## 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 here.

The current number of diﬀerential equations is [10997]. 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 2023.1 94.689 10413 584 Mathematica 13.3.1 93.407 10272 725

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 2023.1 0.138 330.48 25.238 3634236 Mathematica 13.3.1 2.965 521.32 543.363 5732920

The problem which Mathematica produced largest leaf size of $$1763961$$ is 8969.

The problem which Maple produced largest leaf size of $$949416$$ is 11040.

The problem which Mathematica used most CPU time of $$174.413$$ seconds is 5443.

The problem which Maple used most CPU time of $$134.110$$ seconds is 6085.

#### 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] 520 99.04%[885, 3757, 3766, 10779, 10781] 99.62%[6549, 10646] [[_linear, ‘class A‘]] 177 100.00% 98.31%[6546, 6547, 10500] [_separable] 832 99.28%[944, 2513, 5510, 7910, 10363, 10397] 99.40%[408, 409, 5510, 5664, 10397] [_Riccati] 308 53.90%[958, 1697, 1698, 1700, 1701, 1702, 2198, 2795, 2815, 2817, 2830, 3130, 3877, 6591, 7690, 9588, 9592, 9593, 9594, 9599, 9612, 9614, 9615, 9616, 9668, 9685, 9689, 9691, 9692, 9693, 9694, 9697, 9698, 9705, 9706, 9712, 9713, 9714, 9715, 9716, 9729, 9731, 9732, 9733, 9734, 9735, 9736, 9737, 9740, 9741, 9749, 9753, 9754, 9756, 9757, 9758, 9759, 9760, 9766, 9767, 9769, 9770, 9771, 9772, 9773, 9778, 9779, 9784, 9785, 9789, 9790, 9791, 9794, 9798, 9799, 9801, 9802, 9803, 9807, 9808, 9809, 9810, 9813, 9815, 9816, 9819, 9822, 9824, 9825, 9828, 9831, 9833, 9834, 9837, 9840, 9842, 9843, 9846, 9850, 9851, 9852, 9854, 9856, 9857, 9859, 9860, 9862, 9863, 9864, 9865, 9866, 9867, 9868, 9869, 9870, 9871, 9873, 9874, 9875, 9876, 9877, 9878, 9879, 9880, 9881, 9882, 9885, 9886, 9889, 9890, 9891, 9892, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902] 71.43%[958, 1697, 1700, 1701, 1702, 2198, 2815, 2817, 2830, 3877, 6591, 7690, 9592, 9599, 9612, 9614, 9616, 9671, 9679, 9685, 9689, 9691, 9693, 9698, 9714, 9722, 9729, 9732, 9733, 9734, 9736, 9740, 9754, 9756, 9767, 9769, 9785, 9798, 9800, 9807, 9815, 9816, 9819, 9824, 9825, 9828, 9833, 9834, 9837, 9842, 9843, 9846, 9850, 9851, 9856, 9857, 9859, 9860, 9862, 9864, 9865, 9866, 9867, 9868, 9869, 9870, 9871, 9873, 9876, 9877, 9878, 9879, 9881, 9885, 9889, 9890, 9891, 9892, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902] [[_homogeneous, ‘class G‘]] 61 95.08%[2723, 2727, 10800] 93.44%[3486, 3531, 7947, 7962] [_linear] 488 99.59%[5415, 10647] 99.59%[4748, 5415] [[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] 21 100.00% 100.00% [[_homogeneous, ‘class A‘], _rational, _Bernoulli] 71 100.00% 100.00% [[_homogeneous, ‘class A‘], _dAlembert] 125 99.20%[10194] 100.00% [[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] 72 98.61%[5500] 100.00% [[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] 48 100.00% 100.00% [[_homogeneous, ‘class A‘], _rational, _dAlembert] 175 98.86%[5007, 5508] 99.43%[5508] [[_homogeneous, ‘class C‘], _dAlembert] 62 91.94%[2491, 3751, 3769, 6348, 10222] 100.00% [[_homogeneous, ‘class C‘], _Riccati] 18 100.00% 100.00% [[_homogeneous, ‘class G‘], _rational, _Bernoulli] 52 100.00% 100.00% [_Bernoulli] 89 97.75%[4606, 6376] 100.00% [[_1st_order, _with_linear_symmetries], _Bernoulli] 4 100.00% 100.00% [[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] 46 100.00% 100.00% [‘y=_G(x,y’)‘] 119 63.03%[133, 485, 959, 961, 962, 964, 966, 