|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.448 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } \sin \left (x \right ) = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.659 |
|
|
\[
{}x y^{\prime \prime }+y \sin \left (x \right ) = x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.906 |
|
|
\[
{}\ln \left (x \right ) y^{\prime \prime }-y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
35.466 |
|
|
\[
{}y^{\prime \prime \prime }+x \sin \left (y\right ) = 0
\] |
[NONE] |
✗ |
0.051 |
|
|
\[
{}y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
0.625 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.478 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.476 |
|
|
\[
{}y^{\prime \prime }-\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.481 |
|
|
\[
{}y^{\prime \prime } = x^{2} y-y^{\prime }
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.552 |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.665 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{y}+x y
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.428 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.792 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-n y = 0
\] |
[_separable] |
✓ |
0.541 |
|
|
\[
{}9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
[_Jacobi] |
✓ |
0.823 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x^{2}-\frac {1}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.912 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.650 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{9} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.857 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.862 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +4 \left (x^{4}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.994 |
|
|
\[
{}x y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{4} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.221 |
|
|
\[
{}y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
0.902 |
|
|
\[
{}y^{\prime \prime }+\frac {3 y^{\prime }}{x}+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.892 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.033 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \pi ^{2}-x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.419 |
|
|
\[
{}y^{\prime \prime }-4 y = \cos \left (\pi x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.625 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \arcsin \left (\sin \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.125 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.151 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 t x_{1}^{2} \\ x_{2}^{\prime }=\frac {x_{2}+t}{t} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.054 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }={\mathrm e}^{t -x_{1}} \\ x_{2}^{\prime }=2 \,{\mathrm e}^{x_{1}} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.056 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=\frac {y^{2}}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.061 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}^{2}}{x_{2}} \\ x_{2}^{\prime }=x_{2}-x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.056 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {{\mathrm e}^{-x}}{t} \\ y^{\prime }=\frac {x \,{\mathrm e}^{-y}}{t} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.057 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y+t}{x+y} \\ y^{\prime }=\frac {x-t}{x+y} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.059 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {t -y}{y-x} \\ y^{\prime }=\frac {x-t}{y-x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.058 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y+t}{x+y} \\ y^{\prime }=\frac {t +x}{x+y} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.058 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-9 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.441 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+t \\ y^{\prime }=x-t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.363 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+3 x+4 y=0 \\ y^{\prime }+2 x+5 y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.504 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+5 y \\ y^{\prime }=-x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.531 |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }-y^{\prime }+3 x=\sin \left (t \right ) \\ x^{\prime }+y=\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.579 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=z-y \\ y^{\prime }=z \\ z^{\prime }=z-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.557 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+z \\ y^{\prime }=x+z \\ z^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.323 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=y \\ y^{\prime \prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.028 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }+y^{\prime }+x=0 \\ x^{\prime }+y^{\prime \prime }=0 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.027 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=3 x+y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.052 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=x^{2}+y \\ y^{\prime }=-2 x x^{\prime }+x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.044 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x^{2}+y^{2} \\ y^{\prime }=2 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.055 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {1}{y} \\ y^{\prime }=\frac {1}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.056 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {x}{y} \\ y^{\prime }=\frac {y}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.053 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y}{x-y} \\ y^{\prime }=\frac {x}{x-y} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.057 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\sin \left (x\right ) \cos \left (y\right ) \\ y^{\prime }=\cos \left (x\right ) \sin \left (y\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.065 |
|
|
\[
{}\left [\begin {array}{c} {\mathrm e}^{t} x^{\prime }=\frac {1}{y} \\ {\mathrm e}^{t} y^{\prime }=\frac {1}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.063 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\cos \left (x\right )^{2} \cos \left (y\right )^{2}+\sin \left (x\right )^{2} \cos \left (y\right )^{2} \\ y^{\prime }=-\frac {\sin \left (2 x\right ) \sin \left (2 y\right )}{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.061 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 y-x \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.405 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.369 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.662 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.498 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-5 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.519 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+z-x \\ y^{\prime }=x-y+z \\ z^{\prime }=x+y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.339 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y+z \\ y^{\prime }=x+2 y-z \\ z^{\prime }=x-y+2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.428 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y+z \\ y^{\prime }=x+z \\ z^{\prime }=y-2 z-3 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.439 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x-y=-{\mathrm e}^{2 t} \\ y^{\prime }+3 x-2 y=6 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.471 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-\cos \left (t \right ) \\ y^{\prime }=-y-2 x+\cos \left (t \right )+\sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.806 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+\tan \left (t \right )^{2}-1 \\ y^{\prime }=\tan \left (t \right )-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.681 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-2 y+\frac {2}{{\mathrm e}^{t}-1} \\ y^{\prime }=6 x+3 y-\frac {3}{{\mathrm e}^{t}-1} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.065 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+\frac {1}{\cos \left (t \right )} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.599 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.599 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3-2 y \\ y^{\prime }=2 x-2 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.535 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y+\sin \left (t \right ) \\ y^{\prime }=x+\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.534 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+{\mathrm e}^{t} \\ y^{\prime }=x+y-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.352 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-5 y+4 t -1 \\ y^{\prime }=x-2 y+t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.553 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x+{\mathrm e}^{t} \\ y^{\prime }=x-y+{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.516 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y=t^{2} \\ -x+y^{\prime }=t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.529 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }+y={\mathrm e}^{-t} \\ 2 x^{\prime }+y^{\prime }+2 y=\sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.456 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y-2 z+2-t \\ y^{\prime }=-x+1 \\ z^{\prime }=x+y-z+1-t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.028 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+x+2 y=2 \,{\mathrm e}^{-t} \\ y^{\prime }+y+z=1 \\ z^{\prime }+z=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.540 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.410 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x+y \\ y^{\prime }=4 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.415 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-4 y+1 \\ y^{\prime }=-x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.604 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+y+{\mathrm e}^{t} \\ y^{\prime }=x+3 y-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.437 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y+\cos \left (t \right ) \\ y^{\prime }=-x-2 y+\sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.452 |
|
|
\[
{}x^{\prime }+3 x = {\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.395 |
|
|
\[
{}x^{\prime }-3 x = 3 t^{3}+3 t^{2}+2 t +1
\] |
[[_linear, ‘class A‘]] |
✓ |
0.396 |
|
|
\[
{}x^{\prime }-x = \cos \left (t \right )-\sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.436 |
|
|
\[
{}2 x^{\prime }+6 x = t \,{\mathrm e}^{-3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.397 |
|
|
\[
{}x^{\prime }+x = 2 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.438 |
|
|
\[
{}x^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.164 |
|
|
\[
{}x^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.184 |
|
|
\[
{}x^{\prime \prime } = \cos \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.253 |
|
|
\[
{}x^{\prime \prime }+x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.176 |
|
|
\[
{}x^{\prime \prime }+x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.206 |
|
|
\[
{}x^{\prime \prime }-x^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.207 |
|
|
\[
{}x^{\prime \prime }+x = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.198 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime } = 12 t +2
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.210 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+2 x = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.189 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.237 |
|
|
\[
{}2 x^{\prime \prime }-2 x^{\prime } = \left (1+t \right ) {\mathrm e}^{t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.235 |
|
|
\[
{}x^{\prime \prime }+x = 2 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.306 |
|
|
\[
{}y^{\prime } = \frac {x^{4}}{y}
\] |
[_separable] |
✓ |
2.095 |
|