## Chapter 1Introduction and Summary of results

### 1.1 Introduction

This report shows the result of running Maple and Mathematica on my collection of diﬀerential equations. These were collected over time and stored in sqlite3 database. These were collected from a number of textbooks and other references such as Kamke and Murphy collections. All books used are listed in the links below.

The current number of diﬀerential equations is [10044]. Both Maple and Mathematica are given a CPU time limit of 3 minutes to solve each ode else the problem is considered not solved and marked as failed.

When Mathematica returns DifferentialRoot as a solution to an ode then this is considered as not solved. Similarly, when Maple returns DESol or ODSESolStruc, then this is also considered as not solved.

If CAS solves the ODE within the timelimit, then it is counted as solved. No veriﬁcation is done to check that the solution is correct or not.

To reduce the size of latex output, in Maple the command simplify is called on the solution with timeout of 3 minutes. If this times out, then the unsimpliﬁed original ode solution is used otherwise the simpliﬁed one is used.

Similarly for Mathematica, FullSimplify is called on the solution with timeout of 3 minutes. If this timesout, then Simplify is next called. If this also timesout, then the unsimpliﬁed solution is used else the simpliﬁed one is used. The time used for simpliﬁcation is not counted in the CPU time used. The CPU time used only records the time used to solve the ode.

Tests are run under windows 10 with 128 GB RAM running on intel i9-12900K 3.20 GHz

### 1.2 Summary of results

#### 1.2.1 Percentage solved and CPU performance

The following table summarizes perentage solved for each CAS

 System % solved Number solved Number failed Maple 2022.2 94.454 9487 557 Mathematica 13.1 93.260 9367 677

The following table summarizes the run-time performance of each CAS system.

 System mean time (sec) mean leaf size total time (min) total leaf size Maple 2022.2 0.285 273.73 47.695 2749388 Mathematica 13.1 2.448 845.31 409.857 8490335

The problem which Mathematica produced largest leaf size of $$2733033$$ is 9606The problem which Maple produced largest leaf size of $$540884$$ is 9648The problem which Mathematica used most CPU time of $$178.125$$ seconds is 3759The problem which Maple used most CPU time of $$1997.156$$ seconds is 8492

#### 1.2.2 Performance based on ODE type

The following gives the performance of each CAS based on the type of the ODE. The ﬁrst subsection uses the types as classiﬁed by Maple ode advisor.The next subsection uses my own ode solver ODE classiﬁcaiton.

##### Performance using Maple’s ODE types classiﬁcation

The following table gives count of the number of ODE’s for each ODE type, where the ODE type here is as classiﬁed by Maple’s odeadvisor, and the percentage of solved ODE’s of that type for each CAS. It also gives a direct link to the ODE’s that failed if any.

