|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 4 y
\] |
[_quadrature] |
✓ |
0.264 |
|
|
\[
{}2 y^{\prime }+3 y = 0
\] |
[_quadrature] |
✓ |
0.273 |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
0.333 |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
0.364 |
|
|
\[
{}\left (x -2\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.319 |
|
|
\[
{}\left (2 x -1\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
0.334 |
|
|
\[
{}2 \left (x +1\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.338 |
|
|
\[
{}\left (x -1\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
0.385 |
|
|
\[
{}2 \left (x -1\right ) y^{\prime } = 3 y
\] |
[_separable] |
✓ |
0.347 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.364 |
|
|
\[
{}y^{\prime \prime } = 4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.342 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.385 |
|
|
\[
{}y^{\prime \prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.338 |
|
|
\[
{}y^{\prime } x +y = 0
\] |
[_separable] |
✓ |
0.230 |
|
|
\[
{}2 y^{\prime } x = y
\] |
[_separable] |
✓ |
0.269 |
|
|
\[
{}x^{2} y^{\prime }+y = 0
\] |
[_separable] |
✗ |
0.118 |
|
|
\[
{}x^{3} y^{\prime } = 2 y
\] |
[_separable] |
✗ |
0.132 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.395 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.377 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.474 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.482 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.786 |
|
|
\[
{}y^{\prime \prime } = y^{\prime }+y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.471 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.246 |
|
|
\[
{}y^{\prime \prime \prime } = y
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.161 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.459 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.476 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.363 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.489 |
|
|
\[
{}\left (x^{2}-3\right ) y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.384 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.411 |
|
|
\[
{}\left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.477 |
|
|
\[
{}\left (-x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.484 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.508 |
|
|
\[
{}3 y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.418 |
|
|
\[
{}5 y^{\prime \prime }-2 y^{\prime } x +10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.402 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.382 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.414 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.335 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.277 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.459 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.391 |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.399 |
|
|
\[
{}\left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.567 |
|
|
\[
{}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.458 |
|
|
\[
{}\left (4 x^{2}+16 x +17\right ) y^{\prime \prime } = 8 y
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.456 |
|
|
\[
{}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.482 |
|
|
\[
{}y^{\prime \prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.359 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.556 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.435 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }+y x^{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.437 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.484 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{-x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.571 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.791 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } \sin \left (x \right )+x y = 0
\] |
[_Lienard] |
✓ |
1.558 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 \alpha y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.457 |
|
|
\[
{}x y^{\prime \prime }+\left (-x^{3}+x \right ) y^{\prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.883 |
|
|
\[
{}x y^{\prime \prime }+x^{2} y^{\prime }+\left ({\mathrm e}^{x}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.762 |
|
|
\[
{}x^{2} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.257 |
|
|
\[
{}3 x^{3} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.168 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+2 y^{\prime }+3 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.477 |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.646 |
|
|
\[
{}x^{2} y^{\prime \prime }+6 y^{\prime } \sin \left (x \right )+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.758 |
|
|
\[
{}\left (2 x^{3}+6 x^{2}\right ) y^{\prime \prime }+21 y^{\prime } x +9 \left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.933 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x +x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.417 |
|
|
\[
{}\left (1-x \right )^{2} y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.556 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.468 |
|
|
\[
{}\left (x -2\right )^{3} y^{\prime \prime }+3 \left (x -2\right )^{2} y^{\prime }+x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.580 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+\left (x -2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.524 |
|
|
\[
{}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x^{2}+9\right ) y^{\prime }+\left (x^{2}+4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.700 |
|
|
\[
{}\left (x -2\right )^{2} y^{\prime \prime }-\left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.546 |
|
|
\[
{}x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.184 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.712 |
|
|
\[
{}2 x y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.699 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.684 |
|
|
\[
{}3 x y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.704 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.617 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (-2 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.631 |
|
|
\[
{}6 x^{2} y^{\prime \prime }+7 y^{\prime } x -\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.637 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+2 y^{\prime } x +x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.536 |
|
|
\[
{}2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.717 |
|
|
\[
{}2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.605 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+9 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.655 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-4 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.570 |
|
|
\[
{}4 x y^{\prime \prime }+8 y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.618 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.537 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-4 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.724 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.754 |
|
|
\[
{}\left (5 x^{3}+2 x^{2}\right ) y^{\prime \prime }+\left (-x^{2}+3 x \right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.897 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } \sin \left (x \right )-\cos \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.740 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
0.207 |
|
|
\[
{}x^{3} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
0.145 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.658 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.219 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.646 |
|
|
\[
{}x \left (x -1\right ) \left (x +1\right )^{2} y^{\prime \prime }+2 x \left (x -3\right ) \left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.597 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\gamma -\left (\alpha +\beta +1\right ) x \right ) y^{\prime }-\alpha \beta y = 0
\] |
[_Jacobi] |
✓ |
1.110 |
|
|
\[
{}x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.665 |
|
|
\[
{}x y^{\prime \prime }+\left (5-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.677 |
|
|
\[
{}x y^{\prime \prime }+\left (3 x +5\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.760 |
|