|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.325 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.066 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.761 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }+y = \left (t^{2}+1\right ) {\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.839 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = t \,{\mathrm e}^{3 t}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.804 |
|
|
\[
{}3 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (t \right ) {\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.545 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = t^{{5}/{2}} {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.069 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \sqrt {1+t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.480 |
|
|
\[
{}y^{\prime \prime }-y = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.704 |
|
|
\[
{}y^{\prime \prime }+\frac {t^{2} y}{4} = f \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.091 |
|
|
\[
{}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.005 |
|
|
\[
{}m y^{\prime \prime }+c y^{\prime }+k y = F_{0} \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.328 |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.298 |
|
|
\[
{}y^{\prime \prime }-t y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.458 |
|
|
\[
{}\left (t^{2}+2\right ) y^{\prime \prime }-t y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.308 |
|
|
\[
{}y^{\prime \prime }-t^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.237 |
|
|
\[
{}t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.353 |
|
|
\[
{}y^{\prime \prime }+t^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.454 |
|
|
\[
{}y^{\prime \prime }-t^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.191 |
|
|
\[
{}y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.309 |
|
|
\[
{}y^{\prime \prime }-2 t y^{\prime }+\lambda y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.335 |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+\alpha \left (\alpha +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.702 |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-t y^{\prime }+\alpha ^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.669 |
|
|
\[
{}y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.280 |
|
|
\[
{}y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.240 |
|
|
\[
{}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.305 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.268 |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.653 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+{\mathrm e}^{t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.590 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+{\mathrm e}^{-t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.513 |
|
|
\[
{}t^{2} y^{\prime \prime }-5 t y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.135 |
|
|
\[
{}t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.113 |
|
|
\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.206 |
|
|
\[
{}\left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.843 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.250 |
|
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.172 |
|
|
\[
{}\left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.949 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.129 |
|
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.164 |
|
|
\[
{}t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.403 |
|
|
\[
{}t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.720 |
|
|
\[
{}t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.160 |
|
|
\[
{}\sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.788 |
|
|
\[
{}\left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.949 |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (1+t \right )}+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.264 |
|
|
\[
{}t^{3} y^{\prime \prime }+\sin \left (t^{3}\right ) y^{\prime }+t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.937 |
|
|
\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-\left (1+t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.080 |
|
|
\[
{}2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y = 0
\] |
[_Laguerre] |
✓ |
0.784 |
|
|
\[
{}2 t y^{\prime \prime }+\left (1+t \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.854 |
|
|
\[
{}2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (1+t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.779 |
|
|
\[
{}4 t y^{\prime \prime }+3 y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.796 |
|
|
\[
{}2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.027 |
|
|
\[
{}t^{3} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.097 |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.813 |
|
|
\[
{}t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0
\] |
[_Lienard] |
✓ |
0.727 |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-t y = 0
\] |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.061 |
|
|
\[
{}t^{2} y^{\prime \prime }+t \left (1+t \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.034 |
|
|
\[
{}t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
0.868 |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.563 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }-\left (1+t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.501 |
|
|
\[
{}t y^{\prime \prime }+t y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.576 |
|
|
\[
{}t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.699 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+t^{2} y = 0
\] |
[_Lienard] |
✓ |
0.373 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
0.792 |
|
|
\[
{}t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y = 0
\] |
[_Laguerre] |
✓ |
0.934 |
|
|
\[
{}2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.051 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (1+t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.921 |
|
|
\[
{}t y^{\prime \prime }+y^{\prime }-4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.771 |
|
|
\[
{}t^{2} y^{\prime \prime }-t \left (1+t \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.795 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.526 |
|
|
\[
{}t y^{\prime \prime }+3 y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.382 |
|
|
\[
{}\cos \left (t \right ) y+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.338 |
|
|
\[
{}\sqrt {t}\, \sin \left (t \right ) y+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.949 |
|
|
\[
{}\frac {2 t y}{t^{2}+1}+y^{\prime } = \frac {1}{t^{2}+1}
\] |
[_linear] |
✓ |
0.982 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{t} t
\] |
[[_linear, ‘class A‘]] |
✓ |
0.994 |
|
|
\[
{}t^{2} y+y^{\prime } = 1
\] |
[_linear] |
✓ |
1.017 |
|
|
\[
{}t^{2} y+y^{\prime } = t^{2}
\] |
[_separable] |
✓ |
0.867 |
|
|
\[
{}y^{\prime }+\frac {t y}{t^{2}+1} = 1-\frac {t^{3} y}{t^{4}+1}
\] |
[_linear] |
✓ |
1.691 |
|
|
\[
{}\sqrt {t^{2}+1}\, y+y^{\prime } = 0
\] |
[_separable] |
✓ |
3.270 |
|
|
\[
{}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.662 |
|
|
\[
{}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0
\] |
[_separable] |
✓ |
2.418 |
|
|
\[
{}y^{\prime }-2 t y = t
\] |
[_separable] |
✓ |
1.007 |
|
|
\[
{}y^{\prime }+t y = 1+t
\] |
[_linear] |
✓ |
1.157 |
|
|
\[
{}y^{\prime }+y = \frac {1}{t^{2}+1}
\] |
[_linear] |
✓ |
1.598 |
|
|
\[
{}y^{\prime }-2 t y = 1
\] |
[_linear] |
✓ |
1.018 |
|
|
\[
{}t y+\left (t^{2}+1\right ) y^{\prime } = \left (t^{2}+1\right )^{{5}/{2}}
\] |
[_linear] |
✓ |
1.934 |
|
|
\[
{}4 t y+\left (t^{2}+1\right ) y^{\prime } = t
\] |
[_separable] |
✓ |
1.189 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.391 |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
1.617 |
|
|
\[
{}y^{\prime } = \left (1+t \right ) \left (1+y\right )
\] |
[_separable] |
✓ |
0.957 |
|
|
\[
{}y^{\prime } = 1-t +y^{2}-t y^{2}
\] |
[_separable] |
✓ |
1.691 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3+t +y}
\] |
[_separable] |
✓ |
1.234 |
|
|
\[
{}\cos \left (y\right ) \sin \left (t \right ) y^{\prime } = \cos \left (t \right ) \sin \left (y\right )
\] |
[_separable] |
✓ |
3.151 |
|
|
\[
{}t^{2} \left (1+y^{2}\right )+2 y y^{\prime } = 0
\] |
[_separable] |
✓ |
3.304 |
|
|
\[
{}y^{\prime } = \frac {2 t}{y+t^{2} y}
\] |
[_separable] |
✓ |
1.536 |
|
|
\[
{}\sqrt {1+y^{2}}\, y^{\prime } = \frac {t y^{3}}{\sqrt {t^{2}+1}}
\] |
[_separable] |
✓ |
2.333 |
|
|
\[
{}y^{\prime } = \frac {3 t^{2}+4 t +2}{-2+2 y}
\] |
[_separable] |
✓ |
1.778 |
|
|
\[
{}\cos \left (y\right ) y^{\prime } = -\frac {t \sin \left (y\right )}{t^{2}+1}
\] |
[_separable] |
✓ |
2.333 |
|
|
\[
{}y^{\prime } = k \left (a -y\right ) \left (b -y\right )
\] |
[_quadrature] |
✓ |
0.760 |
|
|
\[
{}3 t y^{\prime } = \cos \left (t \right ) y
\] |
[_separable] |
✓ |
2.306 |
|