|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime }+y = t^{3}+\sin \left (3 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.477 |
|
|
\[
{}y^{\prime }-3 y = 2 t -{\mathrm e}^{4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.057 |
|
|
\[
{}y^{\prime }+y = \cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.681 |
|
|
\[
{}y^{\prime } = -\frac {y}{t}+2
\] |
[_linear] |
✓ |
1.599 |
|
|
\[
{}y^{\prime } = \frac {3 y}{t}+t^{5}
\] |
[_linear] |
✓ |
1.157 |
|
|
\[
{}y^{\prime } = -\frac {y}{1+t}+t^{2}
\] |
[_linear] |
✓ |
1.441 |
|
|
\[
{}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
1.233 |
|
|
\[
{}y^{\prime }-\frac {2 t y}{t^{2}+1} = 3
\] |
[_linear] |
✓ |
1.312 |
|
|
\[
{}y^{\prime }-\frac {2 y}{t} = t^{3} {\mathrm e}^{t}
\] |
[_linear] |
✓ |
1.252 |
|
|
\[
{}y^{\prime } = -\frac {y}{1+t}+2
\] |
[_linear] |
✓ |
1.602 |
|
|
\[
{}y^{\prime } = \frac {y}{1+t}+4 t^{2}+4 t
\] |
[_linear] |
✓ |
1.123 |
|
|
\[
{}y^{\prime } = -\frac {y}{t}+2
\] |
[_linear] |
✓ |
2.078 |
|
|
\[
{}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
1.487 |
|
|
\[
{}y^{\prime }-\frac {2 y}{t} = 2 t^{2}
\] |
[_linear] |
✓ |
1.276 |
|
|
\[
{}y^{\prime }-\frac {3 y}{t} = 2 t^{3} {\mathrm e}^{2 t}
\] |
[_linear] |
✓ |
2.113 |
|
|
\[
{}y^{\prime } = \sin \left (t \right ) y+4
\] |
[_linear] |
✓ |
1.546 |
|
|
\[
{}y^{\prime } = t^{2} y+4
\] |
[_linear] |
✓ |
1.178 |
|
|
\[
{}y^{\prime } = \frac {y}{t^{2}}+4 \cos \left (t \right )
\] |
[_linear] |
✓ |
1.859 |
|
|
\[
{}y^{\prime } = y+4 \cos \left (t^{2}\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.381 |
|
|
\[
{}y^{\prime } = -y \,{\mathrm e}^{-t^{2}}+\cos \left (t \right )
\] |
[_linear] |
✓ |
2.575 |
|
|
\[
{}y^{\prime } = \frac {y}{\sqrt {t^{3}-3}}+t
\] |
[_linear] |
✓ |
22.526 |
|
|
\[
{}y^{\prime } = a t y+4 \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
1.090 |
|
|
\[
{}y^{\prime } = t^{r} y+4
\] |
[_linear] |
✓ |
1.286 |
|
|
\[
{}v^{\prime }+\frac {2 v}{5} = 3 \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.322 |
|
|
\[
{}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
1.240 |
|
|
\[
{}y^{\prime }+2 y = 3 \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.842 |
|
|
\[
{}y^{\prime } = 3 y
\] |
[_quadrature] |
✓ |
0.536 |
|
|
\[
{}y^{\prime } = t^{2} \left (t^{2}+1\right )
\] |
[_quadrature] |
✓ |
0.240 |
|
|
\[
{}y^{\prime } = -\sin \left (y\right )^{5}
\] |
[_quadrature] |
✓ |
0.799 |
|
|
\[
{}y^{\prime } = \frac {\left (t^{2}-4\right ) \left (y+1\right ) {\mathrm e}^{y}}{\left (t -1\right ) \left (3-y\right )}
\] |
[_separable] |
✓ |
2.214 |
|
|
\[
{}y^{\prime } = \sin \left (y\right )^{2}
\] |
[_quadrature] |
✓ |
0.508 |
|
|
\[
{}y^{\prime } = \left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right )
\] |
[‘x=_G(y,y’)‘] |
✗ |
3.572 |
|
|
\[
{}y^{\prime } = y+{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.881 |
|
|
\[
{}y^{\prime } = 3-2 y
\] |
[_quadrature] |
✓ |
0.525 |
|
|
\[
{}y^{\prime } = t y
\] |
[_separable] |
✓ |
0.993 |
|
|
\[
{}y^{\prime } = 3 y+{\mathrm e}^{7 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.912 |
|
|
\[
{}y^{\prime } = \frac {t y}{t^{2}+1}
\] |
[_separable] |
✓ |
1.121 |
|
|
\[
{}y^{\prime } = -5 y+\sin \left (3 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.178 |
|
|
\[
{}y^{\prime } = t +\frac {2 y}{1+t}
\] |
[_linear] |
✓ |
0.940 |
|
|
\[
{}y^{\prime } = 3+y^{2}
\] |
[_quadrature] |
✓ |
0.438 |
|
|
\[
{}y^{\prime } = 2 y-y^{2}
\] |
[_quadrature] |
✓ |
0.784 |
|
|
\[
{}y^{\prime } = -3 y+{\mathrm e}^{-2 t}+t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.493 |
|
|
\[
{}x^{\prime } = -x t
\] |
[_separable] |
✓ |
1.479 |
|
|
\[
{}y^{\prime } = 2 y+\cos \left (4 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.380 |
|
|
\[
{}y^{\prime } = 3 y+2 \,{\mathrm e}^{3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.092 |
|
|
\[
{}y^{\prime } = t^{2} y^{3}+y^{3}
\] |
[_separable] |
✓ |
1.827 |
|
|
\[
{}y^{\prime }+5 y = 3 \,{\mathrm e}^{-5 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.094 |
|
|
\[
{}y^{\prime } = 2 t y+3 t \,{\mathrm e}^{t^{2}}
\] |
[_linear] |
✓ |
2.344 |
|
|
\[
{}y^{\prime } = \frac {\left (1+t \right )^{2}}{\left (y+1\right )^{2}}
\] |
[_separable] |
✓ |
3.768 |
|
|
\[
{}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2}
\] |
