Chapter 1
Introduction 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 [15125]. 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, Simplify is next called. If this 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

Table 1.1: Summary of final results

System	% solved	Number solved	Number failed
Maple 2024	95.418	14432	693
Mathematica 14	94.545	14300	825

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

Table 1.2: Summary of run time performance of each CAS system

System	mean time (sec)	mean leaf size	total time (min)	total leaf size
Maple 2024	0.210	149.80	52.971	2265733
Mathematica 14	3.291	225.33	829.513	3408129

The problem which Mathematica produced largest leaf size of \(413606\) is 9721.

The problem which Maple produced largest leaf size of \(949416\) is 12388.

The problem which Mathematica used most CPU time of \(175.525\) seconds is 6197.

The problem which Maple used most CPU time of \(140.984\) seconds is 6839.

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.

Table 1.3: Percentage solved per Maple ODE type

Type of ODE	Count	Mathematica	Maple
[_quadrature]	873	98.05% [885, 4266, 4275, 12127, 12129, 12910, 12911, 12914, 12935, 12936, 12962, 12965, 12966, 12967, 14201, 15125, 15126]	99.77% [7303, 11994]
[[_linear, ‘class A‘]]	299	100.00%	99.00% [7300, 7301, 11518]
[_separable]	1193	99.16% [3022, 6264, 8667, 11415, 14980, 14999, 15000, 15001, 15002, 15006]	99.50% [408, 409, 6264, 6418, 11415, 15001]
[_Riccati]	322	67.39% [958, 1697, 1698, 1700, 1701, 1702, 2707, 3304, 3324, 3326, 3339, 3639, 4386, 7345, 8447, 10339, 10346, 10359, 10363, 10415, 10432, 10436, 10440, 10445, 10452, 10461, 10476, 10479, 10480, 10481, 10483, 10487, 10501, 10503, 10504, 10505, 10514, 10516, 10517, 10532, 10536, 10538, 10541, 10545, 10549, 10554, 10555, 10556, 10557, 10560, 10562, 10563, 10566, 10569, 10571, 10572, 10575, 10578, 10580, 10581, 10584, 10587, 10589, 10590, 10593, 10597, 10598, 10599, 10603, 10604, 10607, 10609, 10611, 10612, 10613, 10614, 10615, 10616, 10617, 10618, 10620, 10621, 10622, 10623, 10624, 10625, 10626, 10627, 10628, 10629, 10632, 10636, 10637, 10638, 10639, 10640, 10641, 10642, 10643, 10644, 10645, 10646, 10647, 10648, 10649]	72.98% [958, 1697, 1700, 1701, 1702, 2707, 3324, 3326, 3339, 4386, 7345, 8447, 10339, 10346, 10359, 10361, 10363, 10418, 10426, 10432, 10436, 10438, 10440, 10445, 10461, 10476, 10479, 10480, 10481, 10483, 10487, 10501, 10503, 10514, 10516, 10532, 10545, 10547, 10554, 10562, 10563, 10566, 10571, 10572, 10575, 10580, 10581, 10584, 10589, 10590, 10593, 10597, 10598, 10603, 10604, 10606, 10607, 10609, 10611, 10612, 10613, 10614, 10615, 10616, 10617, 10618, 10620, 10623, 10624, 10625, 10626, 10628, 10632, 10636, 10637, 10638, 10639, 10640, 10641, 10642, 10643, 10644, 10645, 10646, 10647, 10648, 10649]
[[_homogeneous, ‘class G‘]]	70	94.29% [3232, 3236, 12148, 15095]	94.29% [3995, 4040, 8704, 8719]
[_linear]	687	99.56% [6169, 11995, 15046]	99.56% [5502, 6169, 11995]
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	31	100.00%	100.00%
[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	102	99.02% [14378]	100.00%
[[_homogeneous, ‘class A‘], _dAlembert]	150	99.33% [11212]	100.00%
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	95	100.00%	100.00%
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	60	100.00%	100.00%
[[_homogeneous, ‘class A‘], _rational, _dAlembert]	219	98.63% [2085, 5761, 14384]	100.00%
[[_homogeneous, ‘class C‘], _dAlembert]	81	91.36% [3000, 4260, 4278, 7102, 11240, 14439, 15129]	100.00%
[[_homogeneous, ‘class C‘], _Riccati]	24	100.00%	100.00%
[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	75	100.00%	100.00%
[_Bernoulli]	117	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _Bernoulli]	10	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	48	100.00%	100.00%
