|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}4 x^{2} y^{\prime \prime }+y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.330 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+27 x y^{\prime }+10 y = \frac {1}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
6.957 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.623 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.263 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.254 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 x y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.115 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 x y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.111 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x y^{\prime }-y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.111 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 x y^{\prime } = -8
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.293 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.229 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.054 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.688 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.251 |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.618 |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (4 x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.768 |
|
|
\[
{}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
10.577 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.298 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.881 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.602 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.675 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 x y^{\prime }+125 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.126 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 x y^{\prime }+48 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.138 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+14 x^{3} y^{\prime \prime \prime }+55 x^{2} y^{\prime \prime }+65 x y^{\prime }+15 y = 0
\] |
[[_high_order, _exact, _linear, _homogeneous]] |
✓ |
0.148 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+35 x y^{\prime }+45 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.146 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 x y^{\prime }+4 y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.143 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 x y^{\prime }+58 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.327 |
|
|
\[
{}6 x^{2} y^{\prime \prime }+5 x y^{\prime }-y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.013 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.467 |
|
|
\[
{}\left (-2+x \right ) y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.465 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+16 \left (x +2\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.631 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-18 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.550 |
|
|
\[
{}y^{\prime \prime }-11 y^{\prime }+30 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.539 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.389 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.596 |
|
|
\[
{}\left (-2-2 x \right ) y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.412 |
|
|
\[
{}\left (2+3 x \right ) y^{\prime \prime }+3 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.383 |
|
|
\[
{}\left (1+3 x \right ) y^{\prime \prime }-3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.416 |
|
|
\[
{}\left (-x^{2}+2\right ) y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.478 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+4 y = 0
\] |
[_Hermite] |
✓ |
0.349 |
|
|
\[
{}\left (2 x^{2}+2\right ) y^{\prime \prime }+2 x y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.422 |
|
|
\[
{}\left (3-2 x \right ) y^{\prime \prime }+2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.402 |
|
|
\[
{}y^{\prime \prime }-4 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.259 |
|
|
\[
{}\left (2 x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-3 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.427 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime } = \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.422 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+x y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.457 |
|
|
\[
{}y^{\prime \prime }+\left (y^{2}-1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x], _Van_der_Pol] |
✓ |
0.281 |
|
|
\[
{}y^{\prime \prime }+\left (\frac {{y^{\prime }}^{2}}{3}-1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.277 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.340 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.358 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.378 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+9 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.401 |
|
|
\[
{}y^{\prime \prime }-y \cos \left (x \right ) = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.511 |
|
|
\[
{}x^{2} y^{\prime \prime }+6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.450 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.113 |
|
|
\[
{}\left (x^{2}-3 x -4\right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.474 |
|
|
\[
{}\left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (x +5\right ) y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.615 |
|
|
\[
{}2 x y^{\prime \prime }-5 y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.737 |
|
|
\[
{}5 x y^{\prime \prime }+8 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.538 |
|
|
\[
{}9 x y^{\prime \prime }+14 y^{\prime }+\left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.753 |
|
|
\[
{}7 x y^{\prime \prime }+10 y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.748 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.283 |
|
|
\[
{}x y^{\prime \prime }+2 x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.348 |
|
|
\[
{}y^{\prime \prime }+\frac {8 y^{\prime }}{3 x}-\left (\frac {2}{3 x^{2}}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.684 |
|
|
\[
{}y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.749 |
|
|
\[
{}y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.582 |
|
|
\[
{}y^{\prime \prime }-\left (\frac {1}{x}+2\right ) y^{\prime }+\left (x +\frac {1}{x^{2}}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.728 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 x y^{\prime }-7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.718 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.497 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.496 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.243 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-k^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
0.689 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+k \left (k +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.633 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.772 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.562 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
0.666 |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+k y = 0
\] |
[_Laguerre] |
✓ |
0.819 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.700 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (16 x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.516 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.884 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.874 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.071 |
|
|
\[
{}\left (t +1\right )^{2} y^{\prime \prime }-2 \left (t +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.092 |
|
|
\[
{}t y^{\prime \prime }+2 y^{\prime }+t y = 0
\] |
[_Lienard] |
✓ |
0.152 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.878 |
|
|
\[
{}6 y^{\prime \prime }+5 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.891 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.981 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.869 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+34 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.880 |
|
|
\[
{}2 y^{\prime \prime }-5 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.898 |
|
|
\[
{}15 y^{\prime \prime }-11 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.891 |
|
|
\[
{}20 y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.918 |
|
|
\[
{}12 y^{\prime \prime }+8 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.893 |
|
|
\[
{}2 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.050 |
|
|
\[
{}9 y^{\prime \prime \prime }+36 y^{\prime \prime }+40 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.061 |
|
|
\[
{}9 y^{\prime \prime \prime }+12 y^{\prime \prime }+13 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.059 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = -t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.226 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } = 5 t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.428 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = -3 \sin \left (t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.661 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
15.820 |
|
|
\[
{}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.414 |
|