|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 4 y
\] |
[_quadrature] |
✓ |
0.240 |
|
|
\[
{}2 y^{\prime }+3 y = 0
\] |
[_quadrature] |
✓ |
0.634 |
|
|
\[
{}y^{\prime }+2 y x = 0
\] |
[_separable] |
✓ |
0.237 |
|
|
\[
{}y^{\prime } = y x
\] |
[_separable] |
✓ |
0.566 |
|
|
\[
{}\left (x -2\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.269 |
|
|
\[
{}\left (2 x -1\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
0.261 |
|
|
\[
{}2 \left (x +1\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.612 |
|
|
\[
{}\left (x -1\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
0.272 |
|
|
\[
{}2 \left (x -1\right ) y^{\prime } = 3 y
\] |
[_separable] |
✓ |
0.613 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.251 |
|
|
\[
{}y^{\prime \prime } = 4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.598 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.280 |
|
|
\[
{}y^{\prime \prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.284 |
|
|
\[
{}y^{\prime } x +y = 0
\] |
[_separable] |
✓ |
0.539 |
|
|
\[
{}2 y^{\prime } x = y
\] |
[_separable] |
✓ |
0.261 |
|
|
\[
{}x^{2} y^{\prime }+y = 0
\] |
[_separable] |
✗ |
0.071 |
|
|
\[
{}x^{3} y^{\prime } = 2 y
\] |
[_separable] |
✗ |
0.087 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.372 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.605 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.298 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.661 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.940 |
|
|
\[
{}y^{\prime \prime } = y^{\prime }+y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.297 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.139 |
|
|
\[
{}y^{\prime \prime \prime } = y
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.112 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.677 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.344 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.649 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.354 |
|
|
\[
{}\left (x^{2}-3\right ) y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.290 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.625 |
|
|
\[
{}\left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.332 |
|
|
\[
{}\left (-x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.732 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.338 |
|
|
\[
{}3 y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.646 |
|
|
\[
{}5 y^{\prime \prime }-2 y^{\prime } x +10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.314 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-3 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.306 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 y x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.308 |
|
|
\[
{}y^{\prime \prime }+y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.243 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.596 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.296 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.615 |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.286 |
|
|
\[
{}\left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.736 |
|
|
\[
{}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.293 |
|
|
\[
{}\left (4 x^{2}+16 x +17\right ) y^{\prime \prime } = 8 y
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.341 |
|
|
\[
{}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.748 |
|
|
\[
{}y^{\prime \prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.322 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.808 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.297 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.698 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.321 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{-x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.830 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.524 |
|
|
\[
{}x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
1.577 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 \alpha y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.352 |
|
|
\[
{}x y^{\prime \prime }+\left (-x^{3}+x \right ) y^{\prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.933 |
|
|
\[
{}x y^{\prime \prime }+x^{2} y^{\prime }+\left ({\mathrm e}^{x}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.616 |
|
|
\[
{}x^{2} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.161 |
|
|
\[
{}3 x^{3} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.118 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+2 y^{\prime }+3 y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.557 |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.983 |
|
|
\[
{}x^{2} y^{\prime \prime }+6 \sin \left (x \right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.509 |
|
|
\[
{}\left (2 x^{3}+6 x^{2}\right ) y^{\prime \prime }+21 y^{\prime } x +9 \left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.119 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x +x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.350 |
|
|
\[
{}\left (1-x \right )^{2} y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.517 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.911 |
|
|
\[
{}\left (x -2\right )^{3} y^{\prime \prime }+3 \left (x -2\right )^{2} y^{\prime }+x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.532 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+\left (x -2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.922 |
|
|
\[
{}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x^{2}+9\right ) y^{\prime }+\left (x^{2}+4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.594 |
|
|
\[
{}\left (x -2\right )^{2} y^{\prime \prime }-\left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.465 |
|
|
\[
{}x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.121 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.004 |
|
|
\[
{}2 x y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.964 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.388 |
|
|
\[
{}3 x y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.031 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.959 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (-2 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.899 |
|
|
\[
{}6 x^{2} y^{\prime \prime }+7 y^{\prime } x -\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.325 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+2 y^{\prime } x +x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.854 |
|
|
\[
{}2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.037 |
|
|
\[
{}2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 y x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.926 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+9 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.314 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-4 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.908 |
|
|
\[
{}4 x y^{\prime \prime }+8 y^{\prime }+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.896 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.908 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-4 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.407 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.041 |
|
|
\[
{}\left (5 x^{3}+2 x^{2}\right ) y^{\prime \prime }+\left (-x^{2}+3 x \right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.352 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.038 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
0.138 |
|
|
\[
{}x^{3} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
0.616 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.919 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.303 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.933 |
|
|
\[
{}x \left (x -1\right ) \left (x +1\right )^{2} y^{\prime \prime }+2 x \left (x -3\right ) \left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.356 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) x \right ) y^{\prime }-\alpha \beta y = 0
\] |
[_Jacobi] |
✓ |
1.367 |
|
|
\[
{}x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.387 |
|
|
\[
{}x y^{\prime \prime }+\left (5-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.064 |
|
|
\[
{}x y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.540 |
|