 5.662137425588298e-15 relative error = 7.176212416142804e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.6143742578057187 y2[1] (numeric) = -0.6143742578057119 absolute error = 6.883382752675971e-15 relative error = 1.12038918708288e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.467 Order of pole (three term test) = -15.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.79 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4664 Order of pole (three term test) = -15.31 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) = 0.7951189370037844 absolute error = 5.773159728050814e-15 relative error = 7.260749882031017e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.6064535233783221 y2[1] (numeric) = -0.606453523378315 absolute error = 7.105427357601002e-15 relative error = 1.171635926528939e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.25 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4646 Order of pole (three term test) = -16.16 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.49 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4639 Order of pole (three term test) = -15.53 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) = 0.801143615546934 absolute error = 5.88418203051333e-15 relative error = 7.344728106578359e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.598472144103964 y2[1] (numeric) = -0.5984721441039567 absolute error = 7.327471962526033e-15 relative error = 1.224363077666174e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.94 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4619 Order of pole (three term test) = -16.4 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.19 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4613 Order of pole (three term test) = -15.75 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) = 0.8070881803961464 absolute error = 5.995204332975845e-15 relative error = 7.42818997799378e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.5904309181139206 y2[1] (numeric) = -0.590430918113913 absolute error = 7.549516567451064e-15 relative error = 1.278645195540797e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4591 Order of pole (three term test) = -16.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4584 Order of pole (three term test) = -15.98 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) = 0.8129520370998903 absolute error = 5.995204332975845e-15 relative error = 7.374610136119553e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.5823306495240899 y2[1] (numeric) = -0.5823306495240821 absolute error = 7.771561172376096e-15 relative error = 1.334561589489993e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4561 Order of pole (three term test) = -16.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4554 Order of pole (three term test) = -16.2 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) = 0.818734599277382 absolute error = 5.995204332975845e-15 relative error = 7.322524708577453e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.5741721483545806 y2[1] (numeric) = -0.5741721483545726 absolute error = 7.993605777301127e-15 relative error = 1.392196713164963e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4529 Order of pole (three term test) = -17.08 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4522 Order of pole (three term test) = -16.41 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) = 0.8244352886772226 absolute error = 6.106226635438361e-15 relative error = 7.406556608264103e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.5659562304487112 y2[1] (numeric) = -0.5659562304487029 absolute error = 8.326672684688674e-15 relative error = 1.471257358203651e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4495 Order of pole (three term test) = -17.31 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4489 Order of pole (three term test) = -16.63 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) = 0.8300535352352225 absolute error = 6.106226635438361e-15 relative error = 7.356425069267381e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.5576837173914255 y2[1] (numeric) = -0.557683717391417 absolute error = 8.548717289613705e-15 relative error = 1.532897056704554e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.446 Order of pole (three term test) = -17.54 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4453 Order of pole (three term test) = -16.85 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) = 0.8355887771314079 absolute error = 6.106226635438361e-15 relative error = 7.307693452275888e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.5493554364271356 y2[1] (numeric) = -0.5493554364271268 absolute error = 8.770761894538737e-15 relative error = 1.596555037587592e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4422 Order of pole (three term test) = -17.76 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4416 Order of pole (three term test) = -17.06 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) = 0.8410404608462018 absolute error = 6.106226635438361e-15 relative error = 7.260324466785707e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.5409722203769975 y2[1] (numeric) = -0.5409722203769886 absolute error = 8.992806499463768e-15 relative error = 1.662341643568459e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4383 Order of pole (three term test) = -17.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4377 Order of pole (three term test) = -17.27 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) = 0.8464080412157757 absolute error = 6.106226635438361e-15 relative error = 7.21428240056351e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.5325349075556305 y2[1] (numeric) = -0.5325349075556213 absolute error = 9.214851104388799e-15 relative error = 1.730375037138046e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4342 Order of pole (three term test) = -18.2 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4336 Order of pole (three term test) = -17.48 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) = 0.8516909814865659 absolute error = 6.106226635438361e-15 relative error = 7.169533044462232e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.5240443416872855 y2[1] (numeric) = -0.5240443416872761 absolute error = 9.436895709313831e-15 relative error = 1.800781910730969e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.43 Order of pole (three term test) = -18.41 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4293 Order of pole (three term test) = -17.69 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) = 0.8568887533689474 absolute error = 6.106226635438361e-15 relative error = 7.126043621685006e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.515501371821474 y2[1] (numeric) = -0.5155013718214643 absolute error = 9.769962616701378e-15 relative error = 1.895235037334656e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4255 Order of pole (three term test) = -18.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4249 Order of pole (three term test) = -17.89 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) = 0.8620008370900637 absolute error = 6.106226635438361e-15 relative error = 7.083782721199855e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.5069068522480634 y2[1] (numeric) = -0.5069068522480534 absolute error = 9.992007221626409e-15 relative error = 1.971172253307132e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4209 Order of pole (three term test) = -18.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4203 Order of pole (three term test) = -18.1 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) = 0.8670267214458026 absolute error = 6.106226635438361e-15 relative error = 7.042720235030381e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.4982616424118489 y2[1] (numeric) = -0.4982616424118387 absolute error = 1.021405182655144e-14 relative error = 2.049937413827411e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4161 Order of pole (three term test) = -19.05 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4155 Order of pole (three term test) = -18.3 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) = 0.8719659038519167 absolute error = 6.106226635438361e-15 relative error = 7.002827299168576e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.48956660682661 y2[1] (numeric) = -0.4895666068265995 absolute error = 1.049160758270773e-14 relative error = 2.143039871676449e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4112 Order of pole (three term test) = -19.26 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4106 Order of pole (three term test) = -18.5 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) = 0.8768178903942816 absolute error = 6.106226635438361e-15 relative error = 6.964076237874887e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.4808226149886591 y2[1] (numeric) = -0.4808226149886484 absolute error = 1.076916333886402e-14 relative error = 2.239737275901223e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4061 Order of pole (three term test) = -19.46 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4055 Order of pole (three term test) = -18.69 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) = 0.8815821958782861 absolute error = 6.106226635438361e-15 relative error = 6.926440511148262e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.4720305412898936 y2[1] (numeric) = -0.4720305412898826 absolute error = 1.104671909502031e-14 relative error = 2.340255159090661e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4008 Order of pole (three term test) = -19.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4003 Order of pole (three term test) = -18.89 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) = 0.8862583438773523 absolute error = 6.217248937900877e-15 relative error = 7.015165477258756e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.4631912649303566 y2[1] (numeric) = -0.4631912649303453 absolute error = 1.126876369994534e-14 relative error = 2.432853240796685e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3954 Order of pole (three term test) = -19.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3948 Order of pole (three term test) = -19.08 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) = 0.8908458667805768 absolute error = 6.106226635438361e-15 relative error = 6.854414285498864e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.4543056698303179 y2[1] (numeric) = -0.4543056698303064 absolute error = 1.154631945610163e-14 relative error = 2.541531004976044e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3898 Order of pole (three term test) = -20.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3893 Order of pole (three term test) = -19.27 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) = 0.8953443058394923 absolute error = 6.217248937900877e-15 relative error = 6.943975515733588e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.4453746445418831 y2[1] (numeric) = -0.4453746445418713 absolute error = 1.182387521225792e-14 relative error = 2.654815526020812e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3841 Order of pole (three term test) = -20.25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3835 Order of pole (three term test) = -19.45 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) = 0.8997532112139417 absolute error = 6.217248937900877e-15 relative error = 6.909949150959566e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.4363990821601383 y2[1] (numeric) = -0.4363990821601262 absolute error = 1.204591981718295e-14 relative error = 2.760299072481242e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3782 Order of pole (three term test) = -20.44 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3777 Order of pole (three term test) = -19.64 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) = 0.9040721420170615 absolute error = 6.217248937900877e-15 relative error = 6.876938962005521e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.4273798802338422 y2[1] (numeric) = -0.4273798802338299 absolute error = 1.232347557333924e-14 relative error = 2.883494554445663e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3722 Order of pole (three term test) = -20.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3716 Order of pole (three term test) = -19.82 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) = 0.9083006663593706 absolute error = 6.217248937900877e-15 relative error = 6.844923898185333e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.4183179406756715 y2[1] (numeric) = -0.4183179406756589 absolute error = 1.260103132949553e-14 relative error = 3.012309562707784e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.366 Order of pole (three term test) = -20.