 Type of ODE Count Mathematica Maple [_quadrature] 459 99.13%[885, 3741, 3758, 3767] 99.78%[6550] [[_linear, class A]] 148 100.00% 98.65%[6547, 6548] [_separable] 752 99.47%[944, 2513, 5511, 7911] 99.47%[408, 409, 5511, 5665] [_Riccati] 308 55.19%[958, 1697, 1698, 1700, 1701, 1702, 2198, 2795, 2815, 2817, 2830, 3131, 3878, 6592, 7691, 9592, 9596, 9597, 9598, 9603, 9616, 9618, 9619, 9620, 9672, 9689, 9693, 9695, 9696, 9697, 9702, 9709, 9710, 9716, 9717, 9718, 9719, 9720, 9733, 9734, 9735, 9736, 9737, 9738, 9739, 9740, 9741, 9744, 9745, 9753, 9757, 9758, 9760, 9761, 9762, 9763, 9764, 9770, 9771, 9773, 9774, 9775, 9776, 9777, 9782, 9783, 9788, 9789, 9793, 9794, 9795, 9798, 9802, 9803, 9805, 9806, 9811, 9812, 9813, 9814, 9817, 9819, 9820, 9823, 9826, 9828, 9829, 9832, 9835, 9837, 9838, 9841, 9844, 9846, 9847, 9850, 9854, 9855, 9856, 9860, 9861, 9863, 9864, 9866, 9868, 9869, 9870, 9871, 9872, 9873, 9874, 9875, 9877, 9878, 9879, 9880, 9881, 9882, 9883, 9884, 9885, 9886, 9889, 9890, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902, 9903, 9904, 9905, 9906] 71.75%[958, 1697, 1700, 1701, 1702, 2198, 2815, 2817, 2830, 3878, 6592, 7691, 9596, 9603, 9616, 9618, 9620, 9675, 9683, 9689, 9693, 9695, 9697, 9702, 9718, 9733, 9736, 9737, 9738, 9740, 9744, 9758, 9760, 9771, 9773, 9789, 9802, 9804, 9811, 9819, 9820, 9823, 9828, 9829, 9832, 9837, 9838, 9841, 9846, 9847, 9850, 9854, 9855, 9860, 9861, 9863, 9864, 9866, 9868, 9869, 9870, 9871, 9872, 9873, 9874, 9875, 9877, 9880, 9881, 9882, 9883, 9885, 9889, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902, 9903, 9904, 9905, 9906] [[_homogeneous, class G]] 62 91.94%[2723, 2727, 2888, 3532, 7963] 93.55%[3487, 3532, 7948, 7963] [_linear] 454 99.78%[5416] 99.56%[4749, 5416] [[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class A]] 18 100.00% 100.00% [[_homogeneous, class A], _rational, _Bernoulli] 59 100.00% 100.00% [[_homogeneous, class A], _dAlembert] 111 100.00% 100.00% [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]] 68 98.53%[5501] 100.00% [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]] 45 100.00% 100.00% [[_homogeneous, class A], _rational, _dAlembert] 161 98.14%[3703, 5008, 5509] 99.38%[5509] [[_homogeneous, class C], _dAlembert] 57 92.98%[2491, 3752, 3770, 6349] 98.25%[3752] [[_homogeneous, class C], _Riccati] 15 100.00% 100.00% [[_homogeneous, class G], _rational, _Bernoulli] 47 100.00% 100.00% [_Bernoulli] 84 97.62%[4607, 6377] 100.00% [[_1st_order, _with_linear_symmetries], _Bernoulli] 3 100.00% 100.00% [[_1st_order, _with_symmetry_[F(x),G(x)]]] 45 100.00% 100.00% [y=_G(x,y’)] 109 65.14%[133, 485, 959, 961, 962, 964, 966, 968, 1703, 1706, 1707, 2854, 2859, 2876, 2955, 3503, 3708, 3753, 3779, 3791, 4443, 4487, 5796, 6310, 6500, 7655, 7660, 7663, 7701, 7950, 7975, 8040, 8041, 8086, 8087, 8090, 8111, 8442] 59.63%[133, 485, 959, 961, 962, 964, 966, 968, 1703, 1706, 1707, 2581, 2854, 2859, 2874, 2876, 2887, 2955, 3364, 3503, 3708, 3779, 3790, 4406, 4443, 4487, 5796, 6310, 6500, 7655, 7660, 7663, 7701, 7950, 7975, 8032, 8040, 8041, 8086, 8087, 8090, 8111, 8123, 8140] [[_1st_order, _with_linear_symmetries]] 89 94.38%[2720, 2722, 3782, 3786, 6054] 98.88%[8117] [[_homogeneous, class A], _exact, _rational, _dAlembert] 24 100.00% 100.00% [_exact, _rational] 31 96.77%[119] 100.00% [_exact] 60 98.33%[2628] 100.00% [[_1st_order, _with_linear_symmetries], _exact, _rational] 3 100.00% 100.00% [[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class B]] 2 100.00% 100.00% [[_homogeneous, class G], _exact, _rational] 3 66.67%[146] 100.00% [[_2nd_order, _missing_x]] 408 96.57%[6655, 9190, 9191, 9194, 9195, 9197, 9215, 9216, 9218, 9223, 9241, 9287, 9289, 9415] 96.32%[6655, 9190, 9191, 9194, 9195, 9197, 9215, 9216, 9218, 9223, 9241, 9287, 9288, 9289, 9415] [[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]] 58 100.00% 100.00% [[_Emden, _Fowler]] 233 99.57%[5591] 96.57%[2032, 4210, 4709, 4803, 4835, 4836, 5831, 5864] [[_2nd_order, _exact, _linear, _homogeneous]] 176 100.00% 98.30%[4837, 5707, 5865] [[_2nd_order, _missing_y]] 76 93.42%[6070, 6103, 6105, 6459, 9406] 97.37%[5690, 6552] [[_2nd_order, _with_linear_symmetries]] 2113 96.07%[1105, 1138, 4502, 4741, 4742, 4743, 5060, 5065, 5590, 5828, 6343, 6425, 6426, 6429, 6430, 6434, 6436, 6535, 6798, 6800, 7186, 7220, 7222, 8599, 8606, 8608, 8610, 8611, 8612, 8618, 8652, 8653, 8655, 8657, 8661, 8662, 8663, 8679, 8706, 8737, 8785, 8792, 8796, 8816, 8858, 8885, 8941, 8987, 8998, 9018, 9019, 9020, 9022, 9184, 9227, 9237, 9238, 9239, 9242, 9244, 9245, 9246, 9251, 9252, 9256, 9257, 9259, 9263, 9298, 9321, 9341, 9356, 9358, 9359, 9390, 9397, 9398, 9399, 9410, 9411, 10089, 10090, 10098] 96.83%[1794, 1797, 1805, 2411, 4193, 4206, 4495, 4502, 4768, 4773, 4811, 5065, 5289, 5688, 5696, 5828, 5839, 6426, 6434, 6436, 6535, 8599, 8606, 8608, 8610, 8611, 8618, 8652, 8653, 8655, 8657, 8661, 8737, 8785, 8792, 8796, 8816, 8858, 8987, 9018, 9019, 9020, 9022, 9184, 9227, 9237, 9238, 9239, 9242, 9244, 9245, 9246, 9251, 9252, 9256, 9259, 9261, 9263, 9298, 9321, 9341, 9356, 9390, 9399, 9410, 9411, 9413] [[_2nd_order, _linear, _nonhomogeneous]] 541 99.26%[1162, 1186, 6706, 8656] 96.67%[1162, 1186, 4214, 4215, 4747, 4748, 5080, 5760, 6471, 6472, 6473, 6477, 6478, 6480, 6488, 6553, 6554, 8656] [[_2nd_order, _exact, _linear, _nonhomogeneous]] 33 100.00% 100.00% system of linear ODEs 449 95.32%[5351, 5789, 5790, 9469, 9484, 9494, 9497, 9498, 9499, 9500, 9501, 9506, 9507, 9508, 9511, 9512, 9513, 9514, 9515, 9516, 9518] 95.77%[5351, 5789, 5790, 9469, 9484, 9494, 9497, 9498, 9499, 9500, 9501, 9506, 9507, 9508, 9511, 9513, 9514, 