968, 1703, 1706, 1707, 2854, 2859, 2875, 2954, 3502, 3707, 3752, 3778, 3790, 4442, 4486, 5795, 6309, 6499, 7654, 7659, 7662, 7700, 7949, 7974, 8038, 8039, 8081, 8084, 8088, 8109, 8440, 10201, 10206, 10386, 10866, 10872, 10891] 57.98%[133, 485, 959, 961, 962, 964, 966, 968, 1703, 1706, 1707, 2581, 2854, 2859, 2873, 2875, 2886, 2954, 3363, 3502, 3707, 3778, 3789, 4405, 4442, 4486, 5795, 6309, 6499, 7654, 7659, 7662, 7700, 7949, 7974, 8030, 8038, 8039, 8081, 8084, 8088, 8091, 8109, 8121, 10206, 10386, 10866, 10870, 10872, 10891] [[_1st_order, _with_linear_symmetries]] 94 92.55%[2720, 2722, 3781, 3785, 6043, 6053, 10197] 98.94%[8115] [[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] 28 100.00% 100.00% [_exact, _rational] 33 96.97%[119] 96.97%[10588] [_exact] 65 98.46%[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‘]] 3 100.00% 100.00% [[_homogeneous, ‘class G‘], _exact, _rational] 4 50.00%[146, 10592] 100.00% [[_2nd_order, _missing_x]] 486 96.50%[6654, 9186, 9187, 9190, 9191, 9193, 9211, 9212, 9214, 9219, 9237, 9283, 9285, 9408, 9411, 10571, 10572] 96.50%[6654, 9186, 9187, 9190, 9191, 9193, 9211, 9212, 9214, 9219, 9237, 9283, 9284, 9285, 9411, 10571, 10572] [[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] 62 100.00% 100.00% [[_Emden, _Fowler]] 250 99.60%[5590] 96.40%[2032, 4209, 4708, 4802, 4834, 4835, 5830, 5863, 11058] [[_2nd_order, _exact, _linear, _homogeneous]] 190 99.47%[10910] 97.89%[4836, 5706, 5864, 11059] [[_2nd_order, _missing_y]] 95 94.74%[6102, 6104, 6458, 9402, 10313] 97.89%[5689, 6551] [[_2nd_order, _with_linear_symmetries]] 2196 95.81%[1105, 1138, 4501, 4740, 4741, 4742, 5059, 5064, 5589, 5827, 6342, 6424, 6425, 6428, 6429, 6433, 6435, 6534, 6797, 6799, 7185, 7219, 7221, 8597, 8604, 8606, 8608, 8609, 8610, 8616, 8650, 8651, 8653, 8655, 8659, 8660, 8661, 8677, 8704, 8735, 8783, 8790, 8794, 8814, 8856, 8883, 8939, 8985, 8996, 9016, 9017, 9018, 9020, 9180, 9223, 9233, 9234, 9235, 9238, 9240, 9241, 9242, 9247, 9248, 9252, 9253, 9255, 9259, 9294, 9317, 9337, 9352, 9354, 9355, 9386, 9393, 9394, 9395, 9406, 9407, 10085, 10086, 10094, 10292, 10293, 10311, 10702, 10901, 10902, 10904, 10916, 11064] 96.77%[1794, 1797, 1805, 2411, 4192, 4205, 4494, 4501, 4767, 4772, 4810, 5064, 5288, 5687, 5695, 5827, 5838, 6425, 6433, 6435, 6534, 8597, 8604, 8606, 8608, 8609, 8616, 8650, 8651, 8653, 8655, 8659, 8735, 8783, 8790, 8794, 8814, 8856, 8985, 9016, 9017, 9018, 9020, 9180, 9223, 9233, 9234, 9235, 9238, 9240, 9241, 9242, 9247, 9248, 9252, 9255, 9257, 9259, 9294, 9317, 9337, 9352, 9395, 9406, 9407, 9409, 10311, 10702, 10904, 10916, 11064] [[_2nd_order, _linear, _nonhomogeneous]] 656 98.48%[1162, 1186, 6705, 8654, 10457, 10900, 10903, 10933, 11004, 11006] 96.65%[1162, 1186, 4213, 4214, 4746, 4747, 5759, 6470, 6471, 6472, 6476, 6477, 6479, 6487, 6552, 6553, 8654, 10900, 10903, 10933, 11004, 11006] [[_2nd_order, _exact, _linear, _nonhomogeneous]] 44 100.00% 100.00% system of linear ODEs 547 96.16%[5350, 5788, 5789, 9465, 9480, 9490, 9493, 9494, 9495, 9496, 9497, 9502, 9503, 9504, 9507, 9508, 9509, 9510, 9511, 9512, 9514] 96.53%[5350, 5788, 5789, 5965, 9465, 9480, 9490, 9493, 9494, 9495, 9496, 9497, 9502, 9503, 9507, 9509, 9510, 9512, 9514] [_Gegenbauer] 65 100.00% 100.00% [[_high_order, _missing_x]] 100 97.00%[9119, 9122, 9151] 100.00% [[_3rd_order, _missing_x]] 101 100.00% 100.00% [[_3rd_order, _missing_y]] 38 100.00% 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)]‘]] 