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3654 Order of pole (three term test) = -19.99 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) = 0.9124383613919583 absolute error = 6.106226635438361e-15 relative error = 6.692207269895063e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.4092141696720303 y2[1] (numeric) = -0.4092141696720174 absolute error = 1.287858708565182e-14 relative error = 3.147150817376025e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3596 Order of pole (three term test) = -21 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3591 Order of pole (three term test) = -20.17 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) = 0.9164848133487697 absolute error = 6.106226635438361e-15 relative error = 6.662659922455984e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.4000694775924326 y2[1] (numeric) = -0.4000694775924194 absolute error = 1.315614284180811e-14 relative error = 3.288464523957215e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3532 Order of pole (three term test) = -21.18 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3526 Order of pole (three term test) = -20.34 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) = 0.920439617587981 absolute error = 5.995204332975845e-15 relative error = 6.513414045221524e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.3908847788984657 y2[1] (numeric) = -0.3908847788984523 absolute error = 1.337818744673314e-14 relative error = 3.422539881044636e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3465 Order of pole (three term test) = -21.35 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.346 Order of pole (three term test) = -20.51 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) = 0.9243023786324639 absolute error = 5.995204332975845e-15 relative error = 6.486193773347191e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.3816609920523453 y2[1] (numeric) = -0.3816609920523316 absolute error = 1.371125435412068e-14 relative error = 3.592521803286663e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3398 Order of pole (three term test) = -21.52 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3393 Order of pole (three term test) = -20.67 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) = 0.928072710209333 absolute error = 5.88418203051333e-15 relative error = 6.340216629348093e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.3723990394250693 y2[1] (numeric) = -0.3723990394250554 absolute error = 1.393329895904571e-14 relative error = 3.741497019046217e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3329 Order of pole (three term test) = -21.69 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3324 Order of pole (three term test) = -20.83 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) = 0.9317502352885726 absolute error = 5.88418203051333e-15 relative error = 6.315192427819431e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.3630998472041824 y2[1] (numeric) = -0.3630998472041682 absolute error = 1.4210854715202e-14 relative error = 3.913759486439772e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3258 Order of pole (three term test) = -21.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3254 Order of pole (three term test) = -20.99 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) = 0.9353345861207392 absolute error = 5.773159728050814e-15 relative error = 6.172293651616997e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.3537643453011572 y2[1] (numeric) = -0.3537643453011428 absolute error = 1.448841047135829e-14 relative error = 4.095497656504757e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3187 Order of pole (three term test) = -22.02 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3182 Order of pole (three term test) = -21.15 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) = 0.9388254042737366 absolute error = 5.773159728050814e-15 relative error = 6.149343319609989e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.3443934672584046 y2[1] (numeric) = -0.3443934672583899 absolute error = 1.471045507628332e-14 relative error = 4.271409441470562e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3114 Order of pole (three term test) = -22.18 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3109 Order of pole (three term test) = -21.3 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) = 0.9422223406686585 absolute error = 5.662137425588298e-15 relative error = 6.009343210404175e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.3349881501559197 y2[1] (numeric) = -0.3349881501559047 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 Radius of convergence (three term test) for eq 1 = 0.304 Order of pole (three term test) = -22.33 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3035 Order of pole (three term test) = -21.44 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) = 0.9455250556146962 absolute error = 5.551115123125783e-15 relative error = 5.870933922017513e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.3255493345175751 y2[1] (numeric) = -0.3255493345175599 absolute error = 1.52655665885959e-14 relative error = 4.689171492614977e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2965 Order of pole (three term test) = -22.48 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.296 Order of pole (three term test) = -21.59 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) = 0.9487332188431075 absolute error = 5.440092820663267e-15 relative error = 5.734059599280174e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.316077964217069 y2[1] (numeric) = -0.3160779642170534 absolute error = 1.554312234475219e-14 relative error = 4.917496347223318e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2888 Order of pole (three term test) = -22.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2884 Order of pole (three term test) = -21.73 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) = 0.9518465095402427 absolute error = 5.440092820663267e-15 relative error = 5.715304690554521e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.3065749863835386 y2[1] (numeric) = -0.3065749863835227 absolute error = 1.587618925213974e-14 relative error = 5.178566405374618e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.281 Order of pole (three term test) = -22.77 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2806 Order of pole (three term test) = -21.87 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) = 0.9548646163796267 absolute error = 5.218048215738236e-15 relative error = 5.46469952517721e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.2970413513068481 y2[1] (numeric) = -0.297041351306832 absolute error = 1.615374500829603e-14 relative error = 5.438214220756413e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2732 Order of pole (three term test) = -22.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2728 Order of pole (three term test) = -22 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) = 0.9577872375530906 absolute error = 5.10702591327572e-15 relative error = 5.332108962239813e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.2874780123425605 y2[1] (numeric) = -0.2874780123425442 absolute error = 1.637578961322106e-14 relative error = 5.696362473004568e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2652 Order of pole (three term test) = -23.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2648 Order of pole (three term test) = -22.13 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) = 0.9606140808009526 absolute error = 4.996003610813204e-15 relative error = 5.200843617290725e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.277885925816603 y2[1] (numeric) = -0.2778859258165863 absolute error = 1.665334536937735e-14 relative error = 5.992871110848592e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2571 Order of pole (three term test) = -23.17 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2567 Order of pole (three term test) = -22.25 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) = 0.9633448634412435 absolute error = 4.884981308350689e-15 relative error = 5.070854160057147e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.2682660509296346 y2[1] (numeric) = -0.2682660509296177 absolute error = 1.693090112553364e-14 relative error = 6.311235084298669e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2489 Order of pole (three term test) = -23.3 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2485 Order of pole (three term test) = -22.37 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) = 0.965979312397975 absolute error = 4.662936703425657e-15 relative error = 4.827160005994612e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.2586193496611275 y2[1] (numeric) = -0.2586193496611104 absolute error = 1.715294573045867e-14 relative error = 6.632506714186084e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2406 Order of pole (three term test) = -23.42 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2402 Order of pole (three term test) = -22.49 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) = 0.9685171642284468 absolute error = 4.551914400963142e-15 relative error = 4.699879949561215e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.2489467866731698 y2[1] (numeric) = -0.2489467866731524 absolute error = 1.740274591099933e-14 relative error = 6.990548519851575e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2322 Order of pole (three term test) = -23.54 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2319 Order of pole (three term test) = -22.61 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) = 0.9709581651495908 absolute error = 4.551914400963142e-15 relative error = 4.688064392827751e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.2392493292139997 y2[1] (numeric) = -0.239249329213982 absolute error = 1.768030166715562e-14 relative error = 7.389906473401746e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2237 Order of pole (three term test) = -23.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2234 Order of pole (three term test) = -22.72 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) = 0.9733020710633489 absolute error = 4.440892098500626e-15 relative error = 4.562706923708584e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.2295279470212819 y2[1] (numeric) = -0.229527947021264 absolute error = 1.795785742331191e-14 relative error = 7.823821742128355e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2151 Order of pole (three term test) = -23.77 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2148 Order of pole (three term test) = -22.82 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) = 0.975548647581083 absolute error = 4.329869796038111e-15 relative error = 4.438394545237942e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.2197836122251347 y2[1] (numeric) = -0.2197836122251165 absolute error = 1.820765760385257e-14 relative error = 8.284356335540434e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2065 Order of pole (three term test) = -23.87 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2062 Order of pole (three term test) = -22.92 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) = 0.9776976700470135 absolute error = 4.218847493575595e-15 relative error = 4.315083918909969e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.2100172992509174 y2[1] (numeric) = -0.2100172992508989 absolute error = 1.848521336000886e-14 relative error = 8.801757486617193e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1977 Order of pole (three term test) = -23.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1974 Order of pole (three term test) = -23.02 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) = 0.9797489235606845 absolute error = 3.996802888650564e-15 relative error = 4.079415442606529e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.2002299847217888 y2[1] (numeric) = -0.2002299847217701 absolute error = 1.873501354054952e-14 relative error = 9.356747225736962e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1889 Order of pole (three term test) = -24.07 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1886 Order of pole (three term test) = -23.11 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) = 0.9817022029984543 absolute error = 3.885780586188048e-15 relative error = 3.958207055377446e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.1904226473610458 y2[1] (numeric) = -0.1904226473610268 absolute error = 1.901256929670581e-14 relative error = 9.984405510683573e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.18 Order of pole (three term test) = -24.16 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1798 Order of pole (three term test) = -23.2 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) = 0.9835573130340067 absolute error = 3.774758283725532e-15 relative error = 3.837863064717037e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.1805962678942517 y2[1] (numeric) = -0.1805962678942324 absolute error = 1.926236947724647e-14 relative error = 1.066598424311047e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1711 Order of pole (three term test) = -24.25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1708 Order of pole (three term test) = -23.28 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) = 0.985314068157884 absolute error = 3.552713678800501e-15 relative error = 3.605666247557562e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.1707518289511646 y2[1] (numeric) = -0.170751828951145 absolute error = 1.953992523340276e-14 relative error = 1.144346467819751e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.162 Order of pole (three term test) = -24.33 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1618 Order of pole (three term test) = -23.36 