9516, 9518] [_Gegenbauer] 63 100.00% 100.00% [[_high_order, _missing_x]] 94 96.81%[9123, 9126, 9155] 100.00% [[_3rd_order, _missing_x]] 77 100.00% 100.00% [[_3rd_order, _missing_y]] 30 100.00% 100.00% [[_3rd_order, _exact, _linear, _homogeneous]] 12 100.00% 100.00% [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]] 54 92.59%[8654, 8902, 9023, 10097] 98.15%[5706] [_Lienard] 47 100.00% 100.00% [[_homogeneous, class A], _rational, _Riccati] 27 100.00% 100.00% [x=_G(y,y’)] 12 66.67%[550, 2204, 5430, 8152] 66.67%[550, 2204, 5430, 8152] [[_Abel, 2nd type, class B]] 15 26.67%[553, 1046, 7830, 9924, 9927, 9947, 9948, 9949, 9969, 9982, 9987] 40.00%[553, 1046, 7830, 9927, 9947, 9948, 9949, 9969, 9982] [_exact, _rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]] 6 100.00% 100.00% [[_1st_order, _with_symmetry_[F(x)*G(y),0]]] 21 100.00% 100.00% [[_homogeneous, class D], _rational] 2 100.00% 100.00% [[_1st_order, _with_exponential_symmetries]] 5 100.00% 100.00% [_rational] 95 85.26%[1039, 1075, 2609, 2683, 2684, 3638, 3807, 5358, 8060, 8062, 8069, 8083, 8465, 8474] 81.05%[1039, 1075, 2609, 2683, 2684, 3418, 3638, 3690, 3691, 3807, 5358, 8060, 8062, 8083, 8288, 8465, 8474, 8500] [_rational, [_Abel, 2nd type, class B]] 133 [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]] 4 100.00% 100.00% [NONE] 81 39.51%[710, 1041, 4481, 6357, 6461, 7637, 7668, 7782, 7947, 8155, 8156, 8415, 8417, 9174, 9177, 9178, 9182, 9185, 9187, 9188, 9196, 9198, 9202, 9203, 9204, 9207, 9213, 9221, 9222, 9224, 9228, 9254, 9264, 9272, 9281, 9283, 9308, 9311, 9313, 9314, 9317, 9318, 9330, 9336, 9368, 9380, 9381, 9394, 9430] 35.80%[710, 4481, 5485, 6357, 6461, 7637, 7668, 7782, 7947, 8155, 8156, 8415, 8417, 9174, 9177, 9178, 9185, 9187, 9188, 9196, 9198, 9202, 9203, 9204, 9207, 9213, 9221, 9222, 9224, 9228, 9254, 9264, 9272, 9277, 9281, 9283, 9284, 9285, 9300, 9308, 9311, 9313, 9314, 9317, 9318, 9330, 9336, 9368, 9380, 9381, 9394, 9430] [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]] 19 100.00% 100.00% [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]] 36 100.00% 100.00% [_Gegenbauer, [_2nd_order, _linear, _with_symmetry_[0,F(x)]]] 11 100.00% 100.00% [[_high_order, _with_linear_symmetries]] 37 81.08%[813, 9119, 9120, 9121, 9122, 9151, 9169] 81.08%[813, 9119, 9120, 9121, 9122, 9161, 9169] [[_3rd_order, _with_linear_symmetries]] 96 82.29%[5064, 9036, 9037, 9038, 9039, 9040, 9041, 9042, 9052, 9053, 9055, 9063, 9068, 9079, 9094, 9095, 9110] 83.33%[5064, 9036, 9037, 9038, 9039, 9040, 9041, 9042, 9052, 9053, 9055, 9063, 9068, 9089, 9094, 9110] [[_high_order, _linear, _nonhomogeneous]] 49 95.92%[9131, 9160] 97.96%[9160] [[_1st_order, _with_linear_symmetries], _Clairaut] 45 100.00% 100.00% [[_1st_order, _with_symmetry_[F(x),G(y)]]] 48 100.00% 100.00% [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] 70 100.00% 100.00% [[_homogeneous, class C], _rational, _Riccati] 5 100.00% 100.00% [[_Abel, 2nd type, class A]] 34 14.71%[3168, 3220, 4446, 7786, 7799, 9914, 9915, 9979, 9980, 9981, 9990, 9991, 9992, 9993, 9994, 10008, 10054, 10061, 10062, 10064, 10065, 10067, 10068, 10069, 10070, 10071, 10072, 10073, 10074] 35.29%[3168, 3220, 4446, 7786, 7799, 9979, 9980, 9981, 9990, 9991, 9992, 9993, 9994, 10008, 10054, 10062, 10065, 10069, 10070, 10072, 10073, 10074] [_rational, _Bernoulli] 38 100.00% 100.00% [[_homogeneous, class A]] 7 100.00% 100.00% [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]] 101 98.02%[3943, 10076] 100.00% [[_homogeneous, class G], _rational, _Riccati] 18 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _Riccati] 10 100.00% 100.00% [[_1st_order, _with_symmetry_[F(x),G(y)]], _Riccati] 1 100.00% 100.00% [[_1st_order, _with_symmetry_[F(x),G(y)]], [_Abel, 2nd type, class A]] 1 100.00% 100.00% [_exact, _rational, [_Abel, 2nd type, class B]] 14 100.00% 100.00% [_exact, [_Abel, 2nd type, class B]] 2 100.00% 100.00% [_exact, [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] 6 100.00% 100.00% [_exact, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]] 2 100.00% 100.00% [_exact, _Bernoulli] 6 100.00% 100.00% [[_homogeneous, class A], _exact, _rational, _Bernoulli] 4 100.00% 100.00% [_rational, [_Abel, 2nd type, class C]] 12 83.33%[4409, 4454] 83.33%[4409, 4454] [[_homogeneous, class G], _rational] 69 100.00% 97.10%[3655, 6067] [[_homogeneous, class D], _rational, [_Abel, 2nd type, class B]] 2 100.00% 100.00% [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati] 14 100.00% 100.00% [_rational, _Riccati] 100 94.00%[9610, 9641, 9649, 9658, 9662, 9663] 97.00%[9658, 9662, 9663] [[_3rd_order, _linear, _nonhomogeneous]] 51 100.00% 100.00% [[_high_order, _missing_y]] 18 94.44%[9165] 94.44%[9165] [[_3rd_order, _exact, _linear, _nonhomogeneous]] 4 100.00% 100.00% [[_high_order, _exact, _linear, _nonhomogeneous]] 5 100.00% 100.00% [[_homogeneous, class C], _exact, _rational, [_Abel, 2nd type, class A]] 19 100.00% 100.00% [_exact, [_Abel, 2nd type, class A]] 1 100.00% 100.00% [[_1st_order, _with_linear_symmetries], [_Abel, 2nd type, class A]] 2 100.00% 100.00% [[_Riccati, _special]] 14 100.00% 100.00% [_Abel] 25 76.00%[1704, 2843, 7628, 7629, 7630, 7631] 76.00%[1704, 2843, 7628, 7629, 7630, 7631] [_Laguerre] 33 100.00% 100.00% [_Laguerre, [_2nd_order, _linear, _with_symmetry_[0,F(x)]]] 4 100.00% 100.00% [_Bessel] 15 100.00% 100.00% [_rational, _Abel] 21 95.24%[1897] 100.00% [_exact, _rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]] 9 100.00% 100.00% [[_1st_order, _with_symmetry_[F(x)*G(y),0]], [_Abel, 2nd type, class B]] 1 100.00% 100.00% [[_homogeneous, class C], [_Abel, 2nd type, class C], _dAlembert] 