|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+8 y^{\prime }+7 y = 165 \,{\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.275 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+17 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.270 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t} t^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.234 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.307 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+17 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.278 |
|
|
\[
{}y^{\prime \prime } = {\mathrm e}^{t} \sin \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.282 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+40 y = 122 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.429 |
|
|
\[
{}y^{\prime \prime }-9 y = 24 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.265 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.425 |
|
|
\[
{}y^{\prime \prime }+4 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.266 |
|
|
\[
{}y^{\prime \prime }+4 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.276 |
|
|
\[
{}y^{\prime \prime }+4 y = {\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.372 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.319 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.328 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.251 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.287 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.223 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.284 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.250 |
|
|
\[
{}y^{\prime } = \operatorname {Heaviside}\left (t -3\right )
\] |
[_quadrature] |
✓ |
0.406 |
|
|
\[
{}y^{\prime } = \operatorname {Heaviside}\left (t -3\right )
\] |
[_quadrature] |
✓ |
0.418 |
|
|
\[
{}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.244 |
|
|
\[
{}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.267 |
|
|
\[
{}y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.443 |
|
|
\[
{}y^{\prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\] |
[_quadrature] |
✓ |
0.477 |
|
|
\[
{}y^{\prime \prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.340 |
|
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.274 |
|
|
\[
{}y^{\prime } = 3 \delta \left (t -2\right )
\] |
[_quadrature] |
✓ |
0.426 |
|
|
\[
{}y^{\prime } = \delta \left (t -2\right )-\delta \left (t -4\right )
\] |
[_quadrature] |
✓ |
0.463 |
|
|
\[
{}y^{\prime \prime } = \delta \left (t -3\right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.229 |
|
|
\[
{}y^{\prime \prime } = \delta \left (t -1\right )-\delta \left (t -4\right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.279 |
|
|
\[
{}y^{\prime }+2 y = 4 \delta \left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.467 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t \right )+\delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.830 |
|
|
\[
{}y^{\prime \prime }+y = -2 \delta \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.316 |
|
|
\[
{}y^{\prime }+3 y = \delta \left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.488 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = \delta \left (t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.185 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = \delta \left (t -1\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.462 |
|
|
\[
{}y^{\prime \prime }+16 y = \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.433 |
|
|
\[
{}y^{\prime \prime }-16 y = \delta \left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.419 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.146 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.221 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.564 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.398 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.243 |
|
|
\[
{}y^{\prime \prime \prime }+9 y^{\prime } = \delta \left (t -1\right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
1.358 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = \delta \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.361 |
|
|
\[
{}y^{\prime }-2 y = 0
\] |
[_quadrature] |
✓ |
0.560 |
|
|
\[
{}y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
0.642 |
|
|
\[
{}y^{\prime }+\frac {2 y}{2 x -1} = 0
\] |
[_separable] |
✓ |
0.597 |
|
|
\[
{}\left (x -3\right ) y^{\prime }-2 y = 0
\] |
[_separable] |
✓ |
0.566 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
0.575 |
|
|
\[
{}y^{\prime }+\frac {y}{x -1} = 0
\] |
[_separable] |
✓ |
0.588 |
|
|
\[
{}y^{\prime }+\frac {y}{x -1} = 0
\] |
[_separable] |
✓ |
0.659 |
|
|
\[
{}\left (1-x \right ) y^{\prime }-2 y = 0
\] |
[_separable] |
✓ |
0.619 |
|
|
\[
{}\left (-x^{3}+2\right ) y^{\prime }-3 x^{2} y = 0
\] |
[_separable] |
✓ |
0.666 |
|
|
\[
{}\left (-x^{3}+2\right ) y^{\prime }+3 x^{2} y = 0
\] |
[_separable] |
✓ |
0.586 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
0.612 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[_separable] |
✓ |
0.615 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.546 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.484 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.535 |
|
|
\[
{}y^{\prime \prime }-3 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.440 |
|
|
\[
{}\left (-x^{2}+4\right ) y^{\prime \prime }-5 y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.593 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.572 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.480 |
|
|
\[
{}\left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.747 |
|
|
\[
{}y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.562 |
|
|
\[
{}\left (x^{2}-2 x +2\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.593 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.519 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.562 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\lambda y = 0
\] |
[_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] |
✓ |
0.612 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.569 |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.422 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{2 x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.526 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.630 |
|
|
\[
{}y^{\prime \prime }+x y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.468 |
|
|
\[
{}y^{\prime \prime }-\sin \left (x \right ) y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.716 |
|
|
\[
{}y^{\prime \prime }-y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.155 |
|
|
\[
{}y^{\prime }+\cos \left (y\right ) = 0
\] |
[_quadrature] |
✓ |
0.366 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
0.705 |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = 0
\] |
[_separable] |
✓ |
0.778 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
10.201 |
|
|
\[
{}\sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.041 |
|
|
\[
{}\sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
49.930 |
|
|
\[
{}{\mathrm e}^{3 x} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\frac {2 y}{x^{2}+4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.421 |
|
|
\[
{}y^{\prime \prime }+\frac {\left ({\mathrm e}^{x}+1\right ) y}{1-{\mathrm e}^{x}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.427 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+\left (x^{2}+x -6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.609 |
|
|
\[
{}x y^{\prime \prime }+\left (1-{\mathrm e}^{x}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.731 |
|
|
\[
{}\sin \left (\pi \,x^{2}\right ) y^{\prime \prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.865 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
0.671 |
|
|
\[
{}y^{\prime }+{\mathrm e}^{2 x} y = 0
\] |
[_separable] |
✓ |
0.670 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
0.733 |
|
|
\[
{}y^{\prime }+y \ln \left (x \right ) = 0
\] |
[_separable] |
✓ |
0.664 |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.763 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } x -y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.736 |
|
|
\[
{}x y^{\prime \prime }-3 y^{\prime } x +y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.730 |
|
|
\[
{}y^{\prime \prime }+y \ln \left (x \right ) = 0
\] |
[_Titchmarsh] |
✓ |
0.704 |
|
|
\[
{}\sqrt {x}\, y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.782 |
|
|
\[
{}y^{\prime \prime }+\left (6 x^{2}+2 x +1\right ) y^{\prime }+\left (2+12 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.645 |
|