|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\] |
[_quadrature] |
✓ |
0.458 |
|
|
\[
{}y^{\prime \prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.426 |
|
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.205 |
|
|
\[
{}y^{\prime } = 3 \delta \left (t -2\right )
\] |
[_quadrature] |
✓ |
0.329 |
|
|
\[
{}y^{\prime } = \delta \left (t -2\right )-\delta \left (-4+t \right )
\] |
[_quadrature] |
✓ |
0.371 |
|
|
\[
{}y^{\prime \prime } = \delta \left (t -3\right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.251 |
|
|
\[
{}y^{\prime \prime } = \delta \left (t -1\right )-\delta \left (-4+t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.306 |
|
|
\[
{}y^{\prime }+2 y = 4 \delta \left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.385 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t \right )+\delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.882 |
|
|
\[
{}y^{\prime \prime }+y = -2 \delta \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.332 |
|
|
\[
{}y^{\prime }+3 y = \delta \left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.462 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = \delta \left (t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.194 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = \delta \left (t -1\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.543 |
|
|
\[
{}y^{\prime \prime }+16 y = \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.440 |
|
|
\[
{}y^{\prime \prime }-16 y = \delta \left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.446 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.158 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.225 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.592 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (-4+t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.421 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.254 |
|
|
\[
{}y^{\prime \prime \prime }+9 y^{\prime } = \delta \left (t -1\right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
1.465 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = \delta \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.356 |
|
|
\[
{}y^{\prime }-2 y = 0
\] |
[_quadrature] |
✓ |
0.492 |
|
|
\[
{}y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
0.516 |
|
|
\[
{}y^{\prime }+\frac {2 y}{2 x -1} = 0
\] |
[_separable] |
✓ |
0.527 |
|
|
\[
{}\left (x -3\right ) y^{\prime }-2 y = 0
\] |
[_separable] |
✓ |
0.494 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
0.515 |
|
|
\[
{}y^{\prime }+\frac {y}{x -1} = 0
\] |
[_separable] |
✓ |
0.540 |
|
|
\[
{}y^{\prime }+\frac {y}{x -1} = 0
\] |
[_separable] |
✓ |
0.549 |
|
|
\[
{}\left (1-x \right ) y^{\prime }-2 y = 0
\] |
[_separable] |
✓ |
0.593 |
|
|
\[
{}\left (-x^{3}+2\right ) y^{\prime }-3 x^{2} y = 0
\] |
[_separable] |
✓ |
0.567 |
|
|
\[
{}\left (-x^{3}+2\right ) y^{\prime }+3 x^{2} y = 0
\] |
[_separable] |
✓ |
0.531 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
0.562 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[_separable] |
✓ |
0.613 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.576 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.555 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.565 |
|
|
\[
{}y^{\prime \prime }-3 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.470 |
|
|
\[
{}\left (-x^{2}+4\right ) y^{\prime \prime }-5 x y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.618 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.600 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.501 |
|
|
\[
{}\left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.813 |
|
|
\[
{}y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.589 |
|
|
\[
{}\left (x^{2}-2 x +2\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.629 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.589 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.533 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\lambda y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.653 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\lambda y = 0
\] |
[_Gegenbauer] |
✓ |
0.644 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.519 |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.447 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{2 x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.550 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.664 |
|
|
\[
{}y^{\prime \prime }+x y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.490 |
|
|
\[
{}y^{\prime \prime }-\sin \left (x \right ) y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.774 |
|
|
\[
{}y^{\prime \prime }-y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.159 |
|
|
\[
{}y^{\prime }+\cos \left (y\right ) = 0
\] |
[_quadrature] |
✓ |
0.276 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
0.604 |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = 0
\] |
[_separable] |
✓ |
0.721 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
9.053 |
|
|
\[
{}\sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.071 |
|
|
\[
{}\sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
50.325 |
|
|
\[
{}{\mathrm e}^{3 x} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\frac {2 y}{x^{2}+4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.419 |
|
|
\[
{}y^{\prime \prime }+\frac {\left (1+{\mathrm e}^{x}\right ) y}{1-{\mathrm e}^{x}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.526 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+\left (x^{2}+x -6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.644 |
|
|
\[
{}x y^{\prime \prime }+\left (1-{\mathrm e}^{x}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.762 |
|
|
\[
{}\sin \left (\pi \,x^{2}\right ) y^{\prime \prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.803 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
0.656 |
|
|
\[
{}y^{\prime }+{\mathrm e}^{2 x} y = 0
\] |
[_separable] |
✓ |
0.613 |
|
|
\[
{}y^{\prime }+\cos \left (x \right ) y = 0
\] |
[_separable] |
✓ |
0.663 |
|
|
\[
{}y^{\prime }+y \ln \left (x \right ) = 0
\] |
[_separable] |
✓ |
0.687 |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.793 |
|
|
\[
{}y^{\prime \prime }+3 x y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.761 |
|
|
\[
{}x y^{\prime \prime }-3 x y^{\prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.710 |
|
|
\[
{}y^{\prime \prime }+y \ln \left (x \right ) = 0
\] |
[_Titchmarsh] |
✓ |
0.734 |
|
|
\[
{}\sqrt {x}\, y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.813 |
|
|
\[
{}y^{\prime \prime }+\left (6 x^{2}+2 x +1\right ) y^{\prime }+\left (2+12 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.668 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
0.815 |
|
|
\[
{}y^{\prime }+\sqrt {x^{2}+1}\, y = 0
\] |
[_separable] |
✓ |
0.932 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
1.166 |
|
|
\[
{}y^{\prime }+\sqrt {2 x^{2}+1}\, y = 0
\] |
[_separable] |
✓ |
0.910 |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.795 |
|
|
\[
{}y^{\prime \prime }+\cos \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.937 |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.049 |
|
|
\[
{}\sqrt {x}\, y^{\prime \prime }+y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.825 |
|
|
\[
{}\left (x -3\right )^{2} y^{\prime \prime }-2 \left (x -3\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.507 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.753 |
|
|
\[
{}\left (x -1\right )^{2} y^{\prime \prime }-5 \left (x -1\right ) y^{\prime }+9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.647 |
|
|
\[
{}\left (x +2\right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.537 |
|
|
\[
{}3 \left (-2+x \right )^{2} y^{\prime \prime }-4 \left (x -5\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.678 |
|
|
\[
{}\left (x -5\right )^{2} y^{\prime \prime }+\left (x -5\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.656 |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{-2+x}+\frac {2 y}{x +2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.189 |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.722 |
|
|
\[
{}\left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.562 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x -3}+\frac {y}{x -4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.821 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{\left (x -3\right )^{2}}+\frac {y}{\left (x -4\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.183 |
|
|
\[
{}y^{\prime \prime }+\left (\frac {1}{x}-\frac {1}{3}\right ) y^{\prime }+\left (\frac {1}{x}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.822 |
|
|
\[
{}\left (4 x^{2}-1\right ) y^{\prime \prime }+\left (4-\frac {2}{x}\right ) y^{\prime }+\frac {\left (-x^{2}+1\right ) y}{x^{2}+1} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.523 |
|
|
\[
{}\left (x^{2}+4\right )^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.606 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.949 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.901 |
|