3 100.00% 100.00% [[_homogeneous, class G], _exact, _rational, [_Abel, 2nd type, class B]] 6 100.00% 100.00% [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] 3 100.00% 100.00% [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] 10 100.00% 100.00% [[_3rd_order, _exact, _nonlinear]] 2 50.00%[9420] 50.00%[9420] [_Jacobi] 30 100.00% 100.00% [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]], [_Abel, 2nd type, class B]] 5 100.00% 100.00% [[_2nd_order, _quadrature]] 32 100.00% 96.88%[6551] [[_3rd_order, _quadrature]] 3 100.00% 100.00% [[_homogeneous, class D], _Bernoulli] 3 100.00% 100.00% [[_homogeneous, class G], _exact] 1 100.00% 100.00% [_exact, [_1st_order, _with_symmetry_[F(x)*G(y),0]]] 5 100.00% 100.00% [[_homogeneous, class G], _exact, _rational, _Bernoulli] 8 100.00% 100.00% [_exact, [_1st_order, _with_symmetry_[F(x),G(x)]]] 1 100.00% 100.00% [[_homogeneous, class A], _exact, _rational, _Riccati] 1 100.00% 100.00% [_erf] 4 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _rational, _Clairaut] 10 100.00% 100.00% [[_homogeneous, class D]] 8 100.00% 100.00% [_exact, _rational, _Riccati] 3 100.00% 100.00% [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class B]] 5 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _rational] 22 100.00% 100.00% [[_homogeneous, class D], _rational, _Riccati] 18 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _exact] 2 100.00% 100.00% [[_homogeneous, class C], _exact, _dAlembert] 3 100.00% 100.00% [_exact, _rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]], [_Abel, 2nd type, class A]] 1 100.00% 100.00% [[_homogeneous, class D], _rational, [_Abel, 2nd type, class A]] 2 100.00% 100.00% [_rational, [_Abel, 2nd type, class A]] 37 27.03%[3165, 7783, 7785, 9912, 9916, 9943, 9959, 9977, 9978, 9995, 9997, 9998, 10002, 10004, 10007, 10020, 10051, 10052, 10053, 10055, 10056, 10057, 10058, 10059, 10060, 10077, 10079] 48.65%[3165, 7783, 7785, 9912, 9916, 9977, 9978, 9998, 10004, 10007, 10020, 10051, 10052, 10055, 10056, 10057, 10058, 10059, 10079] [[_homogeneous, class G], _dAlembert] 5 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] 3 100.00% 100.00% [[_homogeneous, class D], _rational, _Bernoulli] 23 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _dAlembert] 45 75.56%[3743, 3744, 3745, 3766, 3797, 6058, 6060, 6062, 6121, 6125, 6501] 100.00% [[_homogeneous, class G], _Abel] 4 100.00% 100.00% [[_homogeneous, class G], _Chini] 4 100.00% 100.00% [_Chini] 3 0.00%[2846, 3134, 7636] 0.00%[2846, 3134, 7636] [_rational, [_Riccati, _special]] 9 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _rational, _Riccati] 2 100.00% 100.00% [[_homogeneous, class D], _Riccati] 20 100.00% 100.00% [[_homogeneous, class G], _rational, [_Riccati, _special]] 4 100.00% 100.00% [[_homogeneous, class G], _Riccati] 4 100.00% 100.00% [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]], [_Abel, 2nd type, class C]] 5 100.00% 100.00% [[_homogeneous, class G], _rational, [_Abel, 2nd type, class A]] 3 100.00% 100.00% [[_homogeneous, class C], _rational, [_Abel, 2nd type, class C], _dAlembert] 1 100.00% 100.00% [[_homogeneous, class A], _rational, [_Abel, 2nd type, class C], _dAlembert] 4 100.00% 100.00% [_exact, _rational, _Bernoulli] 1 100.00% 100.00% [[_homogeneous, class G], _rational, [_Abel, 2nd type, class C]] 5 100.00% 100.00% [[_Abel, 2nd type, class C]] 7 71.43%[3335, 7849] 71.43%[3335, 7849] [[_homogeneous, class C], _rational] 7 100.00% 100.00% [_exact, _rational, [_1st_order, _with_symmetry_[F(x),G(x)]]] 2 100.00% 100.00% [_rational, [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] 16 100.00% 87.50%[3642, 8028] unknown 7 71.43%[7920, 9385] 0.00%[3472, 4272, 7649, 7920, 7932, 9385, 9414] [_dAlembert] 17 100.00% 100.00% [_rational, _dAlembert] 11 90.91%[8010] 100.00% [[_homogeneous, class G], _rational, _dAlembert] 7 100.00% 100.00% [[_homogeneous, class G], _rational, _Clairaut] 4 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _rational, _dAlembert] 10 100.00% 100.00% [[_homogeneous, class C], _rational, _dAlembert] 9 100.00% 100.00% [_rational, [_1st_order, _with_symmetry_[F(x),G(y)]]] 14 100.00% 92.86%[3702] [[_homogeneous, class G], _Clairaut] 1 100.00% 100.00% [_Clairaut] 7 100.00% 85.71%[3845] [[_homogeneous, class A], _exact, _dAlembert] 2 100.00% 100.00% [[_homogeneous, class D], _exact, _rational, _Bernoulli] 1 100.00% 100.00% [[_homogeneous, class D], _exact, _rational, [_Abel, 2nd type, class A]] 2 100.00% 100.00% [[_high_order, _quadrature]] 6 100.00% 100.00% [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] 8 50.00%[4160, 4331, 4332, 4333] 100.00% [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] 53 94.34%[5347, 6086, 6087] 96.23%[6086, 6087] [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] 24 95.83%[4158] 95.83%[9387] [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] 4 100.00% 100.00% [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] 6 100.00% 100.00% [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] 15 93.33%[6464] 100.00% [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] 2 0.00%[4159, 5493] 100.00% [_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] 7 100.00% 100.00% [[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] 3 100.00% 100.00% [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] 3 100.00% 100.00% [[_homogeneous, class G], _rational, _Abel] 2 100.00% 100.00% [[_elliptic, _class_I]] 2 100.00% 100.00% [[_elliptic, _class_II]] 2 100.00% 100.00% [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear]] 1 100.00% 100.00% [_Hermite] 12 