|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.996 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.290 |
|
|
\[
{}y^{\prime }+x y^{\prime \prime }+\frac {\lambda y}{x} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.507 |
|
|
\[
{}y^{\prime }+x y^{\prime \prime }+\frac {\lambda y}{x} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.598 |
|
|
\[
{}2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.876 |
|
|
\[
{}-\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.500 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.437 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.449 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+4 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.461 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+5 y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.454 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-4 y \\ y^{\prime }=2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.527 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=4 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.566 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.603 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+7 y \\ y^{\prime }=3 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.465 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=3 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.470 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x+b y \\ y^{\prime }=c x+d y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.797 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-4 y-x \left (x^{2}+y^{2}\right ) \\ y^{\prime }=4 x+4 y-y \left (x^{2}+y^{2}\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.037 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+\frac {x \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \\ y^{\prime }=-x+\frac {y \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.050 |
|
|
\[
{}x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
2.490 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.785 |
|
|
\[
{}x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
3.659 |
|
|
\[
{}x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
3.215 |
|
|
\[
{}x^{\prime \prime }+\left (x^{2}+1\right ) x^{\prime }+x^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
2.081 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-x^{2} \\ y^{\prime }=2 y-y^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.031 |
|
|
\[
{}x^{\prime } = \sin \left (t \right )+\cos \left (t \right )
\] |
[_quadrature] |
✓ |
0.599 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}-1}
\] |
[_quadrature] |
✓ |
0.526 |
|
|
\[
{}u^{\prime } = 4 t \ln \left (t \right )
\] |
[_quadrature] |
✓ |
0.489 |
|
|
\[
{}z^{\prime } = x \,{\mathrm e}^{-2 x}
\] |
[_quadrature] |
✓ |
0.480 |
|
|
\[
{}T^{\prime } = {\mathrm e}^{-t} \sin \left (2 t \right )
\] |
[_quadrature] |
✓ |
0.628 |
|
|
\[
{}x^{\prime } = \sec \left (t \right )^{2}
\] |
[_quadrature] |
✓ |
0.918 |
|
|
\[
{}y^{\prime } = x -\frac {1}{3} x^{3}
\] |
[_quadrature] |
✓ |
0.713 |
|
|
\[
{}x^{\prime } = 2 \sin \left (t \right )^{2}
\] |
[_quadrature] |
✓ |
0.870 |
|
|
\[
{}x V^{\prime } = x^{2}+1
\] |
[_quadrature] |
✓ |
0.762 |
|
|
\[
{}x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t} = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.868 |
|
|
\[
{}x^{\prime } = -x+1
\] |
[_quadrature] |
✓ |
1.397 |
|
|
\[
{}x^{\prime } = x \left (2-x\right )
\] |
[_quadrature] |
✓ |
2.309 |
|
|
\[
{}x^{\prime } = \left (1+x\right ) \left (2-x\right ) \sin \left (x\right )
\] |
[_quadrature] |
✓ |
7.834 |
|
|
\[
{}x^{\prime } = -x \left (-x+1\right ) \left (2-x\right )
\] |
[_quadrature] |
✓ |
4.442 |
|
|
\[
{}x^{\prime } = x^{2}-x^{4}
\] |
[_quadrature] |
✓ |
1.817 |
|
|
\[
{}x^{\prime } = t^{3} \left (-x+1\right )
\] |
[_separable] |
✓ |
1.813 |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right )
\] |
[_separable] |
✓ |
3.932 |
|
|
\[
{}x^{\prime } = t^{2} x
\] |
[_separable] |
✓ |
1.656 |
|
|
\[
{}x^{\prime } = -x^{2}
\] |
[_quadrature] |
✓ |
1.997 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-t^{2}} y^{2}
\] |
[_separable] |
✓ |
1.897 |
|
|
\[
{}x^{\prime }+p x = q
\] |
[_quadrature] |
✓ |
0.831 |
|
|
\[
{}x y^{\prime } = k y
\] |
[_separable] |
✓ |
1.190 |
|
|
\[
{}i^{\prime } = p \left (t \right ) i
\] |
[_separable] |
✓ |
0.833 |
|
|
\[
{}x^{\prime } = \lambda x
\] |
[_quadrature] |
✓ |
0.802 |
|
|
\[
{}m v^{\prime } = -m g +k v^{2}
\] |
[_quadrature] |
✓ |
2.343 |
|
|
\[
{}x^{\prime } = k x-x^{2}
\] |
[_quadrature] |
✓ |
43.819 |
|
|
\[
{}x^{\prime } = -x \left (k^{2}+x^{2}\right )
\] |
[_quadrature] |
✓ |