[‘y=_G(x,y’)‘]	144	62.50% [133, 485, 959, 961, 962, 964, 966, 968, 1703, 1706, 1707, 2026, 2316, 2319, 3363, 3368, 3384, 3463, 4011, 4216, 4261, 4287, 4299, 4951, 4995, 6549, 7063, 7253, 8411, 8416, 8419, 8457, 8706, 8731, 8795, 8796, 8841, 8845, 8866, 11219, 11224, 11404, 12214, 12220, 12239, 12636, 13289, 13348, 14046, 14133, 14296, 14313, 14441, 14941]	56.94% [133, 485, 959, 961, 962, 964, 966, 968, 1703, 1706, 1707, 2026, 2063, 2316, 2319, 3090, 3363, 3368, 3382, 3384, 3395, 3463, 3872, 4011, 4216, 4287, 4298, 4914, 4951, 4995, 6549, 7063, 7253, 8411, 8416, 8419, 8457, 8706, 8731, 8787, 8795, 8796, 8841, 8845, 8848, 8866, 8878, 11224, 11404, 12214, 12218, 12220, 12239, 12636, 13289, 13348, 14133, 14296, 14313, 14441, 14941, 15059]
[[_1st_order, _with_linear_symmetries]]	104	91.35% [3229, 3231, 4290, 4294, 5346, 6797, 6807, 11215, 15124]	99.04% [8872]
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	38	97.37% [15074]	100.00%
[_exact, _rational]	43	97.67% [119]	100.00%
[_exact]	98	93.88% [3137, 14323, 14328, 15066, 15067, 15073]	97.96% [14323, 14328]
[[_1st_order, _with_linear_symmetries], _exact, _rational]	4	100.00%	100.00%
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	4	100.00%	100.00%
[[_homogeneous, ‘class G‘], _exact, _rational]	11	81.82% [146, 11610]	100.00%
[[_2nd_order, _missing_x]]	795	96.98% [2307, 7411, 9934, 9935, 9936, 9938, 9939, 9941, 9959, 9960, 9962, 9967, 9985, 10031, 10033, 10156, 10159, 11589, 11590, 12570, 12571, 14516, 14517, 15204]	97.61% [7411, 9934, 9935, 9938, 9939, 9941, 9959, 9960, 9962, 9967, 9985, 10031, 10032, 10033, 10159, 11589, 11590, 12570, 12571]
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	119	97.48% [12614, 13569, 13570]	97.48% [12614, 13569, 13570]
[[_Emden, _Fowler]]	346	100.00%	97.40% [2541, 4718, 5217, 5556, 5588, 5589, 6584, 6617, 12406]
[[_2nd_order, _exact, _linear, _homogeneous]]	232	99.57% [12258]	98.28% [5590, 6460, 6618, 12407]
[[_2nd_order, _missing_y]]	168	97.02% [6856, 6858, 7212, 10150, 11331]	98.81% [6443, 7305]
[[_2nd_order, _with_linear_symmetries]]	2808	94.69% [1105, 5010, 5813, 5818, 6581, 7178, 7179, 7182, 7183, 7187, 7189, 7288, 7554, 7556, 7976, 7978, 9353, 9360, 9362, 9364, 9365, 9371, 9405, 9406, 9407, 9409, 9413, 9487, 9535, 9542, 9546, 9565, 9607, 9634, 9690, 9720, 9730, 9736, 9747, 9762, 9767, 9768, 9769, 9771, 9928, 9971, 9981, 9982, 9983, 9986, 9988, 9989, 9990, 9995, 9996, 10000, 10001, 10003, 10005, 10007, 10042, 10065, 10085, 10100, 10102, 10103, 10134, 10141, 10142, 10143, 10154, 10155, 10833, 10841, 10856, 10861, 10872, 10874, 10875, 10876, 10877, 10878, 10881, 10882, 10883, 10884, 10892, 10902, 10908, 10915, 10921, 10922, 10924, 10925, 10926, 10927, 10928, 10943, 10945, 10946, 10966, 10967, 10968, 10972, 11012, 11025, 11029, 11032, 11036, 11039, 11052, 11055, 11056, 11065, 11066, 11067, 11068, 11069, 11070, 11071, 11072, 11073, 11078, 11079, 11081, 11082, 11084, 11085, 11086, 11087, 11095, 11100, 11103, 11118, 11119, 11121, 11310, 11311, 11329, 12050, 12249, 12250, 12252, 12264, 12412, 14050, 14121, 14472, 14473]	95.55% [1794, 1797, 1805, 2400, 2920, 4701, 4714, 5003, 5010, 5521, 5526, 5564, 5818, 6042, 6441, 6449, 6581, 6592, 7179, 7187, 7189, 7288, 9353, 9360, 9362, 9364, 9365, 9371, 9405, 9406, 9407, 9409, 9413, 9487, 9535, 9542, 9546, 9565, 9607, 9736, 9767, 9768, 9769, 9771, 9928, 9971, 9981, 9982, 9983, 9986, 9988, 9989, 9990, 9995, 9996, 10000, 10003, 10005, 10007, 10042, 10065, 10085, 10100, 10143, 10154, 10155, 10157, 10856, 10872, 10874, 10876, 10877, 10882, 10883, 10884, 10915, 10921, 10922, 10925, 10926, 10927, 10928, 10946, 10967, 10968, 10972, 11012, 11022, 11023, 11024, 11027, 11032, 11034, 11039, 11055, 11056, 11065, 11066, 11070, 11071, 11072, 11073, 11081, 11082, 11084, 11087, 11104, 11109, 11111, 11116, 11117, 11118, 11121, 11329, 11904, 11905, 12050, 12252, 12264, 12412, 14050, 14121, 14472, 14473, 14803]
