|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}t y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime } = \frac {45}{8 t^{{7}/{2}}}
\] |
[[_high_order, _missing_y]] |
✓ |
0.551 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-8 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.959 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.019 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-8 y^{\prime } x +8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.092 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-7 y^{\prime } x +7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.277 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+17 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.701 |
|
|
\[
{}9 x^{2} y^{\prime \prime }-9 y^{\prime } x +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.819 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-2 y^{\prime } x +20 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.151 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.749 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.994 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.672 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.917 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.969 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+22 x^{2} y^{\prime \prime }+124 y^{\prime } x +140 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.115 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }-46 y^{\prime } x +100 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.118 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.118 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.122 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.114 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 y^{\prime } x -2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.117 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.113 |
|
|
\[
{}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+7 x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.170 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = \frac {1}{x^{5}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.492 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.565 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
47.500 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
42.040 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.213 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -16 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.583 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 8
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.803 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +36 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
50.037 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-11 y^{\prime } x +16 y = \frac {1}{x^{3}}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.266 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+70 y^{\prime } x +80 y = \frac {1}{x^{13}}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.259 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.791 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-7 y^{\prime } x +7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.026 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.685 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.912 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+10 x^{2} y^{\prime \prime }-20 y^{\prime } x +20 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.209 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 y^{\prime } x +42 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.193 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+5 y^{\prime } x -5 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.205 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+17 y^{\prime } x -17 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.208 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y = \frac {1}{x^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.029 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.909 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.312 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+27 y^{\prime } x +10 y = \frac {1}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.056 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.651 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.144 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.121 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 y^{\prime } x = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.118 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 y^{\prime } x = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.111 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+y^{\prime } x -y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.106 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 y^{\prime } x = -8
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.230 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.214 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.803 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.469 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.089 |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.393 |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (4 x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.437 |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
6.793 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.181 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
42.580 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.516 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.661 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 y^{\prime } x +125 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.123 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 y^{\prime } x +48 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.134 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+14 x^{3} y^{\prime \prime \prime }+55 x^{2} y^{\prime \prime }+65 y^{\prime } x +15 y = 0
\] |
[[_high_order, _exact, _linear, _homogeneous]] |
✓ |
0.137 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+35 y^{\prime } x +45 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.141 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 y^{\prime } x +4 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.135 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 y^{\prime } x +58 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.239 |
|
|
\[
{}6 x^{2} y^{\prime \prime }+5 y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.060 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.613 |
|
|
\[
{}\left (x -2\right ) y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.612 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+16 \left (x +2\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.696 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-18 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.555 |
|
|
\[
{}y^{\prime \prime }-11 y^{\prime }+30 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.554 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.274 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.631 |
|
|
\[
{}\left (-2-2 x \right ) y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.585 |
|
|
\[
{}\left (2+3 x \right ) y^{\prime \prime }+3 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.552 |
|
|
\[
{}\left (3 x +1\right ) y^{\prime \prime }-3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.532 |
|
|
\[
{}\left (-x^{2}+2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.631 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +4 y = 0
\] |
[_Hermite] |
✓ |
0.474 |
|
|
\[
{}\left (2 x^{2}+2\right ) y^{\prime \prime }+2 y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.568 |
|
|
\[
{}\left (3-2 x \right ) y^{\prime \prime }+2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.616 |
|
|
\[
{}y^{\prime \prime }-4 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.478 |
|
|
\[
{}\left (2 x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -3 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.598 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x = \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.587 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y x = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.604 |
|
|
\[
{}y^{\prime \prime }+\left (-1+y^{2}\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x], _Van_der_Pol] |
✓ |
0.207 |
|
|
\[
{}y^{\prime \prime }+\left (\frac {{y^{\prime }}^{2}}{3}-1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.203 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.464 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.476 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.560 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +9 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.566 |
|
|
\[
{}y^{\prime \prime }-y \cos \left (x \right ) = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.674 |
|
|
\[
{}x^{2} y^{\prime \prime }+6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.576 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.130 |
|
|
\[
{}\left (x^{2}-3 x -4\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.633 |
|
|
\[
{}\left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (x +5\right ) y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.685 |
|
|
\[
{}2 x y^{\prime \prime }-5 y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.847 |
|
|
\[
{}5 x y^{\prime \prime }+8 y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.703 |
|
|
\[
{}9 x y^{\prime \prime }+14 y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.831 |
|