|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.329 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+7 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.512 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=7 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.552 |
|
|
\(\left [\begin {array}{cc} 1 & 2 \\ 3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.144 |
|
|
\(\left [\begin {array}{cc} 3 & 2 \\ 6 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.157 |
|
|
\(\left [\begin {array}{cc} 3 & 1 \\ 12 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.153 |
|
|
\(\left [\begin {array}{cc} -2 & 7 \\ 3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.146 |
|
|
\(\left [\begin {array}{cc} 3 & 4 \\ 5 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.148 |
|
|
\(\left [\begin {array}{cc} 3 & -5 \\ -4 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.147 |
|
|
\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ 2 & 3 & -4 \\ 4 & 1 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.249 |
|
|
\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & -6 & 6 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.254 |
|
|
\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & 1 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.269 |
|
|
\(\left [\begin {array}{ccc} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.236 |
|
|
\(\left [\begin {array}{ccc} 1 & 3 & -6 \\ 0 & 2 & 2 \\ 0 & -1 & 5 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.222 |
|
|
\(\left [\begin {array}{ccc} -5 & -12 & 6 \\ 1 & 5 & -1 \\ -7 & -10 & 8 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.252 |
|
|
\(\left [\begin {array}{ccc} -2 & 5 & 5 \\ -1 & 4 & 5 \\ 3 & -3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.262 |
|
|
\(\left [\begin {array}{ccc} -2 & 6 & -18 \\ 12 & -23 & 66 \\ 5 & -10 & 29 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.267 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-z \\ y^{\prime }=2 x+3 y-4 z \\ z^{\prime }=4 x+y-4 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.546 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y-z \\ y^{\prime }=x+3 y+z \\ z^{\prime }=-3 x-6 y+6 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.515 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.345 |
|
|
\[
{}y^{\prime }+y = 2 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.360 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.215 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.263 |
|
|
\[
{}y^{\prime \prime }+4 y = 8
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.319 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.325 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 18 \,{\mathrm e}^{-t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.442 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = t \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.280 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = 4 t \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.271 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+15 y = 9 t \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.296 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y = 20 \sin \left (t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.377 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 36 t \,{\mathrm e}^{4 t}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.335 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.561 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.636 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.644 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = \left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.372 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.734 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.584 |
|
|
\[
{}t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.375 |
|
|
\[
{}t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 x^{\prime } t -6 x = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.132 |
|
|
\[
{}\left (t^{3}-2 t^{2}\right ) x^{\prime \prime }-\left (t^{3}+2 t^{2}-6 t \right ) x^{\prime }+\left (3 t^{2}-6\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.497 |
|
|
\[
{}t^{3} x^{\prime \prime \prime }-\left (3+t \right ) t^{2} x^{\prime \prime }+2 t \left (3+t \right ) x^{\prime }-2 \left (3+t \right ) x = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.056 |
|
|
\[
{}t^{2} x^{\prime \prime }+3 x^{\prime } t +3 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.460 |
|
|
\[
{}\left (2 t +1\right ) x^{\prime \prime }+t^{3} x^{\prime }+x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.737 |
|
|
\[
{}t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.360 |
|
|
\[
{}t^{3} x^{\prime \prime }-\left (t^{3}+2 t^{2}-t \right ) x^{\prime }+\left (t^{2}+t -1\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.529 |
|
|
\[
{}t^{3} x^{\prime \prime }+3 t^{2} x^{\prime }+x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.884 |
|
|
\[
{}\sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.680 |