[[_2nd_order, _linear, _nonhomogeneous]]	1035	98.74% [1162, 1186, 7462, 9408, 12248, 12251, 12281, 12352, 12354, 12748, 12749, 14633, 14870]	97.49% [1162, 1186, 4722, 4723, 5500, 5501, 5833, 6513, 7224, 7225, 7226, 7230, 7231, 7233, 7241, 7306, 7307, 9408, 12248, 12251, 12281, 12352, 12354, 12749, 14633, 14870]
[[_2nd_order, _exact, _linear, _nonhomogeneous]]	67	100.00%	100.00%
system of linear ODEs	774	96.64% [6104, 6542, 6543, 10213, 10228, 10238, 10241, 10242, 10243, 10244, 10245, 10250, 10251, 10254, 10255, 10256, 10257, 10258, 10259, 10261, 12827, 12828, 12829, 12830, 12842, 14043]	96.51% [6104, 6542, 6543, 6716, 6719, 10203, 10213, 10228, 10238, 10241, 10242, 10243, 10244, 10245, 10250, 10251, 10254, 10256, 10257, 10259, 10261, 12827, 12828, 12829, 12830, 12842, 14043]
[_Gegenbauer]	77	100.00%	100.00%
[[_high_order, _missing_x]]	202	100.00%	100.00%
[[_3rd_order, _missing_x]]	181	100.00%	100.00%
[[_3rd_order, _missing_y]]	86	100.00%	100.00%
[[_3rd_order, _exact, _linear, _homogeneous]]	15	100.00%	100.00%
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	76	94.74% [10840, 10933, 11030, 11074]	98.68% [6459]
[_Lienard]	58	100.00%	100.00%
[[_homogeneous, ‘class A‘], _rational, _Riccati]	31	100.00%	100.00%
[‘x=_G(y,y’)‘]	13	61.54% [550, 2713, 6183, 8907, 13034]	61.54% [550, 2713, 6183, 8907, 13034]
[[_Abel, ‘2nd type‘, ‘class B‘]]	15	26.67% [553, 1046, 8586, 10667, 10670, 10690, 10691, 10692, 10712, 10725, 10730]	40.00% [553, 1046, 8586, 10670, 10690, 10691, 10692, 10712, 10725]
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	12	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	29	96.55% [2031]	100.00%
[[_homogeneous, ‘class D‘], _rational]	3	100.00%	100.00%
[[_1st_order, _with_exponential_symmetries]]	9	100.00%	100.00%
[_rational]	111	82.88% [1039, 1075, 1953, 3118, 3192, 3193, 4146, 4315, 6111, 8815, 8817, 8824, 8838, 9219, 9228, 11198, 11604, 14101, 14126]	76.58% [1039, 1075, 1953, 3118, 3192, 3193, 3926, 4146, 4198, 4199, 4315, 6111, 8815, 8817, 8820, 8838, 9219, 9228, 9246, 9254, 11198, 11230, 11604, 12421, 14101, 14126]
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	136	28.68% [1069, 2990, 3092, 3776, 3783, 6185, 7316, 8570, 8573, 8589, 8601, 10653, 10654, 10661, 10662, 10664, 10666, 10669, 10671, 10673, 10674, 10676, 10677, 10678, 10679, 10680, 10683, 10684, 10685, 10687, 10688, 10689, 10696, 10697, 10698, 10699, 10700, 10701, 10704, 10705, 10706, 10707, 10708, 10709, 10710, 10711, 10713, 10714, 10715, 10716, 10717, 10718, 10719, 10731, 10748, 10749, 10752, 10755, 10756, 10757, 10758, 10759, 10760, 10761, 10762, 10764, 10765, 10766, 10767, 10768, 10769, 10770, 10771, 10772, 10773, 10774, 10775, 10776, 10777, 10778, 10779, 10780, 10781, 10782, 10783, 10784, 10785, 10786, 10787, 10788, 10789, 10790, 10791, 10792, 10793, 10823, 10824]	51.47% [2990, 3092, 3776, 3783, 6185, 7316, 8570, 8573, 8589, 8601, 10661, 10664, 10669, 10676, 10677, 10678, 10679, 10680, 10687, 10688, 10697, 10699, 10700, 10704, 10705, 10708, 10709, 10710, 10711, 10713, 10715, 10716, 10717, 10718, 10719, 10748, 10749, 10755, 10757, 10758, 10759, 10760, 10761, 10762, 10764, 10766, 10767, 10769, 10770, 10771, 10772, 10774, 10775, 10777, 10778, 10779, 10781, 10782, 10783, 10784, 10785, 10786, 10787, 10791, 10792, 10823]
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	4	100.00%	100.00%
[NONE]	85	36.47% [710, 1041, 7110, 7214, 8393, 8424, 8538, 8703, 8910, 8911, 9170, 9172, 9918, 9921, 9922, 9926, 9929, 9931, 9932, 9940, 9942, 9946, 9947, 9948, 9951, 9957, 9965, 9966, 9968, 9972, 9998, 10008, 10016, 10025, 10027, 10052, 10055, 10057, 10058, 10061, 10062, 10074, 10080, 10112, 10124, 10125, 10138, 10174, 12238, 12241, 12243, 13529, 14051, 14626]	32.94% [710, 6238, 7110, 7214, 8393, 8424, 8538, 8703, 8910, 8911, 9170, 9172, 9918, 9921, 9922, 9929, 9931, 9932, 9940, 9942, 9946, 9947, 9948, 9951, 9957, 9965, 9966, 9968, 9972, 9998, 10008, 10016, 10021, 10025, 10027, 10028, 10029, 10044, 10052, 10055, 10057, 10058, 10061, 10062, 10074, 10080, 10112, 10124, 10125, 10138, 10174, 12238, 12241, 12243, 13529, 14051, 14626]
