|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 4 y
\] |
[_quadrature] |
✓ |
0.336 |
|
|
\[
{}2 y^{\prime }+3 y = 0
\] |
[_quadrature] |
✓ |
0.351 |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
0.381 |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
0.359 |
|
|
\[
{}\left (-2+x \right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.382 |
|
|
\[
{}\left (2 x -1\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
0.461 |
|
|
\[
{}2 \left (x +1\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.453 |
|
|
\[
{}\left (-1+x \right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
0.384 |
|
|
\[
{}2 \left (-1+x \right ) y^{\prime } = 3 y
\] |
[_separable] |
✓ |
0.474 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime } = 4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.438 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.387 |
|
|
\[
{}y^{\prime \prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.485 |
|
|
\[
{}x y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.287 |
|
|
\[
{}2 x y^{\prime } = y
\] |
[_separable] |
✓ |
0.298 |
|
|
\[
{}x^{2} y^{\prime }+y = 0
\] |
[_separable] |
✗ |
0.065 |
|
|
\[
{}x^{3} y^{\prime } = 2 y
\] |
[_separable] |
✗ |
0.076 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.470 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.486 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.514 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.500 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.759 |
|
|
\[
{}y^{\prime \prime } = y^{\prime }+y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.506 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.296 |
|
|
\[
{}y^{\prime \prime \prime } = y
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.115 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.379 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.384 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.323 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.393 |
|
|
\[
{}\left (x^{2}-3\right ) y^{\prime \prime }+2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.330 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.338 |
|
|
\[
{}\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.376 |
|
|
\[
{}\left (-x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.381 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.380 |
|
|
\[
{}3 y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.322 |
|
|
\[
{}5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.347 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.332 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.336 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.233 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.288 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.351 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.316 |
|
|
\[
{}y^{\prime \prime }+\left (-1+x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.353 |
|
|
\[
{}\left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (-1+x \right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.421 |
|
|
\[
{}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.349 |
|
|
\[
{}\left (4 x^{2}+16 x +17\right ) y^{\prime \prime } = 8 y
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.395 |
|
|
\[
{}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.388 |
|
|
\[
{}y^{\prime \prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.353 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.435 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.345 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.358 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.355 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{-x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.502 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.675 |
|
|
\[
{}x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
1.614 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+2 \alpha y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.376 |
|
|
\[
{}x y^{\prime \prime }+\left (-x^{3}+x \right ) y^{\prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.954 |
|
|
\[
{}x y^{\prime \prime }+x^{2} y^{\prime }+\left (-1+{\mathrm e}^{x}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.695 |
|
|
\[
{}x^{2} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.186 |
|
|
\[
{}3 x^{3} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.114 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+2 y^{\prime }+3 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.350 |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.672 |
|
|
\[
{}x^{2} y^{\prime \prime }+6 \sin \left (x \right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.721 |
|
|
\[
{}\left (2 x^{3}+6 x^{2}\right ) y^{\prime \prime }+21 x y^{\prime }+9 \left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.832 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.383 |
|
|
\[
{}\left (1-x \right )^{2} y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.414 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.370 |
|
|
\[
{}\left (-2+x \right )^{3} y^{\prime \prime }+3 \left (-2+x \right )^{2} y^{\prime }+x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.475 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+\left (-2+x \right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.461 |
|
|
\[
{}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x^{2}+9\right ) y^{\prime }+\left (x^{2}+4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.625 |
|
|
\[
{}\left (-2+x \right )^{2} y^{\prime \prime }-\left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.448 |
|
|
\[
{}x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.118 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.665 |
|
|
\[
{}2 x y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.652 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.660 |
|
|
\[
{}3 x y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.667 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.627 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (-2 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.624 |
|
|
\[
{}6 x^{2} y^{\prime \prime }+7 x y^{\prime }-\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.625 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+2 x y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.563 |
|
|
\[
{}2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.645 |
|
|
\[
{}2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.594 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+9 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.581 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-4 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.582 |
|
|
\[
{}4 x y^{\prime \prime }+8 y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.580 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.501 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-4 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.669 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.742 |
|
|
\[
{}\left (5 x^{3}+2 x^{2}\right ) y^{\prime \prime }+\left (-x^{2}+3 x \right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.831 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.728 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
0.139 |
|
|
\[
{}x^{3} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
0.100 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.658 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.195 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.675 |
|
|
\[
{}x \left (-1+x \right ) \left (x +1\right )^{2} y^{\prime \prime }+2 x \left (x -3\right ) \left (x +1\right ) y^{\prime }-2 \left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.630 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) x \right ) y^{\prime }-\alpha \beta y = 0
\] |
[_Jacobi] |
✓ |
1.117 |
|
|
\[
{}x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.656 |
|
|
\[
{}x y^{\prime \prime }+\left (5-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.660 |
|
|
\[
{}x y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.673 |
|