|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
3.648 |
|
|
\[
{}x^{\prime \prime }+\left (x^{2}+1\right ) x^{\prime }+x^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.793 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-x^{2} \\ y^{\prime }=2 y-y^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.055 |
|
|
\[
{}x^{\prime } = \sin \left (t \right )+\cos \left (t \right )
\] |
[_quadrature] |
✓ |
0.536 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}-1}
\] |
[_quadrature] |
✓ |
0.496 |
|
|
\[
{}u^{\prime } = 4 t \ln \left (t \right )
\] |
[_quadrature] |
✓ |
0.436 |
|
|
\[
{}z^{\prime } = x \,{\mathrm e}^{-2 x}
\] |
[_quadrature] |
✓ |
0.514 |
|
|
\[
{}T^{\prime } = {\mathrm e}^{-t} \sin \left (2 t \right )
\] |
[_quadrature] |
✓ |
0.579 |
|
|
\[
{}x^{\prime } = \sec \left (t \right )^{2}
\] |
[_quadrature] |
✓ |
0.830 |
|
|
\[
{}y^{\prime } = x -\frac {1}{3} x^{3}
\] |
[_quadrature] |
✓ |
0.637 |
|
|
\[
{}x^{\prime } = 2 \sin \left (t \right )^{2}
\] |
[_quadrature] |
✓ |
0.816 |
|
|
\[
{}x V^{\prime } = x^{2}+1
\] |
[_quadrature] |
✓ |
0.775 |
|
|
\[
{}x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t} = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.810 |
|
|
\[
{}x^{\prime } = -x+1
\] |
[_quadrature] |
✓ |
1.119 |
|
|
\[
{}x^{\prime } = x \left (2-x\right )
\] |
[_quadrature] |
✓ |
2.067 |
|
|
\[
{}x^{\prime } = \left (1+x\right ) \left (2-x\right ) \sin \left (x\right )
\] |
[_quadrature] |
✓ |
5.177 |
|
|
\[
{}x^{\prime } = -x \left (-x+1\right ) \left (2-x\right )
\] |
[_quadrature] |
✓ |
214.192 |
|
|
\[
{}x^{\prime } = x^{2}-x^{4}
\] |
[_quadrature] |
✓ |
1.615 |
|
|
\[
{}x^{\prime } = t^{3} \left (-x+1\right )
\] |
[_separable] |
✓ |
1.654 |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right )
\] |
[_separable] |
✓ |
3.763 |
|
|
\[
{}x^{\prime } = t^{2} x
\] |
[_separable] |
✓ |
1.646 |
|
|
\[
{}x^{\prime } = -x^{2}
\] |
[_quadrature] |
✓ |
1.271 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-t^{2}} y^{2}
\] |
[_separable] |
✓ |
1.831 |
|
|
\[
{}x^{\prime }+p x = q
\] |
[_quadrature] |
✓ |
0.646 |
|
|
\[
{}y^{\prime } x = k y
\] |
[_separable] |
✓ |
1.235 |
|
|
\[
{}i^{\prime } = p \left (t \right ) i
\] |
[_separable] |
✓ |
1.040 |
|
|
\[
{}x^{\prime } = \lambda x
\] |
[_quadrature] |
✓ |
0.682 |
|
|
\[
{}m v^{\prime } = -m g +k v^{2}
\] |
[_quadrature] |
✓ |
0.760 |
|
|
\[
{}x^{\prime } = k x-x^{2}
\] |
[_quadrature] |
✓ |
1.552 |
|
|
\[
{}x^{\prime } = -x \left (k^{2}+x^{2}\right )
\] |
[_quadrature] |
✓ |
10.395 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
1.503 |
|
|
\[
{}x^{\prime }+t x = 4 t
\] |
[_separable] |
✓ |
2.092 |
|
|
\[
{}z^{\prime } = z \tan \left (y \right )+\sin \left (y \right )
\] |
[_linear] |
✓ |
1.655 |
|
|
\[
{}y^{\prime }+{\mathrm e}^{-x} y = 1
\] |
[_linear] |
✓ |
1.231 |
|
|
\[
{}x^{\prime }+x \tanh \left (t \right ) = 3
\] |
[_linear] |
✓ |
1.263 |
|
|
\[
{}y^{\prime }+2 y \cot \left (x \right ) = 5
\] |
[_linear] |
✓ |
1.673 |
|
|
\[
{}x^{\prime }+5 x = t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.240 |
|
|
\[
{}x^{\prime }+\left (a +\frac {1}{t}\right ) x = b
\] |
[_linear] |
✓ |
1.064 |
|
|
\[
{}T^{\prime } = -k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.533 |
|
|
\[
{}2 x y-\sec \left (x \right )^{2}+\left (x^{2}+2 y\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.756 |
|
|
\[
{}1+y \,{\mathrm e}^{x}+x \,{\mathrm e}^{x} y+\left (x \,{\mathrm e}^{x}+2\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.720 |
|
|
\[
{}\left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }+\sin \left (y\right )-y \sin \left (x \right ) = 0
\] |
[_exact] |
✓ |
28.708 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+y+\left ({\mathrm e}^{x} \cos \left (y\right )+x +{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.366 |
|
|
\[
{}{\mathrm e}^{-y} \sec \left (x \right )+2 \cos \left (x \right )-{\mathrm e}^{-y} y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.783 |
|
|
\[
{}V^{\prime }\left (x \right )+2 y y^{\prime } = 0
\] |
[_separable] |
✓ |
0.571 |
|
|
\[
{}\left (\frac {1}{y}-a \right ) y^{\prime }+\frac {2}{x}-b = 0
\] |
[_separable] |
✓ |
1.351 |
|
|
\[
{}x y+y^{2}+x^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.536 |
|
|
\[
{}x^{\prime } = \frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{t x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
34.309 |
|
|
\[
{}x^{\prime } = k x-x^{2}
\] |
[_quadrature] |
✓ |
1.289 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }+2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.399 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.495 |
|
|
\[
{}z^{\prime \prime }-4 z^{\prime }+13 z = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.838 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.643 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.332 |