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	29	100.00%	96.55% [1984]
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	58	98.28% [2083]	100.00%
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	21	100.00%	100.00%
[[_high_order, _with_linear_symmetries]]	53	86.79% [813, 9865, 9866, 9867, 9868, 9895, 9913]	86.79% [813, 9865, 9866, 9867, 9868, 9905, 9913]
[[_3rd_order, _with_linear_symmetries]]	155	88.39% [5817, 9784, 9785, 9786, 9787, 9788, 9789, 9790, 9800, 9801, 9803, 9811, 9816, 9827, 9840, 9841, 9856, 13559]	89.03% [5817, 9784, 9785, 9786, 9787, 9788, 9789, 9790, 9800, 9801, 9803, 9811, 9816, 9835, 9840, 9856, 13559]
[[_high_order, _linear, _nonhomogeneous]]	80	97.50% [9875, 9904]	98.75% [9904]
[[_1st_order, _with_linear_symmetries], _Clairaut]	76	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	52	100.00%	100.00%
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	79	98.73% [1985]	98.73% [1985]
[[_homogeneous, ‘class C‘], _rational, _Riccati]	5	100.00%	100.00%
[[_Abel, ‘2nd type‘, ‘class A‘]]	34	14.71% [3676, 3728, 4954, 8542, 8555, 10657, 10658, 10722, 10723, 10724, 10733, 10734, 10735, 10736, 10737, 10751, 10797, 10804, 10805, 10807, 10808, 10810, 10811, 10812, 10813, 10814, 10815, 10816, 10817]	35.29% [3676, 3728, 4954, 8542, 8555, 10722, 10723, 10724, 10733, 10734, 10735, 10736, 10737, 10751, 10797, 10805, 10808, 10812, 10813, 10815, 10816, 10817]
[_rational, _Bernoulli]	46	100.00%	100.00%
[[_homogeneous, ‘class A‘]]	7	100.00%	100.00%
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	162	98.15% [1941, 4451, 10819]	98.77% [1935, 1938]
[[_homogeneous, ‘class G‘], _rational, _Riccati]	21	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‘]]	2	100.00%	100.00%
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	17	100.00%	100.00%
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]]	6	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	10	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	4	100.00%	100.00%
[_exact, _Bernoulli]	7	100.00%	100.00%
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	10	100.00%	100.00%
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	12	83.33% [4917, 4962]	83.33% [4917, 4962]
[[_homogeneous, ‘class G‘], _rational]	98	98.98% [1986]	97.96% [4163, 6820]
[[_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]	102	95.10% [10349, 10392, 10401, 10405, 10406]	98.04% [10401, 10406]
[[_3rd_order, _linear, _nonhomogeneous]]	91	97.80% [12223, 12227]	100.00%
[[_high_order, _missing_y]]	48	97.92% [9909]	97.92% [9909]
[[_3rd_order, _exact, _linear, _nonhomogeneous]]	6	100.00%	100.00%
[[_high_order, _exact, _linear, _nonhomogeneous]]	7	100.00%	100.00%
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	34	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]]	26	100.00%	100.00%
[_Abel]	30	66.67% [1704, 3352, 8384, 8385, 8386, 8387, 12134, 12631, 12938, 13057]	66.67% [1704, 3352, 8384, 8385, 8386, 8387, 12134, 12631, 12938, 13057]
[_Laguerre]	39	100.00%	100.00%
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	4	100.00%	100.00%
[_Bessel]	20	100.00%	100.00%
[_rational, _Abel]	21	95.24% [1897]	100.00%
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	3	100.00%	100.00%
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	5	100.00%	100.00%
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	8	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	11	100.00%	100.00%
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	6	100.00%	100.00%
[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	36	100.00%	100.00%
[[_homogeneous, ‘class D‘], _Bernoulli]	6	100.00%	100.00%
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	11	100.00%	100.00%
[[_homogeneous, ‘class A‘], _exact, _dAlembert]	7	100.00%	100.00%
[[_2nd_order, _quadrature]]	58	98.28% [12198]	98.28% [7304]
[[_high_order, _quadrature]]	10	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	77	89.61% [2308, 2376, 4658, 6100, 6839, 6840, 9914, 15211]	97.40% [2376, 15217]
