|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-16 y = \delta \left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.266 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.218 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.250 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.270 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.271 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.293 |
|
|
\[
{}y^{\prime \prime \prime }+9 y^{\prime } = \delta \left (t -1\right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.308 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = \delta \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.260 |
|
|
\[
{}y^{\prime }-2 y = 0
\] |
[_quadrature] |
✓ |
0.471 |
|
|
\[
{}y^{\prime }-2 y x = 0
\] |
[_separable] |
✓ |
0.481 |
|
|
\[
{}y^{\prime }+\frac {2 y}{2 x -1} = 0
\] |
[_separable] |
✓ |
0.491 |
|
|
\[
{}\left (x -3\right ) y^{\prime }-2 y = 0
\] |
[_separable] |
✓ |
0.456 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-2 y x = 0
\] |
[_separable] |
✓ |
0.461 |
|
|
\[
{}y^{\prime }+\frac {y}{x -1} = 0
\] |
[_separable] |
✓ |
0.477 |
|
|
\[
{}y^{\prime }+\frac {y}{x -1} = 0
\] |
[_separable] |
✓ |
0.498 |
|
|
\[
{}\left (1-x \right ) y^{\prime }-2 y = 0
\] |
[_separable] |
✓ |
0.508 |
|
|
\[
{}\left (-x^{3}+2\right ) y^{\prime }-3 x^{2} y = 0
\] |
[_separable] |
✓ |
0.562 |
|
|
\[
{}\left (-x^{3}+2\right ) y^{\prime }+3 x^{2} y = 0
\] |
[_separable] |
✓ |
0.480 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-y x = 0
\] |
[_separable] |
✓ |
0.549 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[_separable] |
✓ |
0.562 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.538 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.470 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.526 |
|
|
\[
{}y^{\prime \prime }-3 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.430 |
|
|
\[
{}\left (-x^{2}+4\right ) y^{\prime \prime }-5 y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.576 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.556 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.470 |
|
|
\[
{}\left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.731 |
|
|
\[
{}y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.550 |
|
|
\[
{}\left (x^{2}-2 x +2\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.596 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.562 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -2 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.546 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\lambda y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.618 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\lambda y = 0
\] |
[_Gegenbauer] |
✓ |
0.608 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.466 |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.408 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{2 x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.520 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.628 |
|
|
\[
{}y^{\prime \prime }+y x = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.465 |
|
|
\[
{}y^{\prime \prime }-\sin \left (x \right ) y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.707 |
|
|
\[
{}y^{\prime \prime }-y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.142 |
|
|
\[
{}y^{\prime }+\cos \left (y\right ) = 0
\] |
[_quadrature] |
✓ |
0.248 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
0.593 |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = 0
\] |
[_separable] |
✓ |
0.648 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.839 |
|
|
\[
{}\sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.813 |
|
|
\[
{}\sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
11.558 |
|
|
\[
{}{\mathrm e}^{3 x} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\frac {2 y}{x^{2}+4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.048 |
|
|
\[
{}y^{\prime \prime }+\frac {\left (1+{\mathrm e}^{x}\right ) y}{1-{\mathrm e}^{x}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.662 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+\left (x^{2}+x -6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.687 |
|
|
\[
{}x y^{\prime \prime }+\left (1-{\mathrm e}^{x}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.763 |
|
|
\[
{}\sin \left (\pi \,x^{2}\right ) y^{\prime \prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.651 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
0.623 |
|
|
\[
{}y^{\prime }+{\mathrm e}^{2 x} y = 0
\] |
[_separable] |
✓ |
0.562 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
0.686 |
|
|
\[
{}y^{\prime }+y \ln \left (x \right ) = 0
\] |
[_separable] |
✓ |
0.663 |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.823 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } x -y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.756 |
|
|
\[
{}x y^{\prime \prime }-3 y^{\prime } x +y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.709 |
|
|
\[
{}y^{\prime \prime }+y \ln \left (x \right ) = 0
\] |
[_Titchmarsh] |
✓ |
0.716 |
|
|
\[
{}\sqrt {x}\, y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.816 |
|
|
\[
{}y^{\prime \prime }+\left (6 x^{2}+2 x +1\right ) y^{\prime }+\left (2+12 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.671 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
0.782 |
|
|
\[
{}y^{\prime }+\sqrt {x^{2}+1}\, y = 0
\] |
[_separable] |
✓ |
0.951 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
1.210 |
|
|
\[
{}y^{\prime }+\sqrt {2 x^{2}+1}\, y = 0
\] |
[_separable] |
✓ |
0.887 |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.801 |
|
|
\[
{}y^{\prime \prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.900 |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.921 |
|
|
\[
{}\sqrt {x}\, y^{\prime \prime }+y^{\prime }+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.835 |
|
|
\[
{}\left (x -3\right )^{2} y^{\prime \prime }-2 \left (x -3\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.471 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.704 |
|
|
\[
{}\left (x -1\right )^{2} y^{\prime \prime }-5 \left (x -1\right ) y^{\prime }+9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.631 |
|
|
\[
{}\left (x +2\right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.506 |
|
|
\[
{}3 \left (x -2\right )^{2} y^{\prime \prime }-4 \left (x -5\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.611 |
|
|
\[
{}\left (x -5\right )^{2} y^{\prime \prime }+\left (x -5\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.625 |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{x -2}+\frac {2 y}{x +2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.139 |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.684 |
|
|
\[
{}\left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.519 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x -3}+\frac {y}{x -4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.809 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{\left (x -3\right )^{2}}+\frac {y}{\left (x -4\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.086 |
|
|
\[
{}y^{\prime \prime }+\left (\frac {1}{x}-\frac {1}{3}\right ) y^{\prime }+\left (\frac {1}{x}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.773 |
|
|
\[
{}\left (4 x^{2}-1\right ) y^{\prime \prime }+\left (4-\frac {2}{x}\right ) y^{\prime }+\frac {\left (-x^{2}+1\right ) y}{x^{2}+1} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.485 |
|
|
\[
{}\left (x^{2}+4\right )^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.607 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.935 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.831 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x -4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.256 |
|
|
\[
{}\left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 y^{\prime } x +10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.809 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\frac {y}{1-x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.776 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
0.572 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{x^{2}}\right ) y = 0
\] |
[_Bessel] |
✓ |
1.269 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (-2 x^{3}+5 x \right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.853 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.829 |
|
|
\[
{}\left (-3 x^{3}+3 x^{2}\right ) y^{\prime \prime }-\left (5 x^{2}+4 x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.883 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 y x = 0
\] |
[_Laguerre] |
✓ |
1.194 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.804 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-x^{4}+x \right ) y^{\prime }+3 x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.645 |
|
|
\[
{}\left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.796 |
|
|
\[
{}\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.198 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x +2}+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.714 |
|