|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {y}{x}+2 x +1
\] |
[_linear] |
✓ |
1.354 |
|
|
\[
{}r^{\prime }+r \tan \left (\theta \right ) = \sec \left (\theta \right )
\] |
[_linear] |
✓ |
1.745 |
|
|
\[
{}x y^{\prime }+2 y = \frac {1}{x^{3}}
\] |
[_linear] |
✓ |
1.522 |
|
|
\[
{}t +y+1-y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
1.272 |
|
|
\[
{}y^{\prime } = x^{2} {\mathrm e}^{-4 x}-4 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.791 |
|
|
\[
{}y x^{\prime }+2 x = 5 y^{3}
\] |
[_linear] |
✓ |
1.627 |
|
|
\[
{}x y^{\prime }+3 x^{2}+3 y = \frac {\sin \left (x \right )}{x}
\] |
[_linear] |
✓ |
1.894 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y-x = 0
\] |
[_separable] |
✓ |
1.846 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x^{2} y = \left (x +1\right ) \sqrt {-x^{2}+1}
\] |
[_linear] |
✓ |
3.398 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x \,{\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.749 |
|
|
\[
{}y^{\prime }+4 y-{\mathrm e}^{-x} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
1.725 |
|
|
\[
{}t^{2} x^{\prime }+3 t x = t^{4} \ln \left (t \right )+1
\] |
[_linear] |
✓ |
1.718 |
|
|
\[
{}y^{\prime }+\frac {3 y}{x}+2 = 3 x
\] |
[_linear] |
✓ |
1.817 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y \sin \left (x \right ) = 2 x \cos \left (x \right )^{2}
\] |
[_linear] |
✓ |
3.490 |
|
|
\[
{}\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = x \sin \left (x \right )
\] |
[_linear] |
✓ |
2.852 |
|
|
\[
{}y^{\prime }+y \sqrt {1+\sin \left (x \right )^{2}} = x
\] |
[_linear] |
✗ |
741.593 |
|
|
\[
{}\left ({\mathrm e}^{4 y}+2 x \right ) y^{\prime }-1 = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
4.872 |
|
|
\[
{}y^{\prime }+2 y = \frac {x}{y^{2}}
\] |
[_rational, _Bernoulli] |
✓ |
1.644 |
|
|
\[
{}y^{\prime }+\frac {3 y}{x} = x^{2}
\] |
[_linear] |
✓ |
1.738 |
|
|
\[
{}x^{\prime } = \alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x
\] |
[[_linear, ‘class A‘]] |
✓ |
2.082 |
|
|
\[
{}u^{\prime } = \alpha \left (1-u\right )-\beta u
\] |
[_quadrature] |
✓ |
1.149 |
|
|
\[
{}x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime } = 0
\] |
[_linear] |
✓ |
1.659 |
|
|
\[
{}x^{{10}/{3}}-2 y+x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.664 |
|
|
\[
{}\sqrt {-2 y-y^{2}}+\left (-x^{2}+2 x +3\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
13.676 |
|
|
\[
{}y \,{\mathrm e}^{x y}+2 x +\left (x \,{\mathrm e}^{x y}-2 y\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.384 |
|
|
\[
{}y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
0.283 |
|
|
\[
{}y^{2}+\left (2 x y+\cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
0.330 |
|
|
\[
{}2 x +y \cos \left (x y\right )+\left (x \cos \left (x y\right )-2 y\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.451 |
|
|
\[
{}\theta r^{\prime }+3 r-\theta -1 = 0
\] |
[_linear] |
✓ |
0.280 |
|
|
\[
{}2 x y+3+\left (x^{2}-1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
0.269 |
|
|
\[
{}2 x +y+\left (x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.496 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )+2 x -\left (\sin \left (x \right ) \sin \left (y\right )+2 y\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
7.833 |
|
|
\[
{}{\mathrm e}^{t} \left (-t +y\right )+\left (1+{\mathrm e}^{t}\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
0.288 |
|
|
\[
{}\frac {t y^{\prime }}{y}+1+\ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
0.329 |
|
|
\[
{}\cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta } = 0
\] |
[_linear] |
✓ |
0.303 |
|
|
\[
{}y \,{\mathrm e}^{x y}-\frac {1}{y}+\left (x \,{\mathrm e}^{x y}+\frac {x}{y^{2}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.350 |
|
|
\[
{}\frac {1}{y}-\left (3 y-\frac {x}{y^{2}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
0.292 |
|
|
\[
{}2 x +y^{2}-\cos \left (x +y\right )+\left (2 x y-\cos \left (x +y\right )-{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
38.029 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x +y}}{y-1}
\] |
[_separable] |
✓ |
2.539 |
|
|
\[
{}y^{\prime }-4 y = 32 x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.323 |
|
|
\[
{}\left (x^{2}-\frac {2}{y^{3}}\right ) y^{\prime }+2 x y-3 x^{2} = 0
