|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = y^{2}-y^{3}
\] |
[_quadrature] |
✓ |
3.527 |
|
|
\[
{}y^{\prime } = -4 y+9 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.096 |
|
|
\[
{}y^{\prime } = -4 y+3 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.054 |
|
|
\[
{}y^{\prime } = -3 y+4 \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.306 |
|
|
\[
{}y^{\prime } = 2 y+\sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.283 |
|
|
\[
{}y^{\prime } = 3 y-4 \,{\mathrm e}^{3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.006 |
|
|
\[
{}y^{\prime } = \frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.012 |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{\frac {t}{3}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.407 |
|
|
\[
{}y^{\prime }-2 y = 3 \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.478 |
|
|
\[
{}y^{\prime }+y = \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.550 |
|
|
\[
{}y^{\prime }+3 y = \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.608 |
|
|
\[
{}y^{\prime }-2 y = 7 \,{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.258 |
|
|
\[
{}y^{\prime }+2 y = 3 t^{2}+2 t -1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.078 |
|
|
\[
{}y^{\prime }+2 y = t^{2}+2 t +1+{\mathrm e}^{4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.827 |
|
|
\[
{}y^{\prime }+y = t^{3}+\sin \left (3 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.639 |
|
|
\[
{}y^{\prime }-3 y = 2 t -{\mathrm e}^{4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.156 |
|
|
\[
{}y^{\prime }+y = \cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.868 |
|
|
\[
{}y^{\prime } = -\frac {y}{t}+2
\] |
[_linear] |
✓ |
1.850 |
|
|
\[
{}y^{\prime } = \frac {3 y}{t}+t^{5}
\] |
[_linear] |
✓ |
1.339 |
|
|
\[
{}y^{\prime } = -\frac {y}{t +1}+t^{2}
\] |
[_linear] |
✓ |
1.491 |
|
|
\[
{}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
1.404 |
|
|
\[
{}y^{\prime }-\frac {2 t y}{t^{2}+1} = 3
\] |
[_linear] |
✓ |
1.472 |
|
|
\[
{}y^{\prime }-\frac {2 y}{t} = t^{3} {\mathrm e}^{t}
\] |
[_linear] |
✓ |
1.410 |
|
|
\[
{}y^{\prime } = -\frac {y}{t +1}+2
\] |
[_linear] |
✓ |
1.811 |
|
|
\[
{}y^{\prime } = \frac {y}{t +1}+4 t^{2}+4 t
\] |
[_linear] |
✓ |
1.286 |
|
|
\[
{}y^{\prime } = -\frac {y}{t}+2
\] |
[_linear] |
✓ |
2.480 |
|
|
\[
{}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
1.709 |
|
|
\[
{}y^{\prime }-\frac {2 y}{t} = 2 t^{2}
\] |
[_linear] |
✓ |
1.690 |
|
|
\[
{}y^{\prime }-\frac {3 y}{t} = 2 t^{3} {\mathrm e}^{2 t}
\] |
[_linear] |
✓ |
2.388 |
|
|
\[
{}y^{\prime } = \sin \left (t \right ) y+4
\] |
[_linear] |
✓ |
1.749 |
|
|
\[
{}y^{\prime } = t^{2} y+4
\] |
[_linear] |
✓ |
1.277 |
|
|
\[
{}y^{\prime } = \frac {y}{t^{2}}+4 \cos \left (t \right )
\] |
[_linear] |
✓ |
1.968 |
|
|
\[
{}y^{\prime } = y+4 \cos \left (t^{2}\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.526 |
|
|
\[
{}y^{\prime } = -y \,{\mathrm e}^{-t^{2}}+\cos \left (t \right )
\] |
[_linear] |
✓ |
2.618 |
|
|
\[
{}y^{\prime } = \frac {y}{\sqrt {t^{3}-3}}+t
\] |
[_linear] |
✓ |
22.539 |
|
|
\[
{}y^{\prime } = a t y+4 \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
1.178 |
|
|
\[
{}y^{\prime } = t^{r} y+4
\] |
[_linear] |
✓ |
1.398 |
|
|
\[
{}v^{\prime }+\frac {2 v}{5} = 3 \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.441 |
|
|
\[
{}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
1.392 |
|
|
\[
{}y^{\prime }+2 y = 3 \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.984 |
|
|
\[
{}y^{\prime } = 3 y
\] |
[_quadrature] |
✓ |
1.054 |
|
|
\[
{}y^{\prime } = t^{2} \left (t^{2}+1\right )
\] |
[_quadrature] |
✓ |
0.303 |
|
|
\[
{}y^{\prime } = -\sin \left (y\right )^{5}
\] |
[_quadrature] |
✓ |
1.842 |
|
|
\[
{}y^{\prime } = \frac {\left (t^{2}-4\right ) \left (y+1\right ) {\mathrm e}^{y}}{\left (t -1\right ) \left (3-y\right )}
\] |
[_separable] |
✓ |
2.274 |
|
|
\[
{}y^{\prime } = \sin \left (y\right )^{2}
\] |
[_quadrature] |
✓ |
1.117 |
|
|
\[
{}y^{\prime } = \left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right )
\] |
[‘x=_G(y,y’)‘] |
✗ |
10.814 |
|
|
\[
{}y^{\prime } = y+{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.061 |
|
|
\[
{}y^{\prime } = 3-2 y
\] |
[_quadrature] |
✓ |
1.069 |
|
|
\[
{}y^{\prime } = t y
\] |
[_separable] |
✓ |
1.145 |
|
|
\[
{}y^{\prime } = 3 y+{\mathrm e}^{7 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.056 |
|
|
\[
{}y^{\prime } = \frac {t y}{t^{2}+1}