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	24	100.00%	100.00%
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]	10	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	17	58.82% [4668, 4839, 4840, 4841, 13523, 13524, 15210]	100.00%
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	29	93.10% [2304, 13520]	93.10% [2304, 2309]
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	11	100.00%	100.00%
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	37	100.00%	97.30% [10131]
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]	5	100.00%	100.00%
[[_homogeneous, ‘class C‘], _rational, _dAlembert]	13	100.00%	100.00%
[_dAlembert]	25	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _dAlembert]	64	82.81% [2350, 4251, 4252, 4253, 4274, 4305, 6811, 6813, 6874, 6878, 7254]	100.00%
[[_homogeneous, ‘class G‘], _rational, _Clairaut]	10	100.00%	100.00%
[[_homogeneous, ‘class G‘], _Clairaut]	3	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	17	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]	6	100.00%	100.00%
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	11	100.00%	100.00%
[[_3rd_order, _exact, _nonlinear]]	3	66.67% [10164]	66.67% [10164]
[_Jacobi]	35	100.00%	100.00%
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	6	100.00%	100.00%
[[_3rd_order, _quadrature]]	8	100.00%	100.00%
[[_homogeneous, ‘class G‘], _exact]	3	100.00%	100.00%
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]	12	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%
[[_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‘]]	7	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational]	26	100.00%	100.00%
[[_homogeneous, ‘class D‘], _rational, _Riccati]	20	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _exact]	3	100.00%	100.00%
[[_homogeneous, ‘class C‘], _exact, _dAlembert]	5	100.00%	100.00%
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	2	100.00%	100.00%
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	2	100.00%	100.00%
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	40	27.50% [3673, 5247, 8539, 8541, 10655, 10659, 10686, 10702, 10720, 10721, 10738, 10740, 10741, 10745, 10747, 10750, 10763, 10794, 10795, 10796, 10798, 10799, 10800, 10801, 10802, 10803, 10820, 10822, 11599]	45.00% [3673, 5247, 8539, 8541, 10655, 10659, 10720, 10721, 10741, 10747, 10750, 10763, 10794, 10795, 10798, 10799, 10800, 10801, 10802, 10820, 10822, 11599]
[[_homogeneous, ‘class G‘], _dAlembert]	7	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]	5	100.00%	100.00%
[[_homogeneous, ‘class G‘], _Abel]	4	100.00%	100.00%
[[_homogeneous, ‘class G‘], _Chini]	4	100.00%	100.00%
[_Chini]	4	0.00% [3355, 3642, 8392, 14440]	0.00% [3355, 3642, 8392, 14440]
[_rational, [_Riccati, _special]]	9	100.00%	100.00%
[[_1st_order, _with_linear_symmetries], _rational, _Riccati]	3	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 A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	6	100.00%	100.00%
[_exact, _rational, _Bernoulli]	4	75.00% [14327]	75.00% [14327]
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	5	100.00%	100.00%
[[_Abel, ‘2nd type‘, ‘class C‘]]	7	71.43% [3843, 8605]	71.43% [3843, 8605]
[[_homogeneous, ‘class C‘], _rational]	8	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	8	75.00% [8676, 10129]	62.50% [8676, 10129, 10158]
[_rational, _dAlembert]	12	91.67% [8766]	100.00%
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]	9	100.00%	100.00%
[[_homogeneous, ‘class G‘], _rational, _dAlembert]	6	100.00%	100.00%
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	15	100.00%	100.00%
[_Clairaut]	7	100.00%	85.71% [4343]
[[_homogeneous, ‘class D‘], _exact, _rational, _Bernoulli]	1	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	7	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	10	90.00% [12495]	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]	3	66.67% [6246]	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]	16	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]]	3	100.00%	100.00%