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) = 0.9869722926960379 absolute error = 3.441691376337985e-15 relative error = 3.487120562358025e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.1608903149674751 y2[1] (numeric) = -0.1608903149674553 absolute error = 1.978972541394342e-14 relative error = 1.230013467121624e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1529 Order of pole (three term test) = -24.41 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1527 Order of pole (three term test) = -23.44 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) = 0.9885318208273963 absolute error = 3.33066907387547e-15 relative error = 3.369308912168075e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.1510127120863636 y2[1] (numeric) = -0.1510127120863435 absolute error = 2.00672811700997e-14 relative error = 1.328847147558233e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1438 Order of pole (three term test) = -24.49 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1435 Order of pole (three term test) = -23.51 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) = 0.9899924966004457 absolute error = 3.108624468950438e-15 relative error = 3.140048515140482e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.141120008059887 y2[1] (numeric) = -0.1411200080598667 absolute error = 2.031708135064036e-14 relative error = 1.439702394434276e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1345 Order of pole (three term test) = -24.56 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1343 Order of pole (three term test) = -23.58 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) = 0.9913541739488262 absolute error = 2.997602166487923e-15 relative error = 3.023744939255855e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.131213192150204 y2[1] (numeric) = -0.1312131921501835 absolute error = 2.056688153118102e-14 relative error = 1.567440071699303e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1253 Order of pole (three term test) = -24.62 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1251 Order of pole (three term test) = -23.64 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) = 0.9926167167059374 absolute error = 2.775557561562891e-15 relative error = 2.796202718380329e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.12129325503065 y2[1] (numeric) = -0.1212932550306292 absolute error = 2.081668171172169e-14 relative error = 1.716227477485161e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1159 Order of pole (three term test) = -24.68 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1158 Order of pole (three term test) = -23.7 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) = 0.9937799986185559 absolute error = 2.664535259100376e-15 relative error = 2.68121240395694e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.1113611886866703 y2[1] (numeric) = -0.1113611886866493 absolute error = 2.106648189226235e-14 relative error = 1.891725666788249e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1066 Order of pole (three term test) = -24.74 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1064 Order of pole (three term test) = -23.75 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) = 0.9948439033594598 absolute error = 2.442490654175344e-15 relative error = 2.455149643001655e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.1014179863166226 y2[1] (numeric) = -0.1014179863166013 absolute error = 2.131628207280301e-14 relative error = 2.101824621744557e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09716 Order of pole (three term test) = -24.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09702 Order of pole (three term test) = -23.8 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) = 0.9958083245390615 absolute error = 2.220446049250313e-15 relative error = 2.229792616242805e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.09146464223245798 y2[1] (numeric) = -0.09146464223243642 absolute error = 2.156608225334367e-14 relative error = 2.357860013111222e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08771 Order of pole (three term test) = -24.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08758 Order of pole (three term test) = -23.85 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) = 0.9966731657160469 absolute error = 2.109423746787797e-15 relative error = 2.116464874693716e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.08150215176029037 y2[1] (numeric) = -0.08150215176026855 absolute error = 2.181588243388433e-14 relative error = 2.676724719863593e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07822 Order of pole (three term test) = -24.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07811 Order of pole (three term test) = -23.88 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) = 0.9974383404070188 absolute error = 1.887379141862766e-15 relative error = 1.892226381725609e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.07153151114086496 y2[1] (numeric) = -0.0715315111408429 absolute error = 2.206568261442499e-14 relative error = 3.084749960191903e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06871 Order of pole (three term test) = -24.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0686 Order of pole (three term test) = -23.92 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) = 0.9981037720951459 absolute error = 1.554312234475219e-15 relative error = 1.557265164134711e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.06155371742993487 y2[1] (numeric) = -0.06155371742991256 absolute error = 2.230854390106174e-14 relative error = 3.624239904999243e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05916 Order of pole (three term test) = -24.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05907 Order of pole (three term test) = -23.95 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) = 0.9986693942378139 absolute error = 1.443289932012704e-15 relative error = 1.445212940679159e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.05156976839855636 y2[1] (numeric) = -0.05156976839853382 absolute error = 2.254446629379458e-14 relative error = 4.371643890187742e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04959 Order of pole (three term test) = -24.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04952 Order of pole (three term test) = -23.98 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) = 0.9991351502732797 absolute error = 1.110223024625157e-15 relative error = 1.111184031831423e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = -0.04158066243331267 y2[1] (numeric) = -0.04158066243328989 absolute error = 2.278732758043134e-14 relative error = 5.480270454319432e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04001 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03995 Order of pole (three term test) = -24 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) = 0.9995009936263282 absolute error = 9.992007221626409e-16 relative error = 9.996995786241324e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.03158739843647609 y2[1] (numeric) = -0.03158739843645306 absolute error = 2.303018886706809e-14 relative error = 7.290941960093042e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0304 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03036 Order of pole (three term test) = -24.02 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) = 0.9997668877129287 absolute error = 7.771561172376096e-16 relative error = 7.773373241190616e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.0215909757261186 y2[1] (numeric) = -0.02159097572609534 absolute error = 2.325917236589703e-14 relative error = 1.077263605912928e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02079 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02076 Order of pole (three term test) = -24.03 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) = 0.9999328059438941 absolute error = 5.551115123125783e-16 relative error = 5.551488150132017e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.01159239393618092 y2[1] (numeric) = -0.01159239393615743 absolute error = 2.34933600351539e-14 relative error = 2.026618502139491e-10 % Correct digits = 12 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01116 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.01115 Order of pole (three term test) = -24.04 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) = 0.9999987317275397 absolute error = 2.220446049250313e-16 relative error = 2.220448865384459e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = -0.001592652916509921 y2[1] (numeric) = -0.001592652916486198 absolute error = 2.372321089572083e-14 relative error = 1.489540542688169e-09 % Correct digits = 11 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001534 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.001531 Order of pole (three term test) = -24.04 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) = 0.9999646584713421 absolute error = 1.110223024625157e-16 relative error = 1.110262262990742e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 0.008407247367125526 y2[1] (numeric) = 0.008407247367149475 absolute error = 2.39495923093358e-14 relative error = 2.848684148748233e-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) = 0.9998305895825985 absolute error = 2.220446049250313e-16 relative error = 2.220822279679688e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 0.01840630693303028 y2[1] (numeric) = 0.01840630693305445 absolute error = 2.417510636121278e-14 relative error = 1.313414279636419e-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) = 0.999596538468086 absolute error = 4.440892098500626e-16 relative error = 4.442684550815306e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 0.02840352588358026 y2[1] (numeric) = 0.02840352588360466 absolute error = 2.439715096613781e-14 relative error = 8.589479723797783e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9992625285327211 absolute error = 6.661338147750939e-16 relative error = 6.666254320105637e-14 % Correct digits = 16 h = 0.01 y2[1] (analytic) = 0.03839790450521142 y2[1] (numeric) = 0.03839790450523603 absolute error = 2.461225667715894e-14 relative error = 6.409791626472358e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9988285931772188 absolute error = 9.992007221626409e-16 relative error = 1.000372565411086e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.0483884433683902 y2[1] (numeric) = 0.04838844336841502 absolute error = 2.482736238818006e-14 relative error = 5.130845437445621e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9982947757947532 absolute error = 1.221245327087672e-15 relative error = 1.223331381370221e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.0583741434275557 y2[1] (numeric) = 0.05837414342758074 absolute error = 2.504246809920119e-14 relative error = 4.289993245087997e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9976611297666177 absolute error = 1.554312234475219e-15 relative error = 1.557956091602783e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.06835400612102341 y2[1] (numeric) = 0.06835400612104867 absolute error = 2.525757381022231e-14 relative error = 3.695112436497548e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.996927718456887 absolute error = 1.887379141862766e-15 relative error = 1.893195571675123e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.07832703347084051 y2[1] (numeric) = 0.07832703347086596 absolute error = 2.545186283953171e-14 relative error = 3.249435311373933e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.996094615206081 absolute error = 2.109423746787797e-15 relative error = 2.117694157348071e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.08829222818258282 y2[1] (numeric) = 0.08829222818260848 absolute error = 2.566002965664893e-14 relative error = 2.906261421286774e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9951619033238305 absolute error = 2.331468351712829e-15 relative error = 2.342803059407462e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.09824859374508349 y2[1] (numeric) = 0.09824859374510936 absolute error = 2.586819647376615e-14 relative error = 2.632933000637542e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9941296760805464 absolute error = 2.55351295663786e-15 relative error = 2.568591420291695e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.1081951345300832 y2[1] (numeric) = 0.1081951345301093 absolute error = 2.606248550307555e-14 relative error = 2.408840805667558e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9929980366980928 absolute error = 2.886579864025407e-15 relative error = 2.906934109984573e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.1181308558917922 y2[1] (numeric) = 0.1181308558918185 absolute error = 2.625677453238495e-14 relative error = 2.222685540891716e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9917670983394651 absolute error = 3.108624468950438e-15 relative error = 3.134429922262252e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.1280547642663541 y2[1] (numeric) = 0.1280547642663806 absolute error = 2.645106356169435e-14 relative error = 2.065605580021693e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9904369840974732 absolute error = 3.552713678800501e-15 relative error = 