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _Chini] 2 100.00% 100.00% [_exact, [_1st_order, _with_symmetry_[F(x),G(y)]]] 2 100.00% 100.00% [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] 1 100.00% 100.00% [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] 2 100.00% 100.00% [[_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati] 36 100.00% 91.67%[8313, 8369, 8370] [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] 3 100.00% 100.00% [[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] 2 100.00% 100.00% [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] 11 100.00% 100.00% [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] 1 100.00% 100.00% [[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] 1 100.00% 100.00% [[_1st_order, _with_symmetry_[F(x)*G(y),0]], [_Abel, 2nd type, class C]] 3 100.00% 100.00% [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] 2 100.00% 100.00% [[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] 1 100.00% 100.00% [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] 2 100.00% 100.00% [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] 2 100.00% 100.00% [[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] 2 100.00% 100.00% [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] 2 100.00% 100.00% [[_Bessel, _modiﬁed]] 1 100.00% 100.00% [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] 10 10.00%[6354, 6355, 9180, 9243, 9265, 9269, 9271, 9274, 9275] 20.00%[6354, 9180, 9243, 9265, 9269, 9271, 9274, 9275] [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] 3 100.00% 100.00% [[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] 2 50.00%[9205] 50.00%[9205] [_Liouville, [_2nd_order, _reducible, _mu_xy]] 3 100.00% 100.00% [_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] 8 100.00% 100.00% [_Chini, [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] 2 100.00% 100.00% [[_1st_order, _with_exponential_symmetries], _rational, [_Abel, 2nd type, class B]] 1 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _rational, [_Abel, 2nd type, class B]] 1 100.00% 100.00% [[_homogeneous, class C], _rational, [_Abel, 2nd type, class B]] 1 100.00% 100.00% [[_homogeneous, class G], [_Abel, 2nd type, class C]] 1 100.00% 100.00% [[_1st_order, _with_linear_symmetries], [_Abel, 2nd type, class C]] 7 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _rational, [_Abel, 2nd type, class C]] 8 100.00% 100.00% [[_Abel, 2nd type, class C], [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] 4 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _Abel] 13 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _rational, [_Abel, 2nd type, class A]] 7 100.00% 100.00% [[_1st_order, _with_symmetry_[F(x),G(y)]], [_Abel, 2nd type, class C]] 2 100.00% 100.00% [[_homogeneous, class D], _rational, _Abel] 3 100.00% 100.00% [[_homogeneous, class C], _rational, _Abel] 3 100.00% 100.00% [_rational, [_Abel, 2nd type, class C], [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]] 3 100.00% 100.00% [[_homogeneous, class D], _rational, [_Abel, 2nd type, class C]] 1 100.00% 100.00% [[_homogeneous, class C], _Abel] 3 100.00% 100.00% [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class C]] 6 100.00% 100.00% [[_1st_order, _with_symmetry_[F(x),G(x)]], _Abel] 5 100.00% 100.00% [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], _Abel] 10 100.00% 100.00% [[_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class C]] 2 100.00% 100.00% [[_1st_order, _with_symmetry_[F(x),G(y)]], _Abel] 2 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _rational, _Abel] 1 100.00% 100.00% [_Titchmarsh] 1 0.00%[8595] 0.00%[8595] [_ellipsoidal] 2 100.00% 100.00% [_Jacobi, [_2nd_order, _linear, _with_symmetry_[0,F(x)]]] 1 100.00% 100.00% [_Halm] 2 100.00% 100.00% [[_3rd_order, _fully, _exact, _linear]] 4 100.00% 100.00% [[_high_order, _fully, _exact, _linear]] 1 100.00% 100.00% [[_Painleve, 1st]] 1 0.00%[9172] 0.00%[9172] [[_Painleve, 2nd]] 1 0.00%[9175] 0.00%[9175] [[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] 1 0.00%[9206] 0.00%[9206] [[_2nd_order, _with_potential_symmetries]] 2 100.00% 100.00% [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] 6 100.00% 100.00% [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] 1 100.00% 100.00% [[_2nd_order, _reducible, _mu_xy]] 2 50.00%[9367] 50.00%[9367] [[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] 1 0.00%[9292] 0.00%[9292] [[_Painleve, 4th]] 1 0.00%[9316] 0.00%[9316] [[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] 1 100.00% 100.00% [[_Painleve, 3rd]] 1 0.00%[9340] 0.00%[9340] [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] 1 100.00% 100.00% [[_Painleve, 5th]] 1 0.00%[9376] 0.00%[9376] [[_Painleve, 6th]] 1 0.00%[9386] 0.00%[9386] [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] 1 0.00%[9395] 0.00%[9395] [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]] 1 0.00%[9400] 0.00%[9400] [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1]] 1 0.00%[9404] 0.00%[9404] [[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] 6 33.33%[9417, 9418, 9419, 9434] 33.33%[9417, 9418, 9419, 9434] [[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] 1 100.00% 100.00% [[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] 1 100.00% 100.00% [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] 2 100.00% 100.00% [[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] 2 50.00%[9429] 50.00%[9429] [[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]] 1 100.00% 100.00% 62 100.00% 100.00% [[_1st_order, _with_linear_symmetries], [_Abel, 2nd type, class B]] 1 100.00% 100.00%