55 92.73%[8652, 8900, 9021, 10093] 98.18%[5705] [_Lienard] 48 100.00% 100.00% [[_homogeneous, ‘class A‘], _rational, _Riccati] 28 100.00% 100.00% [‘x=_G(y,y’)‘] 12 66.67%[550, 2204, 5429, 8150] 66.67%[550, 2204, 5429, 8150] [[_Abel, ‘2nd type‘, ‘class B‘]] 15 26.67%[553, 1046, 7829, 9920, 9923, 9943, 9944, 9945, 9965, 9978, 9983] 40.00%[553, 1046, 7829, 9923, 9943, 9944, 9945, 9965, 9978] [_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] 8 100.00% 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] 100 85.00%[1039, 1075, 2609, 2683, 2684, 3637, 3806, 5357, 8058, 8060, 8067, 8463, 8472, 10180, 10586] 79.00%[1039, 1075, 2609, 2683, 2684, 3417, 3637, 3689, 3690, 3806, 5357, 8058, 8060, 8286, 8463, 8472, 8490, 8498, 10180, 10212, 10586] [_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] 80 36.25%[710, 1041, 6356, 6460, 7636, 7667, 7781, 7946, 8153, 8154, 8413, 8415, 9170, 9173, 9174, 9178, 9181, 9183, 9184, 9192, 9194, 9198, 9199, 9200, 9203, 9209, 9217, 9218, 9220, 9224, 9250, 9260, 9268, 9277, 9279, 9304, 9307, 9309, 9310, 9313, 9314, 9326, 9332, 9364, 9376, 9377, 9390, 9426, 10890, 10893, 10895] 32.50%[710, 5484, 6356, 6460, 7636, 7667, 7781, 7946, 8153, 8154, 8413, 8415, 9170, 9173, 9174, 9181, 9183, 9184, 9192, 9194, 9198, 9199, 9200, 9203, 9209, 9217, 9218, 9220, 9224, 9250, 9260, 9268, 9273, 9277, 9279, 9280, 9281, 9296, 9304, 9307, 9309, 9310, 9313, 9314, 9326, 9332, 9364, 9376, 9377, 9390, 9426, 10890, 10893, 10895] [_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] 22 100.00% 100.00% [[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] 41 100.00% 100.00% [_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] 12 100.00% 100.00% [[_high_order, _with_linear_symmetries]] 42 83.33%[813, 9115, 9116, 9117, 9118, 9147, 9165] 83.33%[813, 9115, 9116, 9117, 9118, 9157, 9165] [[_3rd_order, _with_linear_symmetries]] 108 84.26%[5063, 9034, 9035, 9036, 9037, 9038, 9039, 9040, 9050, 9051, 9053, 9061, 9066, 9077, 9090, 9091, 9106] 85.19%[5063, 9034, 9035, 9036, 9037, 9038, 9039, 9040, 9050, 9051, 9053, 9061, 9066, 9085, 9090, 9106] [[_high_order, _linear, _nonhomogeneous]] 59 96.61%[9127, 9156] 98.31%[9156] [[_1st_order, _with_linear_symmetries], _Clairaut] 47 97.87%[10208] 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)]‘]] 72 100.00% 100.00% [[_homogeneous, ‘class C‘], _rational, _Riccati] 5 100.00% 100.00% [[_Abel, ‘2nd type‘, ‘class A‘]] 34 14.71%[3167, 3219, 4445, 7785, 7798, 9910, 9911, 9975, 9976, 9977, 9986, 9987, 9988, 9989, 9990, 10004, 10050, 10057, 10058, 10060, 10061, 10063, 10064, 10065, 10066, 10067, 10068, 10069, 10070] 35.29%[3167, 3219, 4445, 7785, 7798, 9975, 9976, 9977, 9986, 9987, 9988, 9989, 9990, 10004, 10050, 10058, 10061, 10065, 10066, 10068, 10069, 10070] [_rational, _Bernoulli] 39 100.00% 100.00% [[_homogeneous, ‘class A‘]] 7 100.00% 100.00% [[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] 112 98.21%[3942, 10072] 100.00% [[_homogeneous, ‘class G‘], _rational, _Riccati] 19 100.00% 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‘]] 15 100.00% 100.00% [_exact, [_Abel, ‘2nd type‘, ‘class B‘]] 4 100.00% 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‘]] 3 100.00% 100.00% [_exact, _Bernoulli] 6 100.00% 100.00% [[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] 5 100.00% 100.00% [_rational, [_Abel, ‘2nd type‘, ‘class C‘]] 12 83.33%[4408, 4453] 83.33%[4408, 4453] [[_homogeneous, ‘class