167.463 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
1.573 |
|
|
\[
{}x^{\prime }+t x = 4 t
\] |
[_separable] |
✓ |
2.009 |
|
|
\[
{}z^{\prime } = z \tan \left (y \right )+\sin \left (y \right )
\] |
[_linear] |
✓ |
1.880 |
|
|
\[
{}y^{\prime }+{\mathrm e}^{-x} y = 1
\] |
[_linear] |
✓ |
1.343 |
|
|
\[
{}x^{\prime }+x \tanh \left (t \right ) = 3
\] |
[_linear] |
✓ |
1.459 |
|
|
\[
{}y^{\prime }+2 y \cot \left (x \right ) = 5
\] |
[_linear] |
✓ |
1.870 |
|
|
\[
{}x^{\prime }+5 x = t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.294 |
|
|
\[
{}x^{\prime }+\left (a +\frac {1}{t}\right ) x = b
\] |
[_linear] |
✓ |
1.151 |
|
|
\[
{}T^{\prime } = -k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.755 |
|
|
\[
{}2 x y-\sec \left (x \right )^{2}+\left (x^{2}+2 y\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.750 |
|
|
\[
{}1+y \,{\mathrm e}^{x}+x \,{\mathrm e}^{x} y+\left (x \,{\mathrm e}^{x}+2\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.865 |
|
|
\[
{}\left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }+\sin \left (y\right )-\sin \left (x \right ) y = 0
\] |
[_exact] |
✓ |
27.749 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+y+\left ({\mathrm e}^{x} \cos \left (y\right )+x +{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.715 |
|
|
\[
{}{\mathrm e}^{-y} \sec \left (x \right )+2 \cos \left (x \right )-{\mathrm e}^{-y} y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.303 |
|
|
\[
{}V^{\prime }\left (x \right )+2 y y^{\prime } = 0
\] |
[_separable] |
✓ |
1.108 |
|
|
\[
{}\left (\frac {1}{y}-a \right ) y^{\prime }+\frac {2}{x}-b = 0
\] |
[_separable] |
✓ |
1.612 |
|
|
\[
{}x y+y^{2}+x^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.648 |
|
|
\[
{}x^{\prime } = \frac {x^{2}+t \sqrt {x^{2}+t^{2}}}{t x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.556 |
|
|
\[
{}x^{\prime } = k x-x^{2}
\] |
[_quadrature] |
✓ |
3.430 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }+2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.184 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.319 |
|
|
\[
{}z^{\prime \prime }-4 z^{\prime }+13 z = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.263 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.321 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.115 |
|
|
\[
{}\theta ^{\prime \prime }+4 \theta = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.194 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.145 |
|
|
\[
{}2 z^{\prime \prime }+7 z^{\prime }-4 z = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.482 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.395 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+10 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.392 |
|
|
\[
{}4 x^{\prime \prime }-20 x^{\prime }+21 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.512 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.470 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.633 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.355 |
|
|
\[
{}y^{\prime \prime }+\omega ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.601 |
|
|
\[
{}x^{\prime \prime }-4 x = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.180 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime } = t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.258 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }-2 x = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.151 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }-2 x = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.184 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.125 |
|
|
\[
{}x^{\prime \prime }+\omega ^{2} x = \sin \left (\alpha t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.364 |
|
|
\[
{}x^{\prime \prime }+\omega ^{2} x = \sin \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.414 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
8.211 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
20.671 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+10 x = {\mathrm e}^{-2 t} \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
13.532 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = {\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.227 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }-2 x = 12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.300 |
|
|
\[
{}x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.970 |
|
|
\[
{}x^{\prime \prime }+\omega ^{2} x = \cos \left (\alpha t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.528 |
|
|
\[
{}x^{\prime \prime }+\omega ^{2} x = \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.486 |
|