3.587016373422149e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.1379658672712013 y2[1] (numeric) = 0.137965867271228 absolute error = 2.664535259100376e-14 relative error = 1.931300336671434e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9890078269824329 absolute error = 3.774758283725532e-15 relative error = 3.816712245081723e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.1478631738042926 y2[1] (numeric) = 0.1478631738043194 absolute error = 2.683964162031316e-14 relative error = 1.81516742335298e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9874797699088649 absolute error = 4.218847493575595e-15 relative error = 4.272338150243763e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.1577456941432223 y2[1] (numeric) = 0.1577456941432493 absolute error = 2.700617507400693e-14 relative error = 1.712007115039677e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9858529656812031 absolute error = 4.440892098500626e-15 relative error = 4.50461909949426e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.167612440044192 y2[1] (numeric) = 0.1676124400442192 absolute error = 2.720046410331634e-14 relative error = 1.62281893254133e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9841275769785145 absolute error = 4.773959005888173e-15 relative error = 4.850955422411027e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.1774624248408339 y2[1] (numeric) = 0.1774624248408613 absolute error = 2.736699755701011e-14 relative error = 1.542129134184635e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9823037763382316 absolute error = 5.10702591327572e-15 relative error = 5.199029094964222e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.1872946635428766 y2[1] (numeric) = 0.1872946635429041 absolute error = 2.750577543508825e-14 relative error = 1.468582975872747e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9803817461388987 absolute error = 5.440092820663267e-15 relative error = 5.54895360107255e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.1971081729346433 y2[1] (numeric) = 0.197108172934671 absolute error = 2.767230888878203e-14 relative error = 1.403914839084707e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.978361678581934 absolute error = 5.773159728050814e-15 relative error = 5.900844089088368e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.2069019716733728 y2[1] (numeric) = 0.2069019716734007 absolute error = 2.78388423424758e-14 relative error = 1.345508799037632e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9762437756724098 absolute error = 5.995204332975845e-15 relative error = 6.141093528454485e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.2166750803873528 y2[1] (numeric) = 0.2166750803873808 absolute error = 2.800537579616957e-14 relative error = 1.292505614679086e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9740282491988521 absolute error = 6.328271240363392e-15 relative error = 6.497009964103625e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.2264265217738559 y2[1] (numeric) = 0.2264265217738841 absolute error = 2.817190924986335e-14 relative error = 1.24419652915042e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.971715320712062 absolute error = 6.661338147750939e-15 relative error = 6.855236308170525e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.2361553206968698 y2[1] (numeric) = 0.2361553206968981 absolute error = 2.831068712794149e-14 relative error = 1.198816399495027e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9693052215029608 absolute error = 6.994405055138486e-15 relative error = 7.215895365025711e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.2458605042846095 y2[1] (numeric) = 0.2458605042846379 absolute error = 2.844946500601964e-14 relative error = 1.157138479350322e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.966798192579461 absolute error = 7.327471962526033e-15 relative error = 7.579112185735426e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.2555411020268037 y2[1] (numeric) = 0.2555411020268323 absolute error = 2.858824288409778e-14 relative error = 1.118733646264825e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9641944846423657 absolute error = 7.66053886991358e-15 relative error = 7.945014197789079e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.2651961458717456 y2[1] (numeric) = 0.2651961458717743 absolute error = 2.875477633779155e-14 relative error = 1.084283342175643e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9614943580602988 absolute error = 7.993605777301127e-15 relative error = 8.313731339440426e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.2748246703230963 y2[1] (numeric) = 0.2748246703231251 absolute error = 2.886579864025407e-14 relative error = 1.050335059305925e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9586980828436685 absolute error = 8.326672684688674e-15 relative error = 8.685396198968307e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.2844257125364344 y2[1] (numeric) = 0.2844257125364634 absolute error = 2.897682094271659e-14 relative error = 1.018783452603804e-11 % Correct digits = 13 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9558059386176663 absolute error = 8.770761894538737e-15 relative error = 9.17629985352818e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.2939983124155396 y2[1] (numeric) = 0.2939983124155687 absolute error = 2.914335439641036e-14 relative error = 9.912762477091674e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9528182145943046 absolute error = 9.103828801926284e-15 relative error = 9.554633467835695e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.303541512708401 y2[1] (numeric) = 0.3035415127084303 absolute error = 2.930988785010413e-14 relative error = 9.655973441188211e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.949735209543496 absolute error = 9.436895709313831e-15 relative error = 9.936343956174604e-13 % Correct digits = 15 h = 0.01 y2[1] (analytic) = 0.3130543591029419 y2[1] (numeric) = 0.3130543591029714 absolute error = 2.942091015256665e-14 relative error = 9.398019640062621e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9465572317631764 absolute error = 9.880984919163893e-15 relative error = 1.043886686149788e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3225359003224504 y2[1] (numeric) = 0.3225359003224799 absolute error = 2.953193245502916e-14 relative error = 9.156169104123002e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9432845990484756 absolute error = 1.021405182655144e-14 relative error = 1.082817618018422e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3319851882207056 y2[1] (numeric) = 0.3319851882207353 absolute error = 2.964295475749168e-14 relative error = 8.928999187091708e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9399176386599378 absolute error = 1.054711873393899e-14 relative error = 1.122132227348785e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3414012778767921 y2[1] (numeric) = 0.3414012778768219 absolute error = 2.97539770599542e-14 relative error = 8.715250641414432e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9364566872907961 absolute error = 1.099120794378905e-14 relative error = 1.173701687750972e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3507832276895911 y2[1] (numeric) = 0.350783227689621 absolute error = 2.986499936241671e-14 relative error = 8.513804824455381e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9329020910333033 absolute error = 1.13242748511766e-14 relative error = 1.213876028365789e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3601300994719396 y2[1] (numeric) = 0.3601300994719695 absolute error = 2.992051051364797e-14 relative error = 8.308250423255527e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9292542053441231 absolute error = 1.165734175856414e-14 relative error = 1.254483616164753e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3694409585444482 y2[1] (numeric) = 0.3694409585444782 absolute error = 3.003153281611048e-14 relative error = 8.128912650733428e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9255133950087843 absolute error = 1.199040866595169e-14 relative error = 1.295541342849795e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3787148738289688 y2[1] (numeric) = 0.3787148738289989 absolute error = 3.008704396734174e-14 relative error = 7.944510777500999e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9216800341052032 absolute error = 1.243449787580175e-14 relative error = 1.349112209843343e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3879509179417013 y2[1] (numeric) = 0.3879509179417314 absolute error = 3.0142555118573e-14 relative error = 7.769682638849336e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9177545059662757 absolute error = 1.27675647831893e-14 relative error = 1.391174295542852e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.3971481672859308 y2[1] (numeric) = 0.3971481672859611 absolute error = 3.025357742103552e-14 relative error = 7.61770540898761e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9137372031415445 absolute error = 1.321165399303936e-14 relative error = 1.445892095409471e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4063057021443875 y2[1] (numeric) = 0.4063057021444179 absolute error = 3.030908857226677e-14 relative error = 7.459675907156215e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9096285273579442 absolute error = 1.365574320288943e-14 relative error = 1.50124394653199e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4154226067712168 y2[1] (numeric) = 0.4154226067712471 absolute error = 3.036459972349803e-14 relative error = 7.309327713169098e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9054288894796294 absolute error = 1.398881011027697e-14 relative error = 1.544992684993345e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4244979694835532 y2[1] (numeric) = 0.4244979694835837 absolute error = 3.047562202596055e-14 relative error = 7.179215029706119e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.9011387094668882 absolute error = 1.432187701766452e-14 relative error = 1.589308823070877e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4335308827526885 y2[1] (numeric) = 0.433530882752719 absolute error = 3.05311331771918e-14 relative error = 7.042435589210045e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8967584163341468 absolute error = 1.476596622751458e-14 relative error = 1.646593548335575e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.442520443294823 y2[1] (numeric) = 0.4425204432948536 absolute error = 3.058664432842306e-14 relative error = 6.911916679077613e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8922884481070681 absolute error = 1.509903313490213e-14 relative error = 1.69216951838091e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4514657521613938 y2[1] (numeric) = 0.4514657521614245 absolute error = 3.064215547965432e-14 relative error = 6.787260236896131e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.88772925177875 absolute error = 1.543210004228968e-14 relative error = 1.738379129826801e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4603659148289687 y2[1] (numeric) = 0.4603659148289994 absolute error = 3.069766663088558e-14 relative error = 6.668101534469623e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8830812832650258 absolute error = 1.587618925213974e-14 relative error = 1.797817432325171e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4692200412886977 y2[1] (numeric) = 0.4692200412887285 absolute error = 3.075317778211684e-14 relative error = 6.554105766167665e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8783450073588738 absolute error = 1.63202784619898e-14 relative error = 1.858071523747088e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4780272461353132 y2[1] (numeric) = 0.478027246135344 absolute error = 3.080868893334809e-14 relative error = 6.444965048002139e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8735208976839376 absolute error = 1.676436767183986e-14 relative error = 1.919171907196355e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4867866486556699 y2[1] (numeric) = 0.4867866486557008 absolute error = 3.086420008457935e-14 relative error = 6.340395770881392e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8686094366471647 absolute error = 1.709743457922741e-14 relative error = 1.968368504632327e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.4954973729168152 y2[1] (numeric) = 0.4954973729168461 absolute error = 3.086420008457935e-14 relative error = 6.228933143054398e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8636111153905659 absolute error = 1.743050148661496e-14 relative error = 2.018327598612682e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5041585478535819 y2[1] (numeric) = 0.5041585478536128 absolute error = 3.086420008457935e-14 relative error = 6.121923394134925e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8585264337421015 absolute error = 1.787459069646502e-14 relative error = 2.082008193801767e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.512769307355694 y2[1] (numeric) = 0.5127693073557249 absolute error = 3.086420008457935e-14 relative error = 6.019120029578857e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8533559001656992 absolute error = 1.831867990631508e-14 relative error = 