G‘], _rational] 77 100.00% 97.40%[3654, 6066] [[_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] 101 94.06%[9606, 9637, 9645, 9654, 9658, 9659] 97.03%[9654, 9658, 9659] [[_3rd_order, _linear, _nonhomogeneous]] 58 98.28%[10879] 100.00% [[_high_order, _missing_y]] 21 95.24%[9161] 95.24%[9161] [[_3rd_order, _exact, _linear, _nonhomogeneous]] 5 100.00% 100.00% [[_high_order, _exact, _linear, _nonhomogeneous]] 5 100.00% 100.00% [[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] 20 100.00% 100.00% [_exact, [_Abel, ‘2nd type‘, ‘class A‘]] 2 100.00% 100.00% [[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] 2 100.00% 100.00% [[_Riccati, _special]] 18 100.00% 100.00% [_Abel] 26 73.08%[1704, 2843, 7627, 7628, 7629, 7630, 10786] 73.08%[1704, 2843, 7627, 7628, 7629, 7630, 10786] [_Laguerre] 34 100.00% 100.00% [_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] 4 100.00% 100.00% [_Bessel] 17 100.00% 100.00% [_rational, _Abel] 21 95.24%[1897] 100.00% [_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] 10 100.00% 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] 4 100.00% 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]] 11 90.91%[9351] 100.00% [[_3rd_order, _exact, _nonlinear]] 2 50.00%[9416] 50.00%[9416] [_Jacobi] 31 100.00% 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]] 35 97.14%[10850] 97.14%[6550] [[_3rd_order, _quadrature]] 4 100.00% 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] 9 100.00% 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] 14 100.00% 100.00% [[_homogeneous, ‘class D‘]] 13 100.00% 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] 23 100.00% 100.00% [[_homogeneous, ‘class D‘], _rational, _Riccati] 19 100.00% 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‘]] 39 28.21%[3164, 7782, 7784, 9908, 9912, 9939, 9955, 9973, 9974, 9991, 9993, 9994, 9998, 10000, 10003, 10016, 10047, 10048, 10049, 10051, 10052, 10053, 10054, 10055, 10056, 10073, 10075, 10581] 46.15%[3164, 7782, 7784, 9908, 9912, 9973, 9974, 9994, 10000, 10003, 10016, 10047, 10048, 10051, 10052, 10053, 10054, 10055, 10073, 10075, 10581] [[_homogeneous, ‘class G‘], _dAlembert] 4 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] 4 100.00% 100.00% [[_homogeneous, ‘class D‘], _rational, _Bernoulli] 25 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _dAlembert] 49 79.59%[3742, 3743, 3744, 3765, 3796, 6057, 6059, 6120, 6124, 6500] 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, 3133, 7635] 0.00%[2846, 3133, 7635] [_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%[3334, 7848] 71.43%[3334, 7848] [[_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)]‘]] 17 100.00% 100.00% unknown 6 50.00%[7919, 9381, 9730] 0.00%[3471, 7919, 7931, 9381, 9410, 9730] [_dAlembert] 17 100.00% 100.00% [_rational, _dAlembert] 11 90.91%[8009] 100.00% [[_homogeneous, ‘class G‘], _rational, _dAlembert] 8 100.00% 100.00% [[_homogeneous, ‘class G‘], _rational, _Clairaut] 5 100.00% 100.00% [[_1st_order, _with_linear_symmetries], _rational, _dAlembert] 10 100.00% 100.00% [[_homogeneous, ‘class C‘], _rational, _dAlembert] 10 100.00% 100.00% [_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] 14 100.00% 100.00% [[_homogeneous, ‘class G‘], _Clairaut] 2 100.00% 100.00% [_Clairaut] 7 100.00% 85.71%[3834] [[_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‘]] 3 100.00% 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]] 9 55.56%[4159, 4330, 4331, 4332] 