|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \pi ^{2}-x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.168 |
|
|
\[
{}y^{\prime \prime }-4 y = \cos \left (\pi x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.449 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \arcsin \left (\sin \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.984 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.203 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 t x_{1}^{2} \\ x_{2}^{\prime }=\frac {x_{2}+t}{t} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.055 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }={\mathrm e}^{t -x_{1}} \\ x_{2}^{\prime }=2 \,{\mathrm e}^{x_{1}} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.051 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=\frac {y^{2}}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.050 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}^{2}}{x_{2}} \\ x_{2}^{\prime }=x_{2}-x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.050 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {{\mathrm e}^{-x}}{t} \\ y^{\prime }=\frac {x \,{\mathrm e}^{-y}}{t} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.051 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y+t}{x+y} \\ y^{\prime }=\frac {x-t}{x+y} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.052 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {t -y}{y-x} \\ y^{\prime }=\frac {x-t}{y-x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.050 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y+t}{x+y} \\ y^{\prime }=\frac {t +x}{x+y} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.051 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-9 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.359 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+t \\ y^{\prime }=x-t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.395 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+3 x+4 y=0 \\ y^{\prime }+2 x+5 y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.450 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+5 y \\ y^{\prime }=-x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.526 |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }-y^{\prime }+3 x=\sin \left (t \right ) \\ x^{\prime }+y=\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.602 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=z-y \\ y^{\prime }=z \\ z^{\prime }=z-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.584 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+z \\ y^{\prime }=x+z \\ z^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.352 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=y \\ y^{\prime \prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.019 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }+y^{\prime }+x=0 \\ x^{\prime }+y^{\prime \prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.023 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=3 x+y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.045 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=x^{2}+y \\ y^{\prime }=-2 x x^{\prime }+x \end {array}\right ]
\] |
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 |
✗ |
0.050 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {1}{y} \\ y^{\prime }=\frac {1}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.050 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {x}{y} \\ y^{\prime }=\frac {y}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.051 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y}{x-y} \\ y^{\prime }=\frac {x}{x-y} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.053 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\sin \left (x\right ) \cos \left (y\right ) \\ y^{\prime }=\cos \left (x\right ) \sin \left (y\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.051 |
|
|
\[
{}\left [\begin {array}{c} {\mathrm e}^{t} x^{\prime }=\frac {1}{y} \\ {\mathrm e}^{t} y^{\prime }=\frac {1}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.058 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\cos \left (x\right )^{2} \cos \left (y\right )^{2}+\sin \left (x\right )^{2} \cos \left (y\right )^{2} \\ y^{\prime }=-\frac {\sin \left (2 x\right ) \sin \left (2 y\right )}{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.057 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 y-x \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.336 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.297 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.622 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.505 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-5 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.434 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+z-x \\ y^{\prime }=x-y+z \\ z^{\prime }=x+y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.372 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y+z \\ y^{\prime }=x+2 y-z \\ z^{\prime }=x-y+2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.461 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y+z \\ y^{\prime }=x+z \\ z^{\prime }=y-2 z-3 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.404 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x-y=-{\mathrm e}^{2 t} \\ y^{\prime }+3 x-2 y=6 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.501 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-\cos \left (t \right ) \\ y^{\prime }=-y-2 x+\cos \left (t \right )+\sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.865 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+\tan \left (t \right )^{2}-1 \\ y^{\prime }=\tan \left (t \right )-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.738 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-2 y+\frac {2}{{\mathrm e}^{t}-1} \\ y^{\prime }=6 x+3 y-\frac {3}{{\mathrm e}^{t}-1} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.058 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+\frac {1}{\cos \left (t \right )} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.641 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.546 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3-2 y \\ y^{\prime }=2 x-2 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.576 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y+\sin \left (t \right ) \\ y^{\prime }=x+\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.574 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+{\mathrm e}^{t} \\ y^{\prime }=x+y-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.358 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-5 y+4 t -1 \\ y^{\prime }=x-2 y+t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.576 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x+{\mathrm e}^{t} \\ y^{\prime }=x-y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.536 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y=t^{2} \\ -x+y^{\prime }=t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.558 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }+y={\mathrm e}^{-t} \\ 2 x^{\prime }+y^{\prime }+2 y=\sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.483 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y-2 z+2-t \\ y^{\prime }=-x+1 \\ z^{\prime }=x+y-z+1-t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.111 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+x+2 y=2 \,{\mathrm e}^{-t} \\ y^{\prime }+y+z=1 \\ z^{\prime }+z=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.567 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.329 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x+y \\ y^{\prime }=4 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.338 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-4 y+1 \\ y^{\prime }=-x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.538 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+y+{\mathrm e}^{t} \\ y^{\prime }=x+3 y-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.411 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y+\cos \left (t \right ) \\ y^{\prime }=-x-2 y+\sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.467 |
|
|
\[
{}x^{\prime }+3 x = {\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.296 |
|
|
\[
{}x^{\prime }-3 x = 3 t^{3}+3 t^{2}+2 t +1
\] |
[[_linear, ‘class A‘]] |
✓ |
0.294 |
|
|
\[
{}x^{\prime }-x = \cos \left (t \right )-\sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.326 |
|
|
\[
{}2 x^{\prime }+6 x = t \,{\mathrm e}^{-3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.304 |
|
|
\[
{}x^{\prime }+x = 2 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.352 |
|
|
\[
{}x^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.187 |
|
|
\[
{}x^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.201 |
|
|
\[
{}x^{\prime \prime } = \cos \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.279 |
|
|
\[
{}x^{\prime \prime }+x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.197 |
|
|
\[
{}x^{\prime \prime }+x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.223 |
|
|
\[
{}x^{\prime \prime }-x^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.218 |
|
|
\[
{}x^{\prime \prime }+x = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.200 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime } = 12 t +2
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.205 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+2 x = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.209 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.256 |
|
|
\[
{}2 x^{\prime \prime }-2 x^{\prime } = \left (t +1\right ) {\mathrm e}^{t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.257 |
|
|
\[
{}x^{\prime \prime }+x = 2 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.335 |
|
|
\[
{}y^{\prime } = \frac {x^{4}}{y}
\] |
[_separable] |
✓ |
1.819 |
|
|
\[
{}y^{\prime } = \frac {x^{2} \left (x^{3}+1\right )}{y}
\] |
[_separable] |
✓ |
1.299 |
|
|
\[
{}y^{\prime }+y^{3} \sin \left (x \right ) = 0
\] |
[_separable] |
✓ |
2.362 |
|
|
\[
{}y^{\prime } = \frac {7 x^{2}-1}{7+5 y}
\] |
[_separable] |
✓ |
1.338 |
|
|
\[
{}y^{\prime } = \sin \left (2 x \right )^{2} \cos \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.489 |
|
|
\[
{}x y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
2.132 |
|
|
\[
{}y^{\prime } y = \left (x +x y^{2}\right ) {\mathrm e}^{x^{2}}
\] |
[_separable] |
✓ |
2.202 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+{\mathrm e}^{-x}}{y^{2}-{\mathrm e}^{y}}
\] |
[_separable] |
✓ |
1.800 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{1+y^{2}}
\] |
[_separable] |
✓ |
1.046 |
|
|
\[
{}y^{\prime } = \frac {\sec \left (x \right )^{2}}{y^{3}+1}
\] |
[_separable] |
✓ |
1.869 |
|
|
\[
{}y^{\prime } = 4 \sqrt {x y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
8.820 |
|
|
\[
{}y^{\prime } = x \left (y-y^{2}\right )
\] |
[_separable] |
✓ |
2.110 |
|
|
\[
{}y^{\prime } = \left (1-12 x \right ) y^{2}
\] |
[_separable] |
✓ |
1.783 |
|
|
\[
{}y^{\prime } = \frac {3-2 x}{y}
\] |
[_separable] |
✓ |
4.174 |
|
|
\[
{}x +y \,{\mathrm e}^{-x} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.589 |
|
|
\[
{}r^{\prime } = \frac {r^{2}}{\theta }
\] |
[_separable] |
✓ |
1.714 |
|
|
\[
{}y^{\prime } = \frac {3 x}{y+x^{2} y}
\] |
[_separable] |
✓ |
2.406 |
|
|
\[
{}y^{\prime } = \frac {2 x}{1+2 y}
\] |
[_separable] |
✓ |
3.277 |
|
|
\[
{}y^{\prime } = 2 x y^{2}+4 x^{3} y^{2}
\] |
[_separable] |
✓ |
1.841 |
|
|
\[
{}y^{\prime } = x^{2} {\mathrm e}^{-3 y}
\] |
[_separable] |
✓ |
1.906 |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) \tan \left (2 x \right )
\] |
[_separable] |
✓ |
3.880 |
|
|
\[
{}y^{\prime } = \frac {x \left (x^{2}+1\right ) y^{5}}{6}
\] |
[_separable] |
✓ |
6.969 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}-{\mathrm e}^{x}}{2 y-11}
\] |
[_separable] |
✓ |
3.056 |
|
|
\[
{}x^{2} y^{\prime } = y-x y
\] |
[_separable] |
✓ |
2.221 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y}
\] |
[_separable] |
✓ |
3.507 |
|