[[_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]]	4	100.00%	100.00%
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]	3	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]	39	100.00%	92.31% [9068, 9124, 9125]
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	6	100.00%	83.33% [15197]
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]	3	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_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]]	7	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]]	2	100.00%	100.00%
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]	12	8.33% [7107, 7108, 9924, 9987, 10009, 10013, 10015, 10018, 10019, 12256, 13250]	25.00% [7107, 9924, 9987, 10009, 10013, 10015, 10018, 10019, 13250]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	3	33.33% [9949, 12269]	33.33% [9949, 12269]
[_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]	2	50.00% [9349]	50.00% [9349]
[_ellipsoidal]	2	100.00%	100.00%
[_Jacobi, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	1	100.00%	100.00%
[_Halm]	4	100.00%	100.00%
[[_3rd_order, _fully, _exact, _linear]]	7	100.00%	100.00%
[[_high_order, _fully, _exact, _linear]]	1	100.00%	100.00%
[[_Painleve, ‘1st‘]]	1	0.00% [9916]	0.00% [9916]
[[_Painleve, ‘2nd‘]]	1	0.00% [9919]	0.00% [9919]
[[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	1	0.00% [9950]	0.00% [9950]
[[_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% [10111]	66.67% [10111]
[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	1	0.00% [10036]	0.00% [10036]
[[_Painleve, ‘4th‘]]	1	0.00% [10060]	0.00% [10060]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]	3	100.00%	100.00%
[[_Painleve, ‘3rd‘]]	1	0.00% [10084]	0.00% [10084]
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]]	1	100.00%	100.00%
[[_Painleve, ‘5th‘]]	1	0.00% [10120]	0.00% [10120]
[[_Painleve, ‘6th‘]]	1	0.00% [10130]	0.00% [10130]
[[_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% [10139]	0.00% [10139]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]]	1	0.00% [10144]	0.00% [10144]
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1]]	1	0.00% [10148]	0.00% [10148]
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]	7	28.57% [10161, 10162, 10163, 10178, 13535]	28.57% [10161, 10162, 10163, 10178, 13535]
[[_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]]	5	100.00%	100.00%
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]	2	50.00% [10173]	50.00% [10173]
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]	2	100.00%	100.00%
	96	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%
[_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% [12226, 12240]	0.00% [12226, 12240]
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	2	100.00%	100.00%
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	1	100.00%	100.00%
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]]	2	100.00%	100.00%
[[_1st_order, _with_exponential_symmetries], _exact]	1	100.00%	100.00%
[[_homogeneous, ‘class C‘], _exact, _rational, _dAlembert]	1	100.00%	100.00%
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]]	2	100.00%	100.00%
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]	1	100.00%	100.00%
[[_high_order, _exact, _linear, _homogeneous]]	3	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	1	100.00%	100.00%
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	1	100.00%	100.00%
[[_2nd_order, _missing_x], _Van_der_Pol]	1	100.00%	100.00%
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	1	100.00%	100.00%
[[_homogeneous, ‘class D‘], _exact, _rational]	1	100.00%	100.00%
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	1	100.00%	100.00%
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]]	1	100.00%	100.00%
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	1	0.00% [15221]	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.