100.00% [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] 60 95.00%[5346, 6085, 6086] 100.00% [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] 26 96.15%[4157] 96.15%[9383] [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] 5 100.00% 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]] 17 94.12%[6463] 100.00% [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] 2 0.00%[4158, 5492] 100.00% [_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] 9 100.00% 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] 15 100.00% 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]] 3 100.00% 100.00% [[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] 36 100.00% 91.67%[8311, 8367, 8368] [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] 4 100.00% 100.00% [[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] 3 100.00% 100.00% [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] 14 100.00% 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]] 3 100.00% 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]] 4 100.00% 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]] 11 9.09%[6353, 6354, 9176, 9239, 9261, 9265, 9267, 9270, 9271, 10908] 27.27%[6353, 9176, 9239, 9261, 9265, 9267, 9270, 9271] [[_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]] 3 33.33%[9201, 10921] 33.33%[9201, 10921] [_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%[8593] 0.00%[8593] [_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]] 6 100.00% 100.00% [[_high_order, _fully, _exact, _linear]] 1 100.00% 100.00% [[_Painleve, ‘1st‘]] 1 0.00%[9168] 0.00%[9168] [[_Painleve, ‘2nd‘]] 1 0.00%[9171] 0.00%[9171] [[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] 1 0.00%[9202] 0.00%[9202] [[_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]] 2 100.00% 100.00% [[_2nd_order, _reducible, _mu_xy]] 3 66.67%[9363] 66.67%[9363] [[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] 1 0.00%[9288] 0.00%[9288] [[_Painleve, ‘4th‘]] 1 0.00%[9312] 0.00%[9312] [[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] 3 100.00% 100.00% [[_Painleve, ‘3rd‘]] 1 0.00%[9336] 0.00%[9336] [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] 1 100.00% 100.00% [[_Painleve, ‘5th‘]] 1 0.00%[9372] 0.00%[9372] [[_Painleve, ‘6th‘]] 1 0.00%[9382] 0.00%[9382] [[_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%[9391] 0.00%[9391] [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]] 1 0.00%[9396] 0.00%[9396] [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1]] 1 0.00%[9400] 0.00%[9400] [[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] 6 33.33%[9413, 9414, 9415, 9430] 33.33%[9413, 9414, 9415, 9430] [[_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%[9425] 50.00%[9425] [[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]] 2 100.00% 100.00% 71 100.00% 100.00% [[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class B‘]] 1 100.00% 100.00% [[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] 1 100.00% 100.00% [[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] 1 100.00% 100.00% [_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] 1 100.00% 100.00% [[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] 2 0.00%[10878, 10892] 0.00%[10878, 10892] [[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] 2 100.00% 100.00%
##### Performance using own ODE types classiﬁcation

The types of the ODE’s are described in my ode solver page at ode types.