|
|
\[
{}\frac {\left (t +1\right ) x^{\prime \prime }}{t}-\frac {x^{\prime }}{t^{2}}+\frac {x}{t^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.211 |
|
|
\[
{}t^{2} x^{\prime \prime }+x^{\prime } t +x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.297 |
|
|
\[
{}\left (t^{4}+t^{2}\right ) x^{\prime \prime }+2 t^{3} x^{\prime }+3 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.969 |
|
|
\[
{}x^{\prime \prime }-\tan \left (t \right ) x^{\prime }+x = 0
\] |
[_Lienard] |
✗ |
1.205 |
|
|
\[
{}f \left (t \right ) x^{\prime \prime }+x g \left (t \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.141 |
|
|
\[
{}x^{\prime \prime }+\left (t +1\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.583 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.599 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.581 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.574 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.729 |
|
|
\[
{}y^{\prime }+x y^{\prime \prime }+\frac {\lambda y}{x} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.559 |
|
|
\[
{}y^{\prime }+x y^{\prime \prime }+\frac {\lambda y}{x} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.572 |
|
|
\[
{}2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.719 |
|
|
\[
{}-\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.358 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.309 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.320 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+4 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.315 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+5 y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.320 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-4 y \\ y^{\prime }=2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.379 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=4 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.479 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.520 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+7 y \\ y^{\prime }=3 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.323 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=3 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.317 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x+b y \\ y^{\prime }=c x+d y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.687 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-4 y-x \left (x^{2}+y^{2}\right ) \\ y^{\prime }=4 x+4 y-y \left (x^{2}+y^{2}\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.055 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+\frac {x \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \\ y^{\prime }=-x+\frac {y \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.087 |
|
|
\[
{}x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.534 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.583 |
|
|
\[
{}x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.615 |
|
|
\[
{}x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.552 |
|
|
\[
{}x^{\prime \prime }+\left (x^{2}+1\right ) x^{\prime }+x^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.507 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-x^{2} \\ y^{\prime }=2 y-y^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.052 |
|
|
\[
{}x^{\prime } = \sin \left (t \right )+\cos \left (t \right )
\] |
[_quadrature] |
✓ |
0.361 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}-1}
\] |
[_quadrature] |
✓ |
0.311 |
|
|
\[
{}u^{\prime } = 4 t \ln \left (t \right )
\] |
[_quadrature] |
✓ |
0.325 |
|
|
\[
{}z^{\prime } = x \,{\mathrm e}^{-2 x}
\] |
[_quadrature] |
✓ |
0.331 |
|
|
\[
{}T^{\prime } = {\mathrm e}^{-t} \sin \left (2 t \right )
\] |
[_quadrature] |
✓ |
0.428 |
|
|
\[
{}x^{\prime } = \sec \left (t \right )^{2}
\] |
[_quadrature] |
✓ |
0.685 |
|
|
\[
{}y^{\prime } = x -\frac {1}{3} x^{3}
\] |
[_quadrature] |
✓ |
0.465 |
|
|
\[
{}x^{\prime } = 2 \sin \left (t \right )^{2}
\] |
[_quadrature] |
✓ |
0.671 |
|
|
\[
{}x V^{\prime } = x^{2}+1
\] |
[_quadrature] |
✓ |
0.551 |
|
|
\[
{}x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t} = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.619 |
|
|
\[
{}x^{\prime } = -x+1
\] |
[_quadrature] |
✓ |
0.897 |
|
|
\[
{}x^{\prime } = x \left (2-x\right )
\] |
[_quadrature] |
✓ |
1.869 |
|
|
\[
{}x^{\prime } = \left (1+x\right ) \left (2-x\right ) \sin \left (x\right )
\] |
[_quadrature] |
✓ |
5.399 |
|
|
\[
{}x^{\prime } = -x \left (-x+1\right ) \left (2-x\right )
\] |
[_quadrature] |
✓ |
219.470 |
|
|
\[
{}x^{\prime } = x^{2}-x^{4}
\] |
[_quadrature] |
✓ |
1.382 |
|
|
\[
{}x^{\prime } = t^{3} \left (-x+1\right )
\] |
[_separable] |
✓ |
1.454 |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right )
\] |
[_separable] |
✓ |
3.577 |
|
|
\[
{}x^{\prime } = t^{2} x
\] |
[_separable] |
✓ |
1.168 |
|
|
\[
{}x^{\prime } = -x^{2}
\] |
[_quadrature] |
✓ |
0.921 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-t^{2}} y^{2}
\] |
[_separable] |
✓ |
1.473 |
|
|
\[
{}x^{\prime }+p x = q
\] |
[_quadrature] |
✓ |
0.737 |
|