|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = -3 y+{\mathrm e}^{-2 t}+t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.029 |
|
|
\[
{}x^{\prime } = -t x
\] |
[_separable] |
✓ |
3.025 |
|
|
\[
{}y^{\prime } = 2 y+\cos \left (4 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.023 |
|
|
\[
{}y^{\prime } = 3 y+2 \,{\mathrm e}^{3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.611 |
|
|
\[
{}y^{\prime } = t^{2} y^{3}+y^{3}
\] |
[_separable] |
✓ |
3.816 |
|
|
\[
{}y^{\prime }+5 y = 3 \,{\mathrm e}^{-5 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.601 |
|
|
\[
{}y^{\prime } = 2 t y+3 t \,{\mathrm e}^{t^{2}}
\] |
[_linear] |
✓ |
3.016 |
|
|
\[
{}y^{\prime } = \frac {\left (t +1\right )^{2}}{\left (y+1\right )^{2}}
\] |
[_separable] |
✓ |
4.015 |
|
|
\[
{}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2}
\] |
[_separable] |
✓ |
2.372 |
|
|
\[
{}y^{\prime } = 1-y^{2}
\] |
[_quadrature] |
✓ |
2.534 |
|
|
\[
{}y^{\prime } = \frac {t^{2}}{y+t^{3} y}
\] |
[_separable] |
✓ |
3.185 |
|
|
\[
{}y^{\prime } = y^{2}-2 y+1
\] |
[_quadrature] |
✓ |
1.423 |
|
|
\[
{}y^{\prime } = \left (y-2\right ) \left (y+1-\cos \left (t \right )\right )
\] |
[_Riccati] |
✓ |
4.549 |
|
|
\[
{}y^{\prime } = \left (y-1\right ) \left (y-2\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right )
\] |
[_Abel] |
✗ |
2.054 |
|
|
\[
{}y^{\prime } = t^{2} y+1+y+t^{2}
\] |
[_separable] |
✓ |
1.656 |
|
|
\[
{}y^{\prime } = \frac {2 y+1}{t}
\] |
[_separable] |
✓ |
2.277 |
|
|
\[
{}y^{\prime } = 3-y^{2}
\] |
[_quadrature] |
✓ |
2.982 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.325 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.433 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.414 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.464 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.595 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 y \\ y^{\prime }=3 \pi y-\frac {x}{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.826 |
|
|
\[
{}\left [\begin {array}{c} p^{\prime }=3 p-2 q-7 r \\ q^{\prime }=-2 p+6 r \\ r^{\prime }=\frac {73 q}{100}+2 r \end {array}\right ]
\] |
system_of_ODEs |
✓ |
74.269 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+2 \pi y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.703 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\beta y \\ y^{\prime }=\gamma x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.525 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.592 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.569 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=2 x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.592 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-3 y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.582 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+3 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.578 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=1 \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.478 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.418 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-2 y \\ y^{\prime }=-x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.470 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x-2 y \\ y^{\prime }=-x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.470 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.461 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {x}{2} \\ y^{\prime }=x-\frac {y}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.444 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=9 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.500 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+4 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.494 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.701 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.638 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.498 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.640 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.628 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.629 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.598 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.600 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.601 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.606 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.613 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.595 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.610 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.581 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.600 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.574 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=-4 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.651 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-5 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.904 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.929 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-6 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.952 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+4 y \\ y^{\prime }=-3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.935 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.570 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=-4 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.646 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-5 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.913 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.918 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-6 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.930 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+4 y \\ y^{\prime }=-3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.932 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {9 x}{10}-2 y \\ y^{\prime }=x+\frac {11 y}{10} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.641 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+10 y \\ y^{\prime }=-x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.539 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.561 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.843 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.587 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.590 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.550 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.582 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.582 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.587 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.545 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y \\ y^{\prime }=3 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.591 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+2 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.602 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.326 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.335 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-y \\ y^{\prime }=4 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.595 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }-7 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.914 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.912 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y}{10} \\ y^{\prime }=\frac {z}{5} \\ z^{\prime }=\frac {2 x}{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.204 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x \\ z^{\prime }=2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.491 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=3 x-2 y \\ z^{\prime }=-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.445 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 z \\ y^{\prime }=-y \\ z^{\prime }=-3 x+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.520 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 y-z \\ z^{\prime }=-y+2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.379 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-2 y \\ z^{\prime }=-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.360 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-2 y \\ z^{\prime }=z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.363 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-4 y \\ z^{\prime }=-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.429 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-4 y \\ z^{\prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.375 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-2 y+z \\ z^{\prime }=-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.358 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=z \\ z^{\prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.296 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=-2 y+3 z \\ z^{\prime }=-x+3 y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.948 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+3 y \\ y^{\prime }=z-y \\ z^{\prime }=5 x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.835 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-10 x+10 y \\ y^{\prime }=28 x-y \\ z^{\prime }=-\frac {8 z}{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.776 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=z-y \\ y^{\prime }=z-x \\ z^{\prime }=z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.384 |
|
|
\(\left [\begin {array}{cc} 1 & 0 \\ 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.119 |
|