2.146663531916482e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.521328790354377 y2[1] (numeric) = 0.5213287903544078 absolute error = 3.086420008457935e-14 relative error = 5.920294573334266e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8481000317104078 absolute error = 1.887379141862766e-14 relative error = 2.225420435436546e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5298361409084636 y2[1] (numeric) = 0.5298361409084945 absolute error = 3.086420008457935e-14 relative error = 5.825234955029533e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8427593539586932 absolute error = 1.920685832601521e-14 relative error = 2.279044217758534e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.538290508289988 y2[1] (numeric) = 0.538290508290019 absolute error = 3.097522238704187e-14 relative error = 5.754369046082991e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8373344009738798 absolute error = 1.965094753586527e-14 relative error = 2.346845837578076e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5466910470692574 y2[1] (numeric) = 0.5466910470692884 absolute error = 3.097522238704187e-14 relative error = 5.665946525573479e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8318257152467453 absolute error = 2.009503674571533e-14 relative error = 2.415774888583967e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5550369171993943 y2[1] (numeric) = 0.5550369171994252 absolute error = 3.086420008457935e-14 relative error = 5.560747245483049e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8262338476412719 absolute error = 2.042810365310288e-14 relative error = 2.472436067757381e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5633272841003404 y2[1] (numeric) = 0.5633272841003713 absolute error = 3.086420008457935e-14 relative error = 5.478910920118293e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8205593573395604 absolute error = 2.087219286295294e-14 relative error = 2.543654237351555e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5715613187423143 y2[1] (numeric) = 0.5715613187423452 absolute error = 3.086420008457935e-14 relative error = 5.39998055720323e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8148028117859121 absolute error = 2.131628207280301e-14 relative error = 2.616127701631356e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5797381977287135 y2[1] (numeric) = 0.5797381977287444 absolute error = 3.086420008457935e-14 relative error = 5.32381688933013e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.8089647866300852 absolute error = 2.176037128265307e-14 relative error = 2.689903397810421e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5878571033784533 y2[1] (numeric) = 0.5878571033784842 absolute error = 3.086420008457935e-14 relative error = 5.250289552886368e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.81 Order of pole (ratio test) Not computed 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) = 0.8030458656697304 absolute error = 2.220446049250313e-14 relative error = 2.765030173461421e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.5959172238077346 y2[1] (numeric) = 0.5959172238077655 absolute error = 3.086420008457935e-14 relative error = 5.179276391336074e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.1 Order of pole (ratio test) Not computed 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) = 0.7970466407920113 absolute error = 2.264854970235319e-14 relative error = 2.841558892945974e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6039177530112312 y2[1] (numeric) = 0.603917753011262 absolute error = 3.086420008457935e-14 relative error = 5.110662822989634e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.4 Order of pole (ratio test) Not computed 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) = 0.7909677119144163 absolute error = 2.309263891220326e-14 relative error = 2.919542550771179e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6118578909426898 y2[1] (numeric) = 0.6118578909427206 absolute error = 3.075317778211684e-14 relative error = 5.026196153936234e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.7 Order of pole (ratio test) Not computed 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) = 0.7848096869247674 absolute error = 2.353672812205332e-14 relative error = 2.99903639241253e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.619736843594934 y2[1] (numeric) = 0.6197368435949647 absolute error = 3.075317778211684e-14 relative error = 4.962296190706618e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15 Order of pole (ratio test) Not computed 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) = 0.7785731816204319 absolute error = 2.40918396343659e-14 relative error = 3.094357756354154e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6275538230792643 y2[1] (numeric) = 0.627553823079295 absolute error = 3.064215547965432e-14 relative error = 4.882793212747906e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.31 Order of pole (ratio test) Not computed 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) = 0.7722588196467433 absolute error = 2.442490654175344e-14 relative error = 3.162787645847209e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6353080477042465 y2[1] (numeric) = 0.6353080477042771 absolute error = 3.05311331771918e-14 relative error = 4.805721143863881e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.63 Order of pole (ratio test) Not computed 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) = 0.7658672324346367 absolute error = 2.498001805406602e-14 relative error = 3.261664293255572e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6429987420538799 y2[1] (numeric) = 0.6429987420539104 absolute error = 3.05311331771918e-14 relative error = 4.748241509721874e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.95 Order of pole (ratio test) Not computed 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) = 0.7593990591375074 absolute error = 2.531308496145357e-14 relative error = 3.333304756816822e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6506251370651384 y2[1] (numeric) = 0.6506251370651688 absolute error = 3.042011087472929e-14 relative error = 4.675520379054112e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.28 Order of pole (ratio test) Not computed 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) = 0.7528549465672947 absolute error = 2.575717417130363e-14 relative error = 3.421266512061154e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6581864701048762 y2[1] (numeric) = 0.6581864701049065 absolute error = 3.030908857226677e-14 relative error = 4.604939473677921e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.61 Order of pole (ratio test) Not computed 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) = 0.7462355491298023 absolute error = 2.631228568361621e-14 relative error = 3.52600270977421e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6656819850460903 y2[1] (numeric) = 0.6656819850461206 absolute error = 3.030908857226677e-14 relative error = 4.553088299387918e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.95 Order of pole (ratio test) Not computed 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) = 0.7395415287592578 absolute error = 2.664535259100376e-14 relative error = 3.602955554870081e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.673110932343533 y2[1] (numeric) = 0.6731109323435632 absolute error = 3.019806626980426e-14 relative error = 4.486343159613427e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.29 Order of pole (ratio test) Not computed 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) = 0.7327735548521199 absolute error = 2.720046410331634e-14 relative error = 3.711987683398948e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6804725691086654 y2[1] (numeric) = 0.6804725691086955 absolute error = 3.008704396734174e-14 relative error = 4.421492552852209e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.64 Order of pole (ratio test) Not computed 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) = 0.7259323042001394 absolute error = 2.76445533131664e-14 relative error = 3.808144802651425e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6877661591839453 y2[1] (numeric) = 0.6877661591839753 absolute error = 2.997602166487923e-14 relative error = 4.358461268354153e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18 Order of pole (ratio test) Not computed 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) = 0.7190184609226805 absolute error = 2.808864252301646e-14 relative error = 3.906525916868756e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.6949909732164435 y2[1] (numeric) = 0.6949909732164734 absolute error = 2.986499936241671e-14 relative error = 4.29717802293178e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.37 Order of pole (ratio test) Not computed 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) = 0.7120327163983093 absolute error = 2.853273173286652e-14 relative error = 4.00722201041451e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7021462887307773 y2[1] (numeric) = 0.7021462887308071 absolute error = 2.97539770599542e-14 relative error = 4.237575208684569e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.92999999999996 y1[1] (analytic) = 0.7049757691956861 y1[1] (numeric) = 0.704975769195657 absolute error = 2.90878432451791e-14 relative error = 4.126077025082112e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7092313902013579 y2[1] (numeric) = 0.7092313902013876 absolute error = 2.964295475749168e-14 relative error = 4.179588659926029e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.93999999999996 y1[1] (analytic) = 0.6978483250035924 y1[1] (numeric) = 0.6978483250035629 absolute error = 2.953193245502916e-14 relative error = 4.231855461554219e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7162455691239427 y2[1] (numeric) = 0.7162455691239722 absolute error = 2.953193245502916e-14 relative error = 4.12315743763e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.94999999999996 y1[1] (analytic) = 0.6906510965605368 y1[1] (numeric) = 0.6906510965605068 absolute error = 2.997602166487923e-14 relative error = 4.340255421899815e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7231881240864843 y2[1] (numeric) = 0.7231881240865137 absolute error = 2.942091015256665e-14 relative error = 4.068223629879226e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.95999999999996 y1[1] (analytic) = 0.6833848035833657 y1[1] (numeric) = 0.6833848035833353 absolute error = 3.042011087472929e-14 relative error = 4.451388253765634e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.730058360839272 y2[1] (numeric) = 0.7300583608393013 absolute error = 2.930988785010413e-14 relative error = 4.014732166947531e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.969999999999959 y1[1] (analytic) = 0.6760501726953219 y1[1] (numeric) = 0.676050172695291 absolute error = 3.086420008457935e-14 relative error = 4.565371229997309e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7368555923643557 y2[1] (numeric) = 0.7368555923643849 absolute error = 2.919886554764162e-14 relative error = 3.962630649779142e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.979999999999959 y1[1] (analytic) = 0.6686479373533817 y1[1] (numeric) = 0.6686479373533504 absolute error = 3.130828929442941e-14 relative error = 4.682327955478748e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7435791389442473 y2[1] (numeric) = 0.7435791389442763 absolute error = 2.897682094271659e-14 relative error = 3.896938392308668e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.989999999999959 y1[1] (analytic) = 0.6611788377749109 y1[1] (numeric) = 0.6611788377748792 absolute error = 3.175237850427948e-14 relative error = 4.802388807714552e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7502283282298917 y2[1] (numeric) = 0.7502283282299205 absolute error = 2.875477633779155e-14 relative error = 3.832803328772765e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.86 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.999999999999959 y1[1] (analytic) = 0.6536436208636431 y1[1] (numeric) = 0.6536436208636111 absolute error = 3.208544541166702e-14 relative error = 4.908706271664263e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7568024953079012 y2[1] (numeric) = 0.7568024953079299 absolute error = 2.864375403532904e-14 relative error = 3.784838741008045e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.55 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.009999999999959 y1[1] (analytic) = 0.6460430401349899 y1[1] (numeric) = 0.6460430401349577 absolute error = 3.219646771412954e-14 relative error = 4.983641292289462e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7633009827670469 y2[1] (numeric) = 0.7633009827670751 absolute error = 2.819966482547898e-14 relative error = 3.694435807386517e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.019999999999959 y1[1] (analytic) = 0.6383778556406909 y1[1] (numeric) = 0.6383778556406583 absolute error = 3.26405569239796e-14 relative error = 5.113046550028083e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7697231407639977 y2[1] (numeric) = 0.7697231407640257 absolute error = 2.797762022055394e-14 relative error = 