|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.995 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.862 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.218 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }+y = \left (t^{2}+1\right ) {\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.229 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = t \,{\mathrm e}^{3 t}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.178 |
|
|
\[
{}3 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (t \right ) {\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.836 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = t^{{5}/{2}} {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.350 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \sqrt {t +1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.060 |
|
|
\[
{}y^{\prime \prime }-y = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.553 |
|
|
\[
{}y^{\prime \prime }+\frac {t^{2} y}{4} = f \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.125 |
|
|
\[
{}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.631 |
|
|
\[
{}m y^{\prime \prime }+c y^{\prime }+k y = F_{0} \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
19.990 |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.332 |
|
|
\[
{}y^{\prime \prime }-t y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.225 |
|
|
\[
{}\left (t^{2}+2\right ) y^{\prime \prime }-t y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.365 |
|
|
\[
{}y^{\prime \prime }-t^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.281 |
|
|
\[
{}t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.408 |
|
|
\[
{}y^{\prime \prime }+t^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.289 |
|
|
\[
{}y^{\prime \prime }-t^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.302 |
|
|
\[
{}y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.372 |
|
|
\[
{}y^{\prime \prime }-2 t y^{\prime }+\lambda y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.388 |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+\alpha \left (1+\alpha \right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.585 |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-t y^{\prime }+\alpha ^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.461 |
|
|
\[
{}y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.328 |
|
|
\[
{}y^{\prime \prime }+t^{3} y^{\prime }+3 t^{2} y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.342 |
|
|
\[
{}\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.375 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.361 |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.519 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+{\mathrm e}^{t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.458 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+{\mathrm e}^{-t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.706 |
|
|
\[
{}t^{2} y^{\prime \prime }-5 t y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.882 |
|
|
\[
{}t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.878 |
|
|
\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.977 |
|
|
\[
{}\left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.871 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.050 |
|
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.977 |
|
|
\[
{}\left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.793 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.160 |
|
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.331 |
|
|
\[
{}t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.603 |
|
|
\[
{}t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.412 |
|
|
\[
{}t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.155 |
|
|
\[
{}\sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.700 |
|
|
\[
{}\left ({\mathrm e}^{t}-1\right ) y^{\prime \prime }+{\mathrm e}^{t} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.784 |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.348 |
|
|
\[
{}t^{3} y^{\prime \prime }+\sin \left (t^{3}\right ) y^{\prime }+t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.748 |
|
|
\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-\left (t +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.712 |
|
|
\[
{}2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y = 0
\] |
[_Laguerre] |
✓ |
0.644 |
|
|
\[
{}2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.694 |
|
|
\[
{}2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.707 |
|
|
\[
{}4 t y^{\prime \prime }+3 y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.663 |
|
|
\[
{}2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.698 |
|
|
\[
{}t^{3} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.104 |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.691 |
|
|
\[
{}t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0
\] |
[_Lienard] |
✓ |
0.602 |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-t y = 0
\] |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.651 |
|
|
\[
{}t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.702 |
|
|
\[
{}t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
0.696 |
|
|
\[
{}t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.352 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }-\left (t +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.251 |
|
|
\[
{}t y^{\prime \prime }+t y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.230 |
|
|
\[
{}t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.551 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+t^{2} y = 0
\] |
[_Lienard] |
✓ |
0.438 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
0.649 |
|
|
\[
{}t y^{\prime \prime }+\left (-t +1\right ) y^{\prime }+\lambda y = 0
\] |
[_Laguerre] |
✓ |
0.757 |
|
|
\[
{}2 \sin \left (t \right ) y^{\prime \prime }+\left (-t +1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.865 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.564 |
|
|
\[
{}t y^{\prime \prime }+y^{\prime }-4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.514 |
|
|
\[
{}t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.560 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.176 |
|
|
\[
{}t y^{\prime \prime }+3 y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.234 |
|
|
\[
{}\cos \left (t \right ) y+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.889 |
|
|
\[
{}\sqrt {t}\, \sin \left (t \right ) y+y^{\prime } = 0
\] |
[_separable] |
✓ |
2.154 |
|
|
\[
{}\frac {2 t y}{t^{2}+1}+y^{\prime } = \frac {1}{t^{2}+1}
\] |
[_linear] |
✓ |
1.217 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{t} t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.296 |
|
|
\[
{}t^{2} y+y^{\prime } = 1
\] |
[_linear] |
✓ |
1.312 |
|
|
\[
{}t^{2} y+y^{\prime } = t^{2}
\] |
[_separable] |
✓ |
1.519 |
|
|
\[
{}\frac {t y}{t^{2}+1}+y^{\prime } = 1-\frac {t^{3} y}{t^{4}+1}
\] |
[_linear] |
✓ |
1.977 |
|
|
\[
{}\sqrt {t^{2}+1}\, y+y^{\prime } = 0
\] |
[_separable] |
✓ |
3.938 |
|
|
\[
{}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.927 |
|
|
\[
{}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.971 |
|
|
\[
{}y^{\prime }-2 t y = t
\] |
[_separable] |
✓ |
1.945 |
|
|
\[
{}t y+y^{\prime } = t +1
\] |
[_linear] |
✓ |
1.557 |
|
|
\[
{}y^{\prime }+y = \frac {1}{t^{2}+1}
\] |
[_linear] |
✓ |
1.865 |
|
|
\[
{}y^{\prime }-2 t y = 1
\] |
[_linear] |
✓ |
1.391 |
|
|
\[
{}t y+\left (t^{2}+1\right ) y^{\prime } = \left (t^{2}+1\right )^{{5}/{2}}
\] |
[_linear] |
✓ |
2.037 |
|
|
\[
{}4 t y+\left (t^{2}+1\right ) y^{\prime } = t
\] |
[_separable] |
✓ |
2.085 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.793 |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
2.267 |
|
|
\[
{}y^{\prime } = \left (t +1\right ) \left (y+1\right )
\] |
[_separable] |
✓ |
1.556 |
|
|
\[
{}y^{\prime } = 1-t +y^{2}-t y^{2}
\] |
[_separable] |
✓ |
2.262 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3+t +y}
\] |
[_separable] |
✓ |
2.721 |
|
|
\[
{}\cos \left (y\right ) \sin \left (t \right ) y^{\prime } = \cos \left (t \right ) \sin \left (y\right )
\] |
[_separable] |
✓ |
3.075 |
|
|
\[
{}t^{2} \left (1+y^{2}\right )+2 y y^{\prime } = 0
\] |
[_separable] |
✓ |
3.022 |
|
|
\[
{}y^{\prime } = \frac {2 t}{y+t^{2} y}
\] |
[_separable] |
✓ |
2.313 |
|
|
\[
{}\sqrt {1+y^{2}}\, y^{\prime } = \frac {t y^{3}}{\sqrt {t^{2}+1}}
\] |
[_separable] |
✓ |
2.730 |
|
|
\[
{}y^{\prime } = \frac {3 t^{2}+4 t +2}{-2+2 y}
\] |
[_separable] |
✓ |
2.423 |
|
|
\[
{}\cos \left (y\right ) y^{\prime } = -\frac {t \sin \left (y\right )}{t^{2}+1}
\] |
[_separable] |
✓ |
3.171 |
|
|
\[
{}y^{\prime } = k \left (a -y\right ) \left (b -y\right )
\] |
[_quadrature] |
✓ |
34.451 |
|
|
\[
{}3 t y^{\prime } = \cos \left (t \right ) y
\] |
[_separable] |
✓ |
3.132 |
|