\] |
[_separable] |
✓ |
1.321 |
|
|
\[
{}y^{\prime } = -5 y+\sin \left (3 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.310 |
|
|
\[
{}y^{\prime } = t +\frac {2 y}{t +1}
\] |
[_linear] |
✓ |
1.019 |
|
|
\[
{}y^{\prime } = 3+y^{2}
\] |
[_quadrature] |
✓ |
1.030 |
|
|
\[
{}y^{\prime } = 2 y-y^{2}
\] |
[_quadrature] |
✓ |
1.807 |
|
|
\[
{}y^{\prime } = -3 y+{\mathrm e}^{-2 t}+t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.595 |
|
|
\[
{}x^{\prime } = -x t
\] |
[_separable] |
✓ |
1.746 |
|
|
\[
{}y^{\prime } = 2 y+\cos \left (4 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.623 |
|
|
\[
{}y^{\prime } = 3 y+2 \,{\mathrm e}^{3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.292 |
|
|
\[
{}y^{\prime } = t^{2} y^{3}+y^{3}
\] |
[_separable] |
✓ |
3.033 |
|
|
\[
{}y^{\prime }+5 y = 3 \,{\mathrm e}^{-5 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.247 |
|
|
\[
{}y^{\prime } = 2 t y+3 t \,{\mathrm e}^{t^{2}}
\] |
[_linear] |
✓ |
2.536 |
|
|
\[
{}y^{\prime } = \frac {\left (t +1\right )^{2}}{\left (y+1\right )^{2}}
\] |
[_separable] |
✓ |
4.305 |
|
|
\[
{}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2}
\] |
[_separable] |
✓ |
1.810 |
|
|
\[
{}y^{\prime } = 1-y^{2}
\] |
[_quadrature] |
✓ |
1.507 |
|
|
\[
{}y^{\prime } = \frac {t^{2}}{y+t^{3} y}
\] |
[_separable] |
✓ |
2.592 |
|
|
\[
{}y^{\prime } = y^{2}-2 y+1
\] |
[_quadrature] |
✓ |
1.066 |
|
|
\[
{}y^{\prime } = \left (y-2\right ) \left (y+1-\cos \left (t \right )\right )
\] |
[_Riccati] |
✓ |
4.221 |
|
|
\[
{}y^{\prime } = \left (-1+y\right ) \left (y-2\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right )
\] |
[_Abel] |
✗ |
1.973 |
|
|
\[
{}y^{\prime } = t^{2} y+1+y+t^{2}
\] |
[_separable] |
✓ |
1.260 |
|
|
\[
{}y^{\prime } = \frac {2 y+1}{t}
\] |
[_separable] |
✓ |
1.651 |
|
|
\[
{}y^{\prime } = 3-y^{2}
\] |
[_quadrature] |
✓ |
1.211 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.250 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.288 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.284 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.335 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.535 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 y \\ y^{\prime }=3 \pi y-\frac {x}{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.688 |
|
|
\[
{}\left [\begin {array}{c} p^{\prime }=3 p-2 q-7 r \\ q^{\prime }=-2 p+6 r \\ r^{\prime }=\frac {73 q}{100}+2 r \end {array}\right ]
\] |
system_of_ODEs |
✓ |
64.736 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+2 \pi y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.632 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\beta y \\ y^{\prime }=\gamma x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.552 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.464 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.426 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=2 x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.455 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-3 y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.498 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+3 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.470 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=1 \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.332 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.296 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-2 y \\ y^{\prime }=-x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.339 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x-2 y \\ y^{\prime }=-x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.344 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.299 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {x}{2} \\ y^{\prime }=x-\frac {y}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.287 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=9 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.349 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+4 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.335 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.487 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.541 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.338 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.534 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.546 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.538 |
|