Table 1.5: Percentage solved per own ODE type

Type of ODE	Count	Mathematica	Maple
quadrature	790	97.85% [885, 4266, 4275, 12127, 12129, 12910, 12911, 12914, 12935, 12936, 12962, 12965, 12966, 12967, 14201, 15125, 15126]	99.87% [11994]
linear	69	98.55% [6169]	98.55% [6169]
separable	126	100.00%	100.00%
homogeneous	70	98.57% [5761]	100.00%
homogeneousTypeD2	5	100.00%	100.00%
exact	308	97.40% [119, 146, 3137, 14323, 14328, 15066, 15067, 15073]	99.35% [14323, 14328]
exactWithIntegrationFactor	135	99.26% [8676]	96.30% [1984, 2063, 3090, 8676, 15059]
exactByInspection	19	100.00%	94.74% [3926]
bernoulli	25	100.00%	100.00%
riccati	478	76.99% [958, 1697, 1698, 1700, 1701, 1702, 2707, 3304, 3324, 3326, 3339, 3639, 4386, 7345, 8447, 10339, 10346, 10349, 10359, 10363, 10392, 10401, 10405, 10406, 10415, 10432, 10436, 10440, 10445, 10452, 10461, 10476, 10479, 10480, 10481, 10483, 10487, 10501, 10503, 10504, 10505, 10514, 10516, 10517, 10532, 10536, 10538, 10541, 10545, 10549, 10554, 10555, 10556, 10557, 10560, 10562, 10563, 10566, 10569, 10571, 10572, 10575, 10578, 10580, 10581, 10584, 10587, 10589, 10590, 10593, 10597, 10598, 10599, 10603, 10604, 10607, 10609, 10611, 10612, 10613, 10614, 10615, 10616, 10617, 10618, 10620, 10621, 10622, 10623, 10624, 10625, 10626, 10627, 10628, 10629, 10632, 10636, 10637, 10638, 10639, 10640, 10641, 10642, 10643, 10644, 10645, 10646, 10647, 10648, 10649]	80.96% [958, 1697, 1700, 1701, 1702, 2707, 3324, 3326, 3339, 4386, 7345, 8447, 9068, 9125, 10339, 10346, 10359, 10361, 10363, 10401, 10406, 10418, 10426, 10432, 10436, 10438, 10440, 10445, 10461, 10476, 10479, 10480, 10481, 10483, 10487, 10501, 10503, 10514, 10516, 10532, 10545, 10547, 10554, 10562, 10563, 10566, 10571, 10572, 10575, 10580, 10581, 10584, 10589, 10590, 10593, 10597, 10598, 10603, 10604, 10606, 10607, 10609, 10611, 10612, 10613, 10614, 10615, 10616, 10617, 10618, 10620, 10623, 10624, 10625, 10626, 10628, 10632, 10636, 10637, 10638, 10639, 10640, 10641, 10642, 10643, 10644, 10645, 10646, 10647, 10648, 10649]
clairaut	115	100.00%	99.13% [4343]
dAlembert	256	92.97% [2350, 3000, 4251, 4252, 4253, 4260, 4274, 4278, 4305, 6811, 6813, 6874, 6878, 7254, 8766, 11212, 11240, 15129]	100.00%
isobaric	13	100.00%	100.00%
polynomial	16	100.00%	100.00%
abelFirstKind	58	82.76% [1704, 1897, 3352, 8384, 8385, 8387, 12134, 12631, 12938, 13057]	84.48% [1704, 3352, 8384, 8385, 8387, 12134, 12631, 12938, 13057]
first order ode series method. Taylor series method	10	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, 6418]
first_order_laplace	72	100.00%	100.00%
first_order_ode_lie_symmetry_calculated	347	95.68% [1986, 2083, 3229, 3231, 3232, 3236, 4290, 4294, 5346, 6797, 6807, 11215, 12148, 15095, 15124]	96.54% [3995, 4040, 4163, 4199, 6820, 8704, 8719, 8820, 8872, 9246, 11230, 12421]