3.634764078001401e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.029999999999959 y1[1] (analytic) = 0.6306488338928077 y1[1] (numeric) = 0.6306488338927746 absolute error = 3.308464613382966e-14 relative error = 5.246128170824956e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.776068327088306 y2[1] (numeric) = 0.7760683270883337 absolute error = 2.775557561562891e-14 relative error = 3.576434528614735e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.039999999999958 y1[1] (analytic) = 0.6228567477870741 y1[1] (numeric) = 0.6228567477870406 absolute error = 3.352873534367973e-14 relative error = 5.383057253983808e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7823359072266267 y2[1] (numeric) = 0.7823359072266544 absolute error = 2.76445533131664e-14 relative error = 3.533591269147555e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.049999999999958 y1[1] (analytic) = 0.6150023765256074 y1[1] (numeric) = 0.6150023765255734 absolute error = 3.397282455352979e-14 relative error = 5.524015166486959e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7885252544261693 y2[1] (numeric) = 0.7885252544261967 absolute error = 2.742250870824137e-14 relative error = 3.477695679918008e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.04 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.059999999999958 y1[1] (analytic) = 0.6070865055389884 y1[1] (numeric) = 0.6070865055389539 absolute error = 3.441691376337985e-14 relative error = 5.669194332169112e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.7946357497573715 y2[1] (numeric) = 0.7946357497573986 absolute error = 2.708944180085382e-14 relative error = 3.409038897271501e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.75 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.069999999999958 y1[1] (analytic) = 0.5991099264077191 y1[1] (numeric) = 0.5991099264076843 absolute error = 3.47499806707674e-14 relative error = 5.800267887252231e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8006667821757921 y2[1] (numeric) = 0.8006667821758191 absolute error = 2.69784194983913e-14 relative error = 3.369494039090534e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.079999999999957 y1[1] (analytic) = 0.5910734367830658 y1[1] (numeric) = 0.5910734367830306 absolute error = 3.519406988061746e-14 relative error = 5.954263495947678e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8066177485832153 y2[1] (numeric) = 0.8066177485832421 absolute error = 2.675637489346627e-14 relative error = 3.317107135376396e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.089999999999957 y1[1] (analytic) = 0.5829778403072937 y1[1] (numeric) = 0.5829778403072581 absolute error = 3.563815909046752e-14 relative error = 6.113124140650403e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8124880538879594 y2[1] (numeric) = 0.812488053887986 absolute error = 2.653433028854124e-14 relative error = 3.265811744747238e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.5748239465332681 absolute error = 3.597122599785507e-14 relative error = 6.257781398077329e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8182771110643858 y2[1] (numeric) = 0.8182771110644121 absolute error = 2.631228568361621e-14 relative error = 3.215571513345904e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.566612570843643 absolute error = 3.652633751016765e-14 relative error = 6.446439664368963e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8239843412116011 y2[1] (numeric) = 0.8239843412116272 absolute error = 2.609024107869118e-14 relative error = 3.166351564439638e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.5583445343691092 absolute error = 3.697042672001771e-14 relative error = 6.621436128463099e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8296091736113466 y2[1] (numeric) = 0.8296091736113724 absolute error = 2.586819647376615e-14 relative error = 3.118118422095079e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.5500206639064241 absolute error = 3.730349362740526e-14 relative error = 6.782198574588323e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8351510457850696 y2[1] (numeric) = 0.8351510457850952 absolute error = 2.564615186884112e-14 relative error = 3.070839939466625e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.5416417918356974 absolute error = 3.774758283725532e-14 relative error = 6.969104564350735e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8406094035501709 y2[1] (numeric) = 0.8406094035501964 absolute error = 2.55351295663786e-14 relative error = 3.037692590462981e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.5332087560371537 absolute error = 3.83026943495679e-14 relative error = 7.183433114308468e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8459837010754229 y2[1] (numeric) = 0.8459837010754481 absolute error = 2.520206265899105e-14 relative error = 2.979024610870628e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.5247223998073455 absolute error = 3.863576125695545e-14 relative error = 7.36308594242173e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8512734009355513 y2[1] (numeric) = 0.8512734009355762 absolute error = 2.498001805406602e-14 relative error = 2.934429529527521e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.5161835717748238 absolute error = 3.896882816434299e-14 relative error = 7.549412708031618e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8564779741649782 y2[1] (numeric) = 0.8564779741650029 absolute error = 2.475797344914099e-14 relative error = 2.890672521179396e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.507593125815276 absolute error = 3.952393967665557e-14 relative error = 7.786539585848548e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.861596900310718 y2[1] (numeric) = 0.8615969003107424 absolute error = 2.442490654175344e-14 relative error = 2.83484150569078e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.4989519209661397 absolute error = 3.991251773527438e-14 relative error = 7.999271284092274e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8666296674844217 y2[1] (numeric) = 0.8666296674844459 absolute error = 2.420286193682841e-14 relative error = 2.792757142399983e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.4902608213406985 absolute error = 4.035660694512444e-14 relative error = 8.231660615824729e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.871575772413566 y2[1] (numeric) = 0.8715757724135899 absolute error = 2.386979502944087e-14 relative error = 2.738694188726779e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.4815206960416727 absolute error = 4.08006961549745e-14 relative error = 8.473300626613148e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8764347204917796 y2[1] (numeric) = 0.8764347204918032 absolute error = 2.353672812205332e-14 relative error = 2.685508409439386e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.4727324190743086 absolute error = 4.124478536482457e-14 relative error = 8.724763460391684e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8812060258283039 y2[1] (numeric) = 0.8812060258283272 absolute error = 2.331468351712829e-14 relative error = 2.645769869221363e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.4638968692589794 absolute error = 4.168887457467463e-14 relative error = 8.986668662210191e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8858892112965813 y2[1] (numeric) = 0.8858892112966043 absolute error = 2.298161660974074e-14 relative error = 2.594186306446266e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.4550149301433037 absolute error = 4.207745263329343e-14 relative error = 9.247488345061017e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8904838085819675 y2[1] (numeric) = 0.8904838085819902 absolute error = 2.264854970235319e-14 relative error = 2.543398261044118e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.4460874899137916 absolute error = 4.25215418431435e-14 relative error = 9.532108118825954e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.894989358228563 y2[1] (numeric) = 0.8949893582285853 absolute error = 2.231548279496565e-14 relative error = 2.49337967985835e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.4371154413070265 absolute error = 4.29101199017623e-14 relative error = 9.816656161459726e-12 % Correct digits = 14 h = 0.01 y2[1] (analytic) = 0.8994054096851575 y2[1] (numeric) = 0.8994054096851796 absolute error = 2.209343819004062e-14 relative error = 2.456449333318393e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.4280996815203922 absolute error = 4.335420911161236e-14 relative error = 1.012712949414862e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9037315213502856 y2[1] (numeric) = 0.9037315213503073 absolute error = 2.176037128265307e-14 relative error = 2.4078358194412e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.4190411121223545 absolute error = 4.379829832146243e-14 relative error = 1.045202894284734e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9079672606163857 y2[1] (numeric) = 0.9079672606164071 absolute error = 2.142730437526552e-14 relative error = 2.359920374300645e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.4099406389623043 absolute error = 4.418687638008123e-14 relative error = 1.07788475160521e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.912112203913061 y2[1] (numeric) = 0.9121122039130821 absolute error = 2.109423746787797e-14 relative error = 2.312680104200052e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.400799172079974 absolute error = 4.463096558993129e-14 relative error = 1.113549345880905e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.916165936749436 y2[1] (numeric) = 0.9161659367494568 absolute error = 2.076117056049043e-14 relative error = 2.266092825296608e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.3916176256144338 absolute error = 4.50195436485501e-14 relative error = 1.149579097159146e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9201280537556052 y2[1] (numeric) = 0.9201280537556256 absolute error = 2.031708135064036e-14 relative error = 2.208071068772866e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.3823969177126791 absolute error = 4.546363285840016e-14 relative error = 1.188912115985063e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9239981587231696 y2[1] (numeric) = 0.9239981587231896 absolute error = 1.998401444325282e-14 relative error = 2.162776435709331e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.3731379704378163 absolute error = 4.579669976578771e-14 relative error = 1.227339573939558e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9277758646448576 y2[1] (numeric) = 0.9277758646448773 absolute error = 1.965094753586527e-14 relative error = 2.118070569057909e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.3638417096768569 absolute error = 4.624078897563777e-14 relative error = 1.270904015284567e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9314607937532251 y2[1] (numeric) = 0.9314607937532444 absolute error = 1.931788062847772e-14 relative error = 2.07393384220052e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.3545090650481302 absolute error = 4.662936703425657e-14 relative error = 1.315322276114992e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9350525775584321 y2[1] (numeric) = 0.9350525775584509 absolute error = 1.887379141862766e-14 relative error = 2.018473813302571e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.3451409698083219 absolute error = 4.701794509287538e-14 relative error = 1.362282348542421e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.938550856885091 y2[1] (numeric) = 0.9385508568851095 absolute error = 1.854072451124011e-14 relative error = 1.975462957092596e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.3357383607591494 absolute error = 4.740652315149418e-14 relative error = 1.41200794107337e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9419552819081846 y2[1] (numeric) = 0.9419552819082027 absolute error = 1.809663530139005e-14 relative error = 1.921177751106235e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.3263021781536819 absolute error = 4.779510121011299e-14 relative error = 1.464749683270439e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9452655121880474 y2[1] (numeric) = 0.9452655121880651 absolute error = 1.765254609153999e-14 relative error = 1.867469601284709e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.3168333656023167 absolute error = 4.818367926873179e-14 relative error = 1.520789301250668e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9484812167044101 y2[1] (numeric) = 0.9484812167044274 absolute error = 1.731947918415244e-14 relative error = 1.826022369144078e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.3073328699784181 absolute error = 4.851674617611934e-14 relative error = 1.57863837276887e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9516020738895008 y2[1] (numeric) = 0.9516020738895177 absolute error = 1.687538997430238e-14 relative error = 1.773366245969524e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.2978016413236316 absolute error = 4.890532423473815e-14 relative error = 1.642211373226884e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9546277716602015 y2[1] (numeric) = 0.9546277716602181 absolute error = 1.654232306691483e-14 relative error = 