[_separable] |
✓ |
1.741 |
|
|
\[
{}y^{\prime } = 1-y^{2}
\] |
[_quadrature] |
✓ |
0.902 |
|
|
\[
{}y^{\prime } = \frac {t^{2}}{y+t^{3} y}
\] |
[_separable] |
✓ |
1.209 |
|
|
\[
{}y^{\prime } = y^{2}-2 y+1
\] |
[_quadrature] |
✓ |
0.401 |
|
|
\[
{}y^{\prime } = \left (y-2\right ) \left (y+1-\cos \left (t \right )\right )
\] |
[_Riccati] |
✓ |
3.211 |
|
|
\[
{}y^{\prime } = \left (y-1\right ) \left (y-2\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right )
\] |
[_Abel] |
✗ |
1.124 |
|
|
\[
{}y^{\prime } = t^{2} y+1+y+t^{2}
\] |
[_separable] |
✓ |
1.063 |
|
|
\[
{}y^{\prime } = \frac {2 y+1}{t}
\] |
[_separable] |
✓ |
1.440 |
|
|
\[
{}y^{\prime } = 3-y^{2}
\] |
[_quadrature] |
✓ |
0.559 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.227 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.264 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.242 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.290 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.483 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 y \\ y^{\prime }=3 \pi y-\frac {x}{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.612 |
|
|
\[
{}\left [\begin {array}{c} p^{\prime }=3 p-2 q-7 r \\ q^{\prime }=-2 p+6 r \\ r^{\prime }=\frac {73 q}{100}+2 r \end {array}\right ]
\] |
system_of_ODEs |
✓ |
56.109 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+2 \pi y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.569 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\beta y \\ y^{\prime }=\gamma x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.494 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.403 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.378 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=2 x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.406 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-3 y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.470 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+3 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.454 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=1 \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.293 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.241 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-2 y \\ y^{\prime }=-x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.295 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x-2 y \\ y^{\prime }=-x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.295 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.262 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {x}{2} \\ y^{\prime }=x-\frac {y}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.251 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=9 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.308 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+4 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.291 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=-x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.471 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.480 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.297 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.478 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.419 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.419 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.391 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.377 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.407 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.476 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.416 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.399 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.392 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.385 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.394 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.434 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=-4 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.477 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-5 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.641 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.655 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-6 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.651 |
|