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 97.50%[3757, 3766, 10779, 10781] 100.00% linear 65 98.46%[5415] 98.46%[5415] separable 96 100.00% 100.00% homogeneous 70 98.57%[5007] 100.00% homogeneousTypeD2 23 100.00% 100.00% exact 222 98.65%[119, 146, 2628] 98.65%[3471, 7931, 10588] exactWithIntegrationFactor 112 99.11%[7919] 98.21%[2581, 7919] exactByInspection 18 100.00% 94.44%[3417] bernoulli 25 100.00% 100.00% riccati 455 67.25%[958, 1697, 1698, 1700, 1701, 1702, 2198, 2795, 2815, 2817, 2830, 3130, 3877, 6591, 7690, 9588, 9592, 9593, 9594, 9599, 9606, 9612, 9614, 9615, 9616, 9637, 9645, 9654, 9658, 9659, 9668, 9685, 9689, 9691, 9692, 9693, 9694, 9697, 9698, 9705, 9706, 9712, 9713, 9714, 9715, 9716, 9729, 9730, 9731, 9732, 9733, 9734, 9735, 9736, 9737, 9740, 9741, 9749, 9753, 9754, 9756, 9757, 9758, 9759, 9760, 9766, 9767, 9769, 9770, 9771, 9772, 9773, 9778, 9779, 9784, 9785, 9789, 9790, 9791, 9794, 9798, 9799, 9801, 9802, 9803, 9807, 9808, 9809, 9810, 9813, 9815, 9816, 9819, 9822, 9824, 9825, 9828, 9831, 9833, 9834, 9837, 9840, 9842, 9843, 9846, 9850, 9851, 9852, 9854, 9856, 9857, 9859, 9860, 9862, 9863, 9864, 9865, 9866, 9867, 9868, 9869, 9870, 9871, 9873, 9874, 9875, 9876, 9877, 9878, 9879, 9880, 9881, 9882, 9885, 9886, 9889, 9890, 9891, 9892, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902] 79.34%[958, 1697, 1700, 1701, 1702, 2198, 2815, 2817, 2830, 3877, 6591, 7690, 8311, 8368, 9592, 9599, 9612, 9614, 9616, 9654, 9658, 9659, 9671, 9679, 9685, 9689, 9691, 9693, 9698, 9714, 9722, 9729, 9730, 9732, 9733, 9734, 9736, 9740, 9754, 9756, 9767, 9769, 9785, 9798, 9800, 9807, 9815, 9816, 9819, 9824, 9825, 9828, 9833, 9834, 9837, 9842, 9843, 9846, 9850, 9851, 9856, 9857, 9859, 9860, 9862, 9864, 9865, 9866, 9867, 9868, 9869, 9870, 9871, 9873, 9876, 9877, 9878, 9879, 9881, 9885, 9889, 9890, 9891, 9892, 9893, 9894, 9895, 9896, 9897, 9898, 9899, 9900, 9901, 9902] clairaut 57 98.25%[10208] 98.25%[3834] dAlembert 70 92.86%[2491, 3751, 3769, 8009, 10222] 100.00% isobaric 144 91.67%[2720, 2722, 2723, 2727, 3781, 3785, 6043, 6053, 8463, 8472, 10197, 10800] 93.75%[3486, 3531, 3654, 6066, 7947, 7962, 8115, 8463, 8472] polynomial 16 100.00% 100.00% abelFirstKind 54 87.04%[1704, 1897, 2843, 7627, 7628, 7630, 10786] 88.89%[1704, 2843, 7627, 7628, 7630, 10786] ﬁrst order ode series method. Taylor series method 2 100.00% 100.00% ﬁrst order ode series method. Regular singular point 8 100.00% 100.00% ﬁrst order ode series method. Irregular singular point 3 100.00% 0.00%[408, 409, 5664] ﬁrst_order_laplace 54 100.00% 98.15%[10500] ﬁrst_order_ode_lie_symmetry_calculated 155 100.00% 99.35%[8490] system of linear ODEs 499 99.40%[5350, 5789, 9480] 99.20%[5350, 5789, 5965, 9480] second_order_laplace 224 