##### Performance using own ODE types classiﬁcation

The following gives the ODE types used and a short description of each type.

1. polynomial. First order Polynomial type such as $$y'=\frac {-6x+y-3}{2x-y-1}$$.
2. quadrature. First order quadrature type ode such as $$y'=1$$.
3. linear. First order linear ode such as $$y'+y=x$$.
4. separable. First order separable such as $$y'=xy$$.
5. riccati. First order Riccati such as $$y'=x^2-y^2$$.
6. exact or exactWithIntegrationFactor. First order exact such as $$(x^2+y) \mathrm {d}x+(e^y+x)\mathrm {d}y=0$$.
7. homogeneous. First order homogeneous such as $$(x+y)y'=x-y$$.
8. bernoulli. First order Bernoulli such as $$2xyy'=x^2+y^2$$.
9. dAlembert. First order dAlembert such as $$y'=\sqrt {x+y}$$.
10. clairaut. First order Clairaut such as $$y=xy'+(y')^3$$.
11. polynomial. First order Polynomial type such as $$y'=\frac {-6x+y-3}{2x-y-1}$$.
12. isobaric. First order isobaric such as $$2 x^3 y'=1+\sqrt {1+ x^2 y}$$.
13. abelFirstKind. First order Abel such as $$y'=e^{-5 x}+y^3$$.
14. system of linear ODEs. These are system of ﬁrst order odes.
15. ﬁrst order ode series method. Ordinary point. First order ode solved using series method. Ordinary point.
16. ﬁrst order ode series method. Regular singular point. First order ode solved using series method. Regular singular point.
17. second order constant coeﬃcients. standard second order ode with constant coeﬃcients.
18. second order Euler ode (type 7). standard second order Euler ode such as $$x^2 y''+x y+y=0$$.
19. second order quadrature. Such as $$A(x) y'=F(x)$$.
20. second order missing y (type 3). Such as $$x^2 y''+x y'=\sin x$$.
21. second order Airy ode. Such as $$y''-xy=0$$ or $$y''+y'-xy=f(x)$$.
22. second order type 5. Such as $$3 y''-y^3=5$$.
23. second order type 6. Such as $$y^2 y''+y^2=5$$.
24. second order with basic integrating factor (type 13). Such as $$y''+4 x y'+(2+4 x^2)y=0$$.
25. second order. Tranformation on independent variable. p=0 method. (type 15). Transformation on independent variable.
26. second order. Tranformation on independent variable. q=constant method. (type 8). Transformation on independent variable.
27. second order. Tranformation on dependent variable. special case method. (type 9). Transformation on dependent variable using $$y(x)=v(x)x^n$$.
28. second order type 11. Such as $$x y y''+x (y')^2 - y y'=0$$.
29. kovacic type. Any second order ODE which is solvable using Kovacic algorithm.
30. reduction of order. Second order ode where one solution is given.
31. second order series method. Ordinary point. Second order solved using series method. Ordinary point.
32. second order series method. Regular singular point. Complex roots. Second order solved using series method. Regular singular point. Complex roots.
33. second order series method. Regular singular point. Diﬀerence is integer. Second order solved using series method. Regular singular point. Diﬀerence between roots is integer.
34. second order series method. Regular singular point. Diﬀerence not integer. Second order solved using series method. Regular singular point. Diﬀerence between roots is not integer.
35. second order series method. Regular singular point. Repeated root. Second order solved using series method. Regular singular point. root is repeated.
36. second order series method. Irregular singular point. Second order solved using Asymptotic methods. Irregular singular point.
37. second order ode. Lagrange adjoint equation method (type 16). Second order solved using Lagrange adjoint method such as $$y''+x^2 y'+y=0$$.
38. second order transformation, Reduction to Lower Order. (type 17). Such as $$y (y'')^2 + *y')^3=0$$.
39. second order ode. Liouville ode (type 18). Such as $$y''+(3+x+\sin x)y'+(1+y) (y')^2 = 0$$.
40. second order ode. Liouville transformation (type 19). Such as $$y''-\frac {1}{\sqrt {x}}+\frac {1}{4 x^2}(x+\sqrt {x}-8) y=0$$.
41. Higher order linear constant coeﬃcients ODE.
42. Higher order ODE, non constant coeﬃcients of type Euler. Higher order but Euler type.
43. second order ode with degree not 1. Any second order of degree not one.
44. second order ode. Lagrange adjoint equation method (type 16). Uses transformation to adjoint form.
45. unknown or NONE Any unknown ode type.