1.732855837427182e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.28824063275288 absolute error = 4.923839114212569e-14 relative error = 1.70823907343873e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9575580074492568 y2[1] (numeric) = 0.9575580074492729 absolute error = 1.609823385706477e-14 relative error = 1.681175838103766e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.2786508003590528 absolute error = 4.957145804951324e-14 relative error = 1.778981362537972e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9603924882355295 y2[1] (numeric) = 0.9603924882355451 absolute error = 1.565414464721471e-14 relative error = 1.629973665868119e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.2690331031173979 absolute error = 4.996003610813204e-14 relative error = 1.857021887983864e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.963130930573303 y2[1] (numeric) = 0.9631309305733182 absolute error = 1.521005543736464e-14 relative error = 1.579230295128293e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.2593885027896247 absolute error = 5.029310301551959e-14 relative error = 1.938910262969509e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9657730606206257 y2[1] (numeric) = 0.9657730606206404 absolute error = 1.465494392505207e-14 relative error = 1.517431425932972e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.249717963827729 absolute error = 5.065392549852277e-14 relative error = 2.028445399845432e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9683186141666945 y2[1] (numeric) = 0.9683186141667087 absolute error = 1.4210854715202e-14 relative error = 1.467580454128875e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.2400224532775481 absolute error = 5.101474798152594e-14 relative error = 2.125415655281408e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9707673366582761 y2[1] (numeric) = 0.9707673366582898 absolute error = 1.376676550535194e-14 relative error = 1.418132335678084e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.2303029406820574 absolute error = 5.134781488891349e-14 relative error = 2.229577040433443e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.973118983225162 y2[1] (numeric) = 0.9731189832251753 absolute error = 1.332267629550188e-14 relative error = 1.369069612777172e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.2205603979844171 absolute error = 5.170863737191667e-14 relative error = 2.344420750254442e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9753733187046552 y2[1] (numeric) = 0.975373318704668 absolute error = 1.287858708565182e-14 relative error = 1.320375166993006e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.210795799430778 absolute error = 5.204170427930421e-14 relative error = 2.4688207459457e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9775301176650862 y2[1] (numeric) = 0.9775301176650987 absolute error = 1.243449787580175e-14 relative error = 1.272032201473506e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.2010101214728585 absolute error = 5.237477118669176e-14 relative error = 2.605578803838992e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9795891644283565 y2[1] (numeric) = 0.9795891644283685 absolute error = 1.199040866595169e-14 relative error = 1.224024223762086e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.1912043426702995 absolute error = 5.270783809407931e-14 relative error = 2.756623482393954e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9815502530915056 y2[1] (numeric) = 0.9815502530915171 absolute error = 1.154631945610163e-14 relative error = 1.176335029178095e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.1813794435928099 absolute error = 5.304090500146685e-14 relative error = 2.924306302346269e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9834131875473012 y2[1] (numeric) = 0.9834131875473123 absolute error = 1.110223024625157e-14 relative error = 1.128948684727452e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.17153640672211 absolute error = 5.33739719088544e-14 relative error = 3.111524423809572e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9851777815038505 y2[1] (numeric) = 0.985177781503861 absolute error = 1.054711873393899e-14 relative error = 1.070580247743616e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.1616762163536845 absolute error = 5.367928324062632e-14 relative error = 3.320171912186462e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9868438585032281 y2[1] (numeric) = 0.9868438585032382 absolute error = 1.010302952408892e-14 relative error = 1.023771839590962e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 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) = 0.1517998584983534 absolute error = 5.395683899678261e-14 relative error = 3.554472285450036e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9884112519391225 y2[1] (numeric) = 0.9884112519391322 absolute error = 9.658940314238862e-15 relative error = 9.772187735913965e-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] = 4.569999999999947 y1[1] (analytic) = 0.1419083207837261 y1[1] (numeric) = 0.1419083207836719 absolute error = 5.426215032855453e-14 relative error = 3.823746911307067e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9898798050734964 y2[1] (numeric) = 0.9898798050735055 absolute error = 9.103828801926284e-15 relative error = 9.196903255593081e-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] = 4.579999999999947 y1[1] (analytic) = 0.1320025923552231 y1[1] (numeric) = 0.1320025923551685 absolute error = 5.456746166032644e-14 relative error = 4.13381742636415e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9912493710522599 y2[1] (numeric) = 0.9912493710522685 absolute error = 8.659739592076221e-15 relative error = 8.736186720485363e-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] = 4.589999999999947 y1[1] (analytic) = 0.1220836637774863 y1[1] (numeric) = 0.1220836637774315 absolute error = 5.484501741648273e-14 relative error = 4.492412475140414e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9925198129199566 y2[1] (numeric) = 0.9925198129199647 absolute error = 8.104628079763643e-15 relative error = 8.165709111559321e-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] = 4.599999999999946 y1[1] (analytic) = 0.1121525269351078 y1[1] (numeric) = 0.1121525269350527 absolute error = 5.513645096044684e-14 relative error = 4.916202288723208e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9936910036334584 y2[1] (numeric) = 0.9936910036334661 absolute error = 7.66053886991358e-15 relative error = 7.709176033497949e-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] = 4.609999999999946 y1[1] (analytic) = 0.102210174933496 y1[1] (numeric) = 0.1022101749334405 absolute error = 5.542788450441094e-14 relative error = 5.422932163111513e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.99476282607467 y2[1] (numeric) = 0.9947628260746771 absolute error = 7.105427357601002e-15 relative error = 7.142835630115963e-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] = 4.619999999999946 y1[1] (analytic) = 0.09225760199956561 y1[1] (numeric) = 0.0922576019995099 absolute error = 5.570544026056723e-14 relative error = 6.038032536422258e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9957351730622404 y2[1] (numeric) = 0.995735173062247 absolute error = 6.661338147750939e-15 relative error = 6.689869282476937e-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] = 4.629999999999946 y1[1] (analytic) = 0.08229580338231637 y1[1] (numeric) = 0.08229580338226039 absolute error = 5.598299601672352e-14 relative error = 6.802655021987802e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9966079473622811 y2[1] (numeric) = 0.9966079473622872 absolute error = 6.106226635438361e-15 relative error = 6.127009775107343e-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] = 4.639999999999946 y1[1] (analytic) = 0.07232577525330852 y1[1] (numeric) = 0.07232577525325226 absolute error = 5.626055177287981e-14 relative error = 7.778769266673873e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9973810616980894 y2[1] (numeric) = 0.9973810616980949 absolute error = 5.551115123125783e-15 relative error = 5.56569132531426e-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] = 4.649999999999945 y1[1] (analytic) = 0.06234851460704662 y1[1] (numeric) = 0.06234851460699009 absolute error = 5.652422974122828e-14 relative error = 9.065850260824005e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.998054438758876 y2[1] (numeric) = 0.998054438758881 absolute error = 4.996003610813204e-15 relative error = 5.005742589578532e-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] = 4.659999999999945 y1[1] (analytic) = 0.05236501916128092 y1[1] (numeric) = 0.05236501916122414 absolute error = 5.678096881567285e-14 relative error = 1.084330144915847e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.998628011207496 y2[1] (numeric) = 0.9986280112075004 absolute error = 4.440892098500626e-15 relative error = 4.446993323500809e-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] = 4.669999999999945 y1[1] (analytic) = 0.04237628725723648 y1[1] (numeric) = 0.04237628725717944 absolute error = 5.703770789011742e-14 relative error = 1.34598171717786e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9991017216871825 y2[1] (numeric) = 0.9991017216871864 absolute error = 3.885780586188048e-15 relative error = 3.889274236887644e-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] = 4.679999999999945 y1[1] (analytic) = 0.03238331775977977 y1[1] (numeric) = 0.03238331775972248 absolute error = 5.728750807065808e-14 relative error = 1.769043817425323e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9994755228272822 y2[1] (numeric) = 0.9994755228272856 absolute error = 3.33066907387547e-15 relative error = 3.332416850443507e-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] = 4.689999999999944 y1[1] (analytic) = 0.02238710995753308 y1[1] (numeric) = 0.02238710995747555 absolute error = 5.753036935729483e-14 relative error = 2.569798847034131e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9997493772479927 y2[1] (numeric) = 0.9997493772479955 absolute error = 2.775557561562891e-15 relative error = 2.776253353818695e-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] = 4.699999999999944 y1[1] (analytic) = 0.01238866346294651 y1[1] (numeric) = 0.01238866346288874 absolute error = 5.776976119697963e-14 relative error = 4.663114900954757e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9999232575641002 y2[1] (numeric) = 0.9999232575641024 absolute error = 2.220446049250313e-15 relative error = 2.220616464767019e-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] = 4.709999999999944 y1[1] (analytic) = 0.002388978112337493 y1[1] (numeric) = 0.002388978112279491 absolute error = 5.800221414276052e-14 relative error = 2.427908980966272e-09 % Correct digits = 11 h = 0.01 y2[1] (analytic) = 0.9999971463877179 y2[1] (numeric) = 0.9999971463877194 absolute error = 1.554312234475219e-15 relative error = 1.554316669892359e-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] = 4.719999999999944 y1[1] (analytic) = -0.007610946134091949 y1[1] (numeric) = -0.007610946134150177 absolute error = 5.82285955563755e-14 relative error = 7.650638242668717e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9999710363300249 y2[1] (numeric) = 0.9999710363300259 absolute error = 9.992007221626409e-16 relative error = 9.992296635208444e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007339 Order of pole (three term test) = -0.8943 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.007329 Order of pole (three term test) = -0.8902 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) = -0.01761010929230886 absolute error = 5.844630335261058e-14 relative error = 3.318906338550138e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9998449300020054 y2[1] (numeric) = 0.9998449300020058 absolute error = 4.440892098500626e-16 relative error = 4.441580854434817e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01698 Order of pole (three term test) = -0.9004 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.01696 Order of pole (three term test) = -0.8961 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) = -0.02760751145421336 absolute error = 5.866140906363171e-14 relative error = 2.124835089212782e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.999618840014187 y2[1] (numeric) = 0.9996188400141869 absolute error = 1.110223024625157e-16 relative error = 1.110646358575434e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02661 Order of pole (three term test) = -0.9113 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02657 Order of pole (three term test) = -0.9066 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) = -0.03760215288797862 absolute error = 5.886957588074893e-14 relative error = 1.565590567545978e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9992927889753801 y2[1] (numeric) = 0.9992927889753794 absolute error = 6.661338147750939e-16 relative error = 6.666052453536775e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03623 Order of pole (three term test) = -0.927 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03618 Order of pole (three term test) = -0.9217 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) = -0.04759303413779011 