system of linear ODEs	752	96.94% [6104, 6542, 6543, 10228, 10238, 10241, 10242, 10243, 10244, 10245, 10254, 10255, 10256, 10257, 10258, 10259, 10261, 12827, 12828, 12829, 12830, 12842, 14043]	96.81% [6104, 6542, 6543, 6716, 6719, 10203, 10228, 10238, 10241, 10242, 10243, 10244, 10245, 10254, 10256, 10257, 10259, 10261, 12827, 12828, 12829, 12830, 12842, 14043]
second_order_laplace	318	100.00%	99.69% [6513]
reduction_of_order	150	98.00% [12050, 14472, 14473]	98.00% [12050, 14472, 14473]
second_order_linear_constant_coeff	2	100.00%	0.00% [7306, 7307]
second_order_airy	15	100.00%	100.00%
second_order_change_of_variable_on_x_method_1	1	100.00%	100.00%
second_order_change_of_variable_on_x_method_2	5	100.00%	100.00%
second_order_change_of_variable_on_y_method_2	16	87.50% [9747, 10927]	93.75% [10927]
second_order_change_of_variable_on_y_method_1	4	100.00%	100.00%
second_order_integrable_as_is	12	83.33% [10144, 12269]	83.33% [10144, 12269]
second_order_ode_lagrange_adjoint_equation_method	9	88.89% [10881]	100.00%
second_order_nonlinear_solved_by_mainardi_lioville_method	14	100.00%	100.00%
second_order_bessel_ode	130	90.77% [7288, 9349, 9634, 9690, 10833, 10892, 10943, 10945, 11036, 11079, 12412, 12748]	97.69% [7288, 9349, 12412]
second_order_bessel_ode_form_A	7	100.00%	100.00%
second_order_ode_missing_x	162	88.27% [2307, 2308, 9934, 9935, 9936, 9939, 9941, 9959, 9960, 9962, 9985, 10031, 10033, 10156, 10159, 12495, 12570, 12571, 15211]	90.12% [9934, 9935, 9939, 9941, 9959, 9960, 9962, 9985, 10031, 10032, 10033, 10131, 10159, 12570, 12571, 15217]
second_order_ode_missing_y	59	88.14% [2304, 6856, 6858, 7212, 10150, 11331, 13520]	96.61% [2304, 2309]
second order series method. Taylor series method	8	87.50% [2376]	87.50% [2376]
second order series method. Regular singular point. Difference not integer	264	100.00%	97.73% [7224, 7225, 7226, 7230, 7231, 7233]
second order series method. Regular singular point. Repeated root	208	100.00%	99.52% [7241]
second order series method. Regular singular point. Difference is integer	322	100.00%	99.69% [5501]
second order series method. Irregular singular point	38	94.74% [5010, 6581]	0.00% [1794, 1797, 1805, 2400, 2541, 2920, 4701, 4714, 4718, 4722, 4723, 5003, 5010, 5217, 5500, 5521, 5526, 5556, 5564, 5588, 5589, 5590, 6042, 6441, 6443, 6449, 6459, 6460, 6581, 6584, 6592, 6617, 6618, 11904, 11905, 12406, 12407, 14803]
second order series method. Regular singular point. Complex roots	30	100.00%	100.00%
second_order_ode_high_degree	1	100.00%	100.00%
higher_order_linear_constant_coefficients_ODE	669	100.00%	100.00%
higher_order_ODE_non_constant_coefficients_of_type_Euler	96	100.00%	100.00%
higher_order_laplace	29	100.00%	100.00%