The following table gives count of the number of ODE’s for each ODE type, where the ODE type here is as classiﬁed by my own ode solver, and the percentage of solved ODE’s of that type for each CAS. It also gives a direct link to the ODE’s that failed if any.

 Type of ODE Count Mathematica Maple quadrature 160 100.00% 100.00% linear 747 99.73%[5416, 5511] 99.73%[5416, 5511] separable 730 99.04%[885, 944, 2513, 3741, 3758, 3767, 7911] 100.00% homogeneous 455 99.12%[3703, 5008, 5501, 5509] 99.78%[5509] homogeneousTypeC 22 100.00% 100.00% exact 218 98.17%[119, 146, 2628, 4481] 98.17%[3472, 4272, 4481, 7932] exactWithIntegrationFactor 186 99.46%[7920] 97.31%[2581, 3642, 7649, 7920, 8028] bernoulli 261 99.23%[4607, 6377] 100.00% riccati 548 73.72%[958, 1697, 1698, 1700, 1701, 1702, 2198, 2795, 2815, 2817, 2830, 3131, 3878, 6592, 7691, 9592, 9596, 9597, 9598, 9603, 9610, 9616, 9618, 9619, 9620, 9641, 9649, 9658, 9662, 9663, 9672, 9689, 9693, 9695, 9696, 9697, 9702, 9709, 9710, 9716, 9717, 9718, 9719, 9720, 9733, 9734, 9735, 9736, 9737, 9738, 9739, 9740, 9741, 9744, 9745, 9753, 9757, 9758, 9760, 9761, 9762, 9763, 9764, 9770, 9771, 9773, 9774, 9775, 9776, 9777, 9782, 9783, 9788, 9789, 9793, 9794, 9795, 9798, 9802, 9803, 9805, 9806, 9811, 9812, 9813, 9814, 9817, 9819, 9820, 9823, 9826, 9828, 9829, 9832, 9835, 9837, 9838, 9841, 9844, 9846, 9847, 9850, 9854, 9855, 9856, 9860, 9861, 9863, 9864, 9866, 9868, 9869, 9870, 9871, 9872, 9873, 9874, 9875, 9877, 9878, 9879, 9880, 9881, 9882, 9883, 9884, 9885, 9886, 9889, 9890, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902, 9903, 9904, 9905, 9906] 83.03%[958, 1697, 1700, 1701, 1702, 2198, 2815, 2817, 2830, 3878, 6592, 7691, 8313, 8369, 8370, 9596, 9603, 9616, 9618, 9620, 9658, 9662, 9663, 9675, 9683, 9689, 9693, 9695, 9697, 9702, 9718, 9733, 9736, 9737, 9738, 9740, 9744, 9758, 9760, 9771, 9773, 9789, 9802, 9804, 9811, 9819, 9820, 9823, 9828, 9829, 9832, 9837, 9838, 9841, 9846, 9847, 9850, 9854, 9855, 9860, 9861, 9863, 9864, 9866, 9868, 9869, 9870, 9871, 9872, 9873, 9874, 9875, 9877, 9880, 9881, 9882, 9883, 9885, 9889, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902, 9903, 9904, 9905, 9906] clairaut 74 100.00% 98.65%[3845] dAlembert 147 89.12%[2491, 3743, 3744, 3745, 3752, 3766, 3770, 3797, 6058, 6060, 6062, 6121, 6125, 6349, 6501, 8010] 99.32%[3752] isobaric 199 93.97%[2720, 2722, 2723, 2727, 2888, 3532, 3782, 3786, 6054, 7963, 8465, 8474] 95.48%[3487, 3532, 3655, 6067, 7948, 7963, 8117, 8465, 8474] ﬁrst order special form ID 1 5 100.00% 100.00% polynomial 92 97.83%[3943, 10076] 100.00% abelFirstKind 78 92.31%[1704, 1897, 2843, 7628, 7629, 7631] 93.59%[1704, 2843, 7628, 7629, 7631] diﬀerentialType 67 100.00% 100.00% ﬁrst order ode series method. Ordinary point 42 100.00% 92.86%[6547, 6548, 6550] ﬁrst order ode series method. Regular singular point 9 100.00% 88.89%[4749] ﬁrst order ode series method. Irregular singular point 3 100.00% 0.00%[408, 409, 5665] ﬁrst_order_laplace 42 100.00% 100.00% system of linear ODEs 403 99.26%[5351, 5790, 9484] 99.26%[5351, 5790, 9484] second_order_laplace 159 100.00% 99.37%[5760] reduction_of_order 90 96.67%[1138, 5590, 5591] 100.00% second_order_ode_quadrature 20 100.00% 100.00% second_order_linear_constant_coeﬀ 685 100.00% 100.00% second_order_airy 23 100.00% 100.00% second_order_euler_ode 164 100.00% 100.00% second_order_change_of_variable_on_y_general_n 51 96.08%[8902, 8998] 100.00% second_order_integrable_as_is 69 86.96%[4159, 4160, 4331, 4332, 4333, 5493, 9205, 9395, 9400] 95.65%[9205, 9395, 9400] second_order_ode_can_be_made_integrable 20 85.00%[5347, 6086, 6087] 90.00%[6086, 6087] second_order_ode_solved_by_an_integrating_factor 17 100.00% 100.00% second_order_change_of_variable_on_x_p1_zero_method 65 96.92%[8654, 9023] 100.00% second_order_ode_lagrange_adjoint_equation_method 17 100.00% 100.00% second_order_nonlinear_solved_by_mainardi_lioville_method 10 100.00% 100.00% second_order_change_of_variable_on_y_n_one_case 36 97.22%[8706] 100.00% second_order_bessel_ode 112 100.00% 100.00% second_order_ode_missing_x 128 89.06%[4158, 9190, 9191, 9195, 9197, 9215, 9216, 9218, 9223, 9241, 9287, 9289, 9404, 9415] 88.28%[9190, 9191, 9195, 9197, 9215, 9216, 9218, 9223, 9241, 9287, 9288, 9289, 9387, 9404, 9415] second_order_ode_missing_y 69 91.30%[6070, 6103, 6105, 6459, 6464, 9406] 100.00% second order series method. Ordinary point 456 100.00% 100.00% second order series method. Regular singular point. Diﬀerence not integer 188 100.00% 100.00% second order series method. Regular singular point. Repeated root 167 100.00% 100.00% second order series method. Regular singular point. Diﬀerence is integer 260 100.00% 100.00% second order series method. Irregular singular point 29 93.10%[4502, 5828] 0.00%[1794, 1797, 1805, 2032, 2411, 4193, 4206, 4210, 4495, 4502, 4709, 4768, 4773, 4803, 4811, 4835, 4836, 4837, 5289, 5688, 5690, 5696, 5706, 5707, 5828, 5831, 5839, 5864, 5865] second order series method. Regular singular point. Complex roots 24 87.50%[4741, 4742, 4743] 100.00% second_order_ode_high_degree 1 100.00% 100.00% Higher order linear constant coeﬃcients ODE 300 99.00%[9123, 9126, 9155] 100.00% Higher order ODE, non constant coeﬃcients of type Euler 41 100.00% 100.00% higher_order_laplace 9 100.00% 100.00%

