|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }+3 x+4 y=0 \\ y^{\prime }+2 x+5 y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.400 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+5 y \\ y^{\prime }=-x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.496 |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }-y^{\prime }+3 x=\sin \left (t \right ) \\ x^{\prime }+y=\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.593 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=z-y \\ y^{\prime }=z \\ z^{\prime }=z-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.549 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+z \\ y^{\prime }=x+z \\ z^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.334 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=y \\ y^{\prime \prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.026 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }+y^{\prime }+x=0 \\ x^{\prime }+y^{\prime \prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.020 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=3 x+y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.043 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=x^{2}+y \\ y^{\prime }=-2 x x^{\prime }+x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.000 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x^{2}+y^{2} \\ y^{\prime }=2 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.046 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {1}{y} \\ y^{\prime }=\frac {1}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.046 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {x}{y} \\ y^{\prime }=\frac {y}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.047 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y}{x-y} \\ y^{\prime }=\frac {x}{x-y} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.047 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\sin \left (x\right ) \cos \left (y\right ) \\ y^{\prime }=\cos \left (x\right ) \sin \left (y\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.048 |
|
|
\[
{}\left [\begin {array}{c} {\mathrm e}^{t} x^{\prime }=\frac {1}{y} \\ {\mathrm e}^{t} y^{\prime }=\frac {1}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.054 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\cos \left (x\right )^{2} \cos \left (y\right )^{2}+\sin \left (x\right )^{2} \cos \left (y\right )^{2} \\ y^{\prime }=-\frac {\sin \left (2 x\right ) \sin \left (2 y\right )}{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.051 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 y-x \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.315 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=-x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.279 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.572 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.428 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-5 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.425 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+z-x \\ y^{\prime }=x-y+z \\ z^{\prime }=x+y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.347 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y+z \\ y^{\prime }=x+2 y-z \\ z^{\prime }=x-y+2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.462 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y+z \\ y^{\prime }=x+z \\ z^{\prime }=y-2 z-3 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.453 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x-y=-{\mathrm e}^{2 t} \\ y^{\prime }+3 x-2 y=6 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.499 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-\cos \left (t \right ) \\ y^{\prime }=-y-2 x+\cos \left (t \right )+\sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.889 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+\tan \left (t \right )^{2}-1 \\ y^{\prime }=\tan \left (t \right )-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.708 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-2 y+\frac {2}{{\mathrm e}^{t}-1} \\ y^{\prime }=6 x+3 y-\frac {3}{{\mathrm e}^{t}-1} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.056 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+\frac {1}{\cos \left (t \right )} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.644 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.506 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3-2 y \\ y^{\prime }=2 x-2 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.539 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y+\sin \left (t \right ) \\ y^{\prime }=x+\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.569 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+{\mathrm e}^{t} \\ y^{\prime }=x+y-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.354 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-5 y+4 t -1 \\ y^{\prime }=x-2 y+t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.571 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x+{\mathrm e}^{t} \\ y^{\prime }=x-y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.510 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y=t^{2} \\ y^{\prime }-x=t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.548 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }+y={\mathrm e}^{-t} \\ 2 x^{\prime }+y^{\prime }+2 y=\sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.464 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y-2 z+2-t \\ y^{\prime }=-x+1 \\ z^{\prime }=x+y-z+1-t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.033 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+x+2 y=2 \,{\mathrm e}^{-t} \\ y^{\prime }+y+z=1 \\ z^{\prime }+z=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.577 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.317 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x+y \\ y^{\prime }=4 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.325 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-4 y+1 \\ y^{\prime }=-x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.530 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+y+{\mathrm e}^{t} \\ y^{\prime }=x+3 y-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.460 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y+\cos \left (t \right ) \\ y^{\prime }=-x-2 y+\sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.474 |
|
|
\[
{}x^{\prime }+3 x = {\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.255 |
|
|
\[
{}x^{\prime }-3 x = 3 t^{3}+3 t^{2}+2 t +1
\] |
[[_linear, ‘class A‘]] |
✓ |
0.265 |
|
|
\[
{}x^{\prime }-x = \cos \left (t \right )-\sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.286 |
|
|
\[
{}2 x^{\prime }+6 x = t \,{\mathrm e}^{-3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.254 |
|
|
\[
{}x^{\prime }+x = 2 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.303 |
|
|
\[
{}x^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.204 |
|
|
\[
{}x^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.227 |
|
|
\[
{}x^{\prime \prime } = \cos \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.292 |
|
|
\[
{}x^{\prime \prime }+x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.218 |
|
|
\[
{}x^{\prime \prime }+x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.264 |
|
|
\[
{}x^{\prime \prime }-x^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.300 |
|
|
\[
{}x^{\prime \prime }+x = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.247 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime } = 12 t +2
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.248 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+2 x = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.251 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.300 |
|
|
\[
{}2 x^{\prime \prime }-2 x^{\prime } = \left (1+t \right ) {\mathrm e}^{t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.296 |
|
|
\[
{}x^{\prime \prime }+x = 2 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.366 |
|