|
|
\[
{}\theta ^{\prime \prime }+4 \theta = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.910 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.775 |
|
|
\[
{}2 z^{\prime \prime }+7 z^{\prime }-4 z = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.661 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.499 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+10 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.382 |
|
|
\[
{}4 x^{\prime \prime }-20 x^{\prime }+21 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.689 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.652 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.861 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.511 |
|
|
\[
{}y^{\prime \prime }+\omega ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.879 |
|
|
\[
{}x^{\prime \prime }-4 x = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.309 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime } = t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.226 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }-2 x = 3 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.288 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }-2 x = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.338 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.356 |
|
|
\[
{}x^{\prime \prime }+\omega ^{2} x = \sin \left (\alpha t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.364 |
|
|
\[
{}x^{\prime \prime }+\omega ^{2} x = \sin \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.457 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.241 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
18.445 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+10 x = {\mathrm e}^{-2 t} \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.271 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = {\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.371 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }-2 x = 12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.480 |
|
|
\[
{}x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.703 |
|
|
\[
{}x^{\prime \prime }+\omega ^{2} x = \cos \left (\alpha t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.805 |
|
|
\[
{}x^{\prime \prime }+\omega ^{2} x = \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.695 |
|
|
\[
{}x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x = {\mathrm e}^{-t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.114 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y = \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.137 |
|
|
\[
{}x^{\prime \prime \prime \prime }-4 x^{\prime \prime \prime }+8 x^{\prime \prime }-8 x^{\prime }+4 x = \sin \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.160 |
|
|
\[
{}x^{\prime \prime \prime \prime }-5 x^{\prime \prime }+4 x = {\mathrm e}^{t}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.119 |
|
|
\[
{}t^{2} y^{\prime \prime }-\left (t^{2}+2 t \right ) y^{\prime }+\left (t +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.323 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.328 |
|
|
\[
{}\left (t \cos \left (t \right )-\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.514 |
|
|
\[
{}\left (-t^{2}+t \right ) x^{\prime \prime }+\left (-t^{2}+2\right ) x^{\prime }+\left (2-t \right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.334 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[_Hermite] |
✓ |
0.327 |
|
|
\[
{}\tan \left (t \right ) x^{\prime \prime }-3 x^{\prime }+\left (\tan \left (t \right )+3 \cot \left (t \right )\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.319 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.248 |
|
|
\[
{}x^{\prime \prime }-x = \frac {1}{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.311 |
|
|
\[
{}y^{\prime \prime }+4 y = \cot \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.478 |
|
|
\[
{}t^{2} x^{\prime \prime }-2 x = t^{3}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.929 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.025 |
|
|
\[
{}\left (\tan \left (x \right )^{2}-1\right ) y^{\prime \prime }-4 \tan \left (x \right )^{3} y^{\prime }+2 y \sec \left (x \right )^{4} = \left (\tan \left (x \right )^{2}-1\right ) \left (1-2 \sin \left (x \right )^{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.545 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.954 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.917 |
|
|
\[
{}t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
4.337 |
|
|
\[
{}t^{2} x^{\prime \prime }+t x^{\prime }-x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.639 |
|
|
\[
{}x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.924 |
|