These are direct links to the ode problems based on status of solving.

Not solved by Mathematica

Not solved by Maple

Solved by Maple but not by Mathematica

(216) [119, 146, 885, 944, 1041, 1069, 1105, 1138, 1698, 1897, 2491, 2513, 2628, 2720, 2722, 2723, 2727, 2795, 2888, 3131, 3703, 3741, 3743, 3744, 3745, 3753, 3758, 3766, 3767, 3770, 3782, 3786, 3791, 3797, 3943, 4158, 4159, 4160, 4331, 4332, 4333, 4607, 4741, 4742, 4743, 5008, 5060, 5347, 5493, 5501, 5590, 5591, 6054, 6058, 6060, 6062, 6070, 6103, 6105, 6121, 6125, 6343, 6349, 6355, 6377, 6425, 6429, 6430, 6459, 6464, 6501, 6706, 6798, 6800, 7186, 7220, 7222, 7911, 8010, 8069, 8442, 8612, 8654, 8662, 8663, 8679, 8706, 8885, 8902, 8941, 8998, 9023, 9079, 9095, 9123, 9126, 9131, 9151, 9155, 9182, 9257, 9358, 9359, 9397, 9398, 9406, 9512, 9515, 9592, 9597, 9598, 9610, 9619, 9641, 9649, 9672, 9696, 9709, 9710, 9716, 9717, 9719, 9720, 9734, 9735, 9739, 9741, 9745, 9753, 9757, 9761, 9762, 9763, 9764, 9770, 9774, 9775, 9776, 9777, 9782, 9783, 9788, 9793, 9794, 9795, 9798, 9803, 9805, 9806, 9812, 9813, 9814, 9817, 9826, 9835, 9844, 9856, 9878, 9879, 9884, 9886, 9890, 9910, 9911, 9914, 9915, 9919, 9923, 9924, 9928, 9930, 9931, 9936, 9940, 9941, 9942, 9943, 9946, 9953, 9955, 9958, 9959, 9963, 9964, 9971, 9987, 9988, 9995, 9997, 10002, 10009, 10013, 10019, 10022, 10025, 10030, 10033, 10037, 10045, 10046, 10047, 10050, 10053, 10060, 10061, 10064, 10067, 10068, 10071, 10076, 10077, 10081, 10089, 10090, 10097, 10098]

Solved by Mathematica but not by Maple

(96) [408, 409, 1794, 1797, 1805, 2032, 2411, 2581, 2874, 2887, 3364, 3418, 3472, 3487, 3642, 3655, 3690, 3691, 3702, 3790, 3845, 4193, 4206, 4210, 4214, 4215, 4272, 4406, 4495, 4709, 4747, 4748, 4749, 4768, 4773, 4803, 4811, 4835, 4836, 4837, 5080, 5289, 5485, 5665, 5688, 5690, 5696, 5706, 5707, 5760, 5831, 5839, 5864, 5865, 6067, 6471, 6472, 6473, 6477, 6478, 6480, 6488, 6547, 6548, 6550, 6551, 6552, 6553, 6554, 7649, 7932, 7948, 8028, 8032, 8117, 8123, 8140, 8288, 8313, 8369, 8370, 8500, 9089, 9161, 9261, 9277, 9284, 9285, 9288, 9300, 9387, 9413, 9414, 9675, 9683, 9804]

Both systems unable to solve