absolute error = 5.907080380396224e-14 relative error = 1.241164907305874e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9988668094904168 y2[1] (numeric) = 0.9988668094904156 absolute error = 1.221245327087672e-15 relative error = 1.222630800707758e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04584 Order of pole (three term test) = -0.9476 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04578 Order of pole (three term test) = -0.9414 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) = -0.05757915612384854 absolute error = 5.926509283327164e-14 relative error = 1.029280330296223e-10 % Correct digits = 12 h = 0.01 y2[1] (analytic) = 0.9983409441568909 y2[1] (numeric) = 0.998340944156889 absolute error = 1.887379141862766e-15 relative error = 1.890515612836732e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05543 Order of pole (three term test) = -0.973 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05535 Order of pole (three term test) = -0.9658 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) = -0.06755952024227706 absolute error = 5.945244296867713e-14 relative error = 8.800009644166419e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9977152455608972 y2[1] (numeric) = 0.9977152455608947 absolute error = 2.442490654175344e-15 relative error = 2.448083924789804e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.065 Order of pole (three term test) = -1.003 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06491 Order of pole (three term test) = -0.9947 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) = -0.07753312846498077 absolute error = 5.964673199798654e-14 relative error = 7.693064007467845e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.996989776271774 y2[1] (numeric) = 0.996989776271771 absolute error = 2.997602166487923e-15 relative error = 3.006652864282524e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07454 Order of pole (three term test) = -1.038 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07444 Order of pole (three term test) = -1.028 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) = -0.0874989834394487 absolute error = 5.981326545168031e-14 relative error = 6.835881184049795e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9961646088358458 y2[1] (numeric) = 0.9961646088358421 absolute error = 3.663735981263017e-15 relative error = 3.677841943757259e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08405 Order of pole (three term test) = -1.078 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08393 Order of pole (three term test) = -1.066 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) = -0.09745608858848827 absolute error = 5.99936766931819e-14 relative error = 6.155970095059347e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9952398257691683 y2[1] (numeric) = 0.995239825769164 absolute error = 4.218847493575595e-15 relative error = 4.239025995885033e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09353 Order of pole (three term test) = -1.122 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0934 Order of pole (three term test) = -1.109 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) = -0.1074034482098821 absolute error = 6.016021014687567e-14 relative error = 5.601329487052173e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9942155195492777 y2[1] (numeric) = 0.9942155195492728 absolute error = 4.884981308350689e-15 relative error = 4.91340279074025e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.103 Order of pole (three term test) = -1.172 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1028 Order of pole (three term test) = -1.156 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) = -0.1173400675759576 absolute error = 6.032674360056944e-14 relative error = 5.141188755626823e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9930917926059423 y2[1] (numeric) = 0.9930917926059368 absolute error = 5.440092820663267e-15 relative error = 5.477935535433319e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1124 Order of pole (three term test) = -1.226 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1122 Order of pole (three term test) = -1.208 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) = -0.1272649530330585 absolute error = 6.04793992664554e-14 relative error = 4.752243082254856e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9918687573109201 y2[1] (numeric) = 0.991868757310914 absolute error = 6.106226635438361e-15 relative error = 6.156284881876009e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1217 Order of pole (three term test) = -1.284 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1216 Order of pole (three term test) = -1.264 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) = -0.1371771121009099 absolute error = 6.061817714453355e-14 relative error = 4.418971664891776e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9905465359667213 y2[1] (numeric) = 0.9905465359667146 absolute error = 6.661338147750939e-15 relative error = 6.724911860147816e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.131 Order of pole (three term test) = -1.348 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1308 Order of pole (three term test) = -1.325 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) = -0.147075553571865 absolute error = 6.078471059822732e-14 relative error = 4.132890145373576e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9891252607943786 y2[1] (numeric) = 0.9891252607943712 absolute error = 7.327471962526033e-15 relative error = 7.408032382714856e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1403 Order of pole (three term test) = -1.416 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1401 Order of pole (three term test) = -1.39 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) = -0.1569592876100256 absolute error = 6.092348847630547e-14 relative error = 3.88148349830034e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9876050739202247 y2[1] (numeric) = 0.9876050739202168 absolute error = 7.882583474838611e-15 relative error = 7.981513747746641e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1495 Order of pole (three term test) = -1.488 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1493 Order of pole (three term test) = -1.46 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) = -0.1668273258502241 absolute error = 6.103451077876798e-14 relative error = 3.658543974599611e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9859861273616802 y2[1] (numeric) = 0.9859861273616718 absolute error = 8.43769498715119e-15 relative error = 8.557620389374979e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1586 Order of pole (three term test) = -1.566 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1584 Order of pole (three term test) = -1.534 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) = -0.1766786814968598 absolute error = 6.11455330812305e-14 relative error = 3.460832544323601e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.984268583012052 y2[1] (numeric) = 0.984268583012043 absolute error = 8.992806499463768e-15 relative error = 9.136537175599005e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1677 Order of pole (three term test) = -1.648 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1675 Order of pole (three term test) = -1.613 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) = -0.1865123694225777 absolute error = 6.125655538369301e-14 relative error = 3.284315971823041e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9824526126243437 y2[1] (numeric) = 0.982452612624334 absolute error = 9.658940314238862e-15 relative error = 9.831456693303244e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1767 Order of pole (three term test) = -1.734 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1764 Order of pole (three term test) = -1.695 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) = -0.1963274062667797 absolute error = 6.136757768615553e-14 relative error = 3.125777437449834e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9805383977940807 y2[1] (numeric) = 0.9805383977940704 absolute error = 1.032507412901396e-14 relative error = 1.053000489551689e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1856 Order of pole (three term test) = -1.825 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1854 Order of pole (three term test) = -1.782 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) = -0.2061228105339607 absolute error = 6.145084441300241e-14 relative error = 2.981273360955658e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.978526129941151 y2[1] (numeric) = 0.97852612994114 absolute error = 1.099120794378905e-14 relative error = 1.123241128415249e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1945 Order of pole (three term test) = -1.92 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1942 Order of pole (three term test) = -1.874 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) = -0.2158976026918567 absolute error = 6.156186671546493e-14 relative error = 2.851438179392276e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9764160102906628 y2[1] (numeric) = 0.9764160102906512 absolute error = 1.165734175856414e-14 relative error = 1.193890886231366e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2033 Order of pole (three term test) = -2.02 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.203 Order of pole (three term test) = -1.969 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) = -0.2256508052693977 absolute error = 6.164513344231182e-14 relative error = 2.731881828151794e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9742082498528229 y2[1] (numeric) = 0.9742082498528106 absolute error = 1.232347557333924e-14 relative error = 1.264973436141707e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.212 Order of pole (three term test) = -2.124 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2117 Order of pole (three term test) = -2.069 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) = -0.2353814429544533 absolute error = 6.17284001691587e-14 relative error = 2.622483718103446e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9719030694018352 y2[1] (numeric) = 0.9719030694018223 absolute error = 1.298960938811433e-14 relative error = 1.336512847532098e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2206 Order of pole (three term test) = -2.232 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2203 Order of pole (three term test) = -2.173 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) = -0.2450885426913641 absolute error = 6.178391132038996e-14 relative error = 2.520881255481982e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9695006994538239 y2[1] (numeric) = 0.9695006994538102 absolute error = 1.365574320288943e-14 relative error = 1.408533610195691e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2291 Order of pole (three term test) = -2.345 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2288 Order of pole (three term test) = -2.281 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) = -0.2547711337782456 absolute error = 6.189493362285248e-14 relative error = 2.429432750287215e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9670013802437817 y2[1] (numeric) = 0.9670013802437674 absolute error = 1.432187701766452e-14 relative error = 1.481060659298538e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2375 Order of pole (three term test) = -2.462 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2372 Order of pole (three term test) = -2.394 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) = -0.2644282479640577 absolute error = 6.195044477408373e-14 relative error = 2.342807368391248e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9644053617015469 y2[1] (numeric) = 0.9644053617015319 absolute error = 1.498801083243961e-14 relative error = 1.554119401202368e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2459 Order of pole (three term test) = -2.583 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2455 Order of pole (three term test) = -2.51 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) = -0.2740589195454297 absolute error = 6.200595592531499e-14 relative error = 2.262504574862069e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9617129034268105 y2[1] (numeric) = 0.9617129034267948 absolute error = 1.565414464721471e-14 relative error = 1.627735740202225e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2541 Order of pole (three term test) = -2.709 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2538 Order of pole (three term test) = -2.63 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) = -0.2836621854632287 absolute error = 6.206146707654625e-14 relative error = 2.187865364402084e-11 % Correct digits = 13 h = 0.01 y2[1] (analytic) = 0.9589242746631561 y2[1] (numeric) = 0.9589242746631398 absolute error = 1.63202784619898e-14 relative error = 1.701936106239741e-12 % Correct digits = 14 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2623 Order of pole (three term test) = -2.838 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2619 Order of pole (three term test) = -2.754 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 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 100.4 %