|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.149 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.980 |
|
|
\[
{}y^{\prime \prime }-y y^{\prime } = 2 x
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
6.595 |
|
|
\[
{}y^{\prime }-y^{2}-x -x^{2} = 0
\] |
[_Riccati] |
✓ |
6.290 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.786 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-2 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.790 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-3 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.795 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{2}-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.285 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.376 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{4}-6 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.389 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.379 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.893 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.260 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.297 |
|
|
\[
{}y^{\prime \prime }-a x y^{\prime }-b x y-c x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.658 |
|
|
\[
{}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.666 |
|
|
\[
{}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.667 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.033 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{2} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.991 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.401 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.397 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-x y-x^{2}-2 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.399 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-x y-x^{2}-4 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.400 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{3}+1 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.031 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-x y-x^{3}-x^{2} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.403 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.406 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.403 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.402 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.404 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.407 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{4}+3 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.412 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.079 |
|
|
\[
{}y^{\prime \prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.906 |
|
|
\[
{}y^{\prime \prime }-x y-x^{6}+64 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.520 |
|
|
\[
{}y^{\prime \prime }-x y-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.377 |
|
|
\[
{}y^{\prime \prime }-x y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.676 |
|
|
\[
{}y^{\prime \prime }-x y-x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.191 |
|
|
\[
{}y^{\prime \prime }-x y-x^{6}-x^{3}+42 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.675 |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.755 |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
73.569 |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{4} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.659 |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{4}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.338 |
|
|
\[
{}y^{\prime \prime }-2 x^{2} y-x^{4}+1 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.227 |
|
|
\[
{}y^{\prime \prime }-x^{3} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
14.740 |
|
|
\[
{}y^{\prime \prime }-x^{3} y-x^{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
333.730 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.721 |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.747 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.955 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.847 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{3}-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.727 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.732 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-x y-x^{2}-\frac {1}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
167.143 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.793 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
488.635 |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x y-x^{3}-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.747 |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.767 |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.760 |
|
|
\[
{}y^{\prime \prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.037 |
|
|
\[
{}y^{\prime \prime }+c y^{\prime }+k y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.228 |
|
|
\[
{}w^{\prime } = -\frac {1}{2}-\frac {\sqrt {1-12 w}}{2}
\] |
[_quadrature] |
✓ |
17.113 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.957 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.834 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.155 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.937 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.887 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.665 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.956 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.664 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
63.447 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.008 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
38.453 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime }+y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.591 |
|
|
\[
{}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.699 |
|
|
\[
{}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.648 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.208 |
|
|
\[
{}x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.163 |
|
|
\[
{}x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
4.302 |
|
|
\[
{}5 x^{5} y^{\prime \prime \prime \prime }+4 x^{4} y^{\prime \prime \prime }+x^{2} y^{\prime }+x y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.328 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.790 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = x
\] |
[[_2nd_order, _missing_y]] |
✗ |
1843.976 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+x {y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.425 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y {y^{\prime }}^{2} = 0
\] |
[NONE] |
✗ |
0.118 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.552 |
|
|
\[
{}y^{\prime \prime }+\sin \left (y\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.441 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.826 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.191 |
|
|
\[
{}y^{\prime } = 2 x^{2} \sin \left (\frac {y}{x}\right )^{2}+\frac {y}{x}
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
3.556 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 8 \sqrt {x}\, \left (1+\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.755 |
|
|
\[
{}v v^{\prime } = \frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3}
\] |
[_rational, _Bernoulli] |
✓ |
1.716 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.615 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.689 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.712 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.642 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}+x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.694 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.679 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.725 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.684 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.660 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \sin \left (x \right )+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.713 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.737 |
|