100.00% 99.55%[5759] reduction_of_order 105 96.19%[1138, 5589, 5590, 10702] 99.05%[10702] second_order_linear_constant_coeﬀ 1 100.00% 0.00%[6552] second_order_airy 15 100.00% 100.00% second_order_change_of_variable_on_x_q1_constant_method 1 0.00%[8652] 100.00% second_order_change_of_variable_on_y_general_n 9 88.89%[8996] 100.00% second_order_integrable_as_is 10 80.00%[9396, 10921] 80.00%[9396, 10921] second_order_change_of_variable_on_x_p1_zero_method 3 100.00% 100.00% second_order_ode_lagrange_adjoint_equation_method 3 100.00% 100.00% second_order_nonlinear_solved_by_mainardi_lioville_method 14 100.00% 100.00% second_order_change_of_variable_on_y_n_one_case 17 100.00% 100.00% second_order_bessel_ode 68 100.00% 100.00% second_order_bessel_ode_form_A 3 100.00% 100.00% second_order_ode_missing_x 123 89.43%[4157, 9186, 9187, 9191, 9193, 9211, 9212, 9214, 9237, 9283, 9285, 9408, 9411] 89.43%[9186, 9187, 9191, 9193, 9211, 9212, 9214, 9237, 9283, 9284, 9285, 9383, 9411] second_order_ode_missing_y 41 85.37%[6102, 6104, 6458, 6463, 9402, 10313] 100.00% second order series method. Regular singular point. Diﬀerence not integer 210 100.00% 97.14%[6470, 6471, 6472, 6476, 6477, 6479] second order series method. Regular singular point. Repeated root 172 100.00% 99.42%[6487] second order series method. Regular singular point. Diﬀerence is integer 266 100.00% 99.62%[4747] second order series method. Irregular singular point 34 94.12%[4501, 5827] 0.00%[1794, 1797, 1805, 2032, 2411, 4192, 4205, 4209, 4213, 4214, 4494, 4501, 4708, 4746, 4767, 4772, 4802, 4810, 4834, 4835, 4836, 5288, 5687, 5689, 5695, 5705, 5706, 5827, 5830, 5838, 5863, 5864, 11058, 11059] second order series method. Regular singular point. Complex roots 24 87.50%[4740, 4741, 4742] 100.00% second_order_ode_high_degree 1 100.00% 100.00% higher_order_linear_constant_coeﬃcients_ODE 352 99.15%[9119, 9122, 9151] 100.00% higher_order_ODE_non_constant_coeﬃcients_of_type_Euler 46 100.00% 100.00% higher_order_laplace 23 100.00% 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
Solved by Mathematica but not by Maple

(102) [408, 409, 1794, 1797, 1805, 2032, 2411, 2581, 2873, 2886, 3363, 3417, 3471, 3486, 3531, 3654, 3689, 3690, 3789, 3834, 4192, 4205, 4209, 4213, 4214, 4405, 4494, 4708, 4746, 4747, 4748, 4767, 4772, 4802, 4810, 4834, 4835, 4836, 5288, 5484, 5664, 5687, 5689, 5695, 5705, 5706, 5759, 5830, 5838, 5863, 5864, 5965, 6066, 6470, 6471, 6472, 6476, 6477, 6479, 6487, 6546, 6547, 6549, 6550, 6551, 6552, 6553, 7931, 7947, 7962, 8030, 8091, 8115, 8121, 8286, 8311, 8367, 8368, 8490, 8498, 9085, 9157, 9257, 9273, 9280, 9281, 9284, 9296, 9383, 9409, 9410, 9671, 9679, 9722, 9800, 10212, 10500, 10588, 10646, 10870, 11058, 11059]

Both systems unable to solve