\] |
[_exact, _rational] |
✓ |
2.050 |
|
|
\[
{}y^{\prime }+\frac {3 y}{x} = x^{2}-4 x +3
\] |
[_linear] |
✓ |
1.971 |
|
|
\[
{}2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.459 |
|
|
\[
{}t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}} = 0
\] |
[_separable] |
✓ |
1.692 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-x^{2} y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.414 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.145 |
|
|
\[
{}\left (x^{2}-2\right ) y^{\prime \prime }+2 y^{\prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.738 |
|
|
\[
{}\left (x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }-6 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.370 |
|
|
\[
{}\left (t^{2}-t -2\right ) x^{\prime \prime }+\left (t +1\right ) x^{\prime }-\left (t -2\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.546 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+\left (x^{2}-2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.440 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.575 |
|
|
\[
{}{\mathrm e}^{x} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.805 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-y \ln \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
6.130 |
|
|
\[
{}y^{\prime }+\left (x +2\right ) y = 0
\] |
[_separable] |
✓ |
0.462 |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.323 |
|
|
\[
{}z^{\prime }-x^{2} z = 0
\] |
[_separable] |
✓ |
0.415 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.361 |
|
|
\[
{}y^{\prime \prime }+\left (-1+x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.380 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.519 |
|
|
\[
{}w^{\prime \prime }-x^{2} w^{\prime }+w = 0
\] |
[_Lienard] |
✓ |
0.393 |
|
|
\[
{}\left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.391 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-3 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.498 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-3 y = 0
\] |
[_Hermite] |
✓ |
0.429 |
|
|
\[
{}\left (x^{2}+x +1\right ) y^{\prime \prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.477 |
|
|
\[
{}\left (x^{2}-5 x +6\right ) y^{\prime \prime }-3 x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.467 |
|
|
\[
{}y^{\prime \prime }-\tan \left (x \right ) y^{\prime }+y = 0
\] |
[_Lienard] |
✓ |
1.833 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }-x y^{\prime }+2 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.662 |
|
|
\[
{}y^{\prime }+2 \left (-1+x \right ) y = 0
\] |
[_separable] |
✓ |
0.462 |
|
|
\[
{}y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
0.485 |
|
|
\[
{}\left (x^{2}-2 x \right ) y^{\prime \prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.416 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.457 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.493 |
|
|
\[
{}y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.434 |
|
|
\[
{}x^{\prime }+\sin \left (t \right ) x = 0
\] |
[_separable] |
✓ |
0.563 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
0.571 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.747 |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.521 |
|
|
\[
{}y^{\prime \prime }-{\mathrm e}^{2 x} y^{\prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.038 |
|
|
\[
{}y^{\prime }-x y = \sin \left (x \right )
\] |
[_linear] |
✓ |
0.510 |
|
|
\[
{}w^{\prime }+w x = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
0.485 |
|
|
\[
{}z^{\prime \prime }+x z^{\prime }+z = x^{2}+2 x +1
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.391 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+3 y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.362 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.542 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+2 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.397 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.490 |
|
|
\[
{}y^{\prime \prime }-y \sin \left (x \right ) = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.590 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.588 |
|
|
\[
{}x^{\prime \prime }-\omega ^{2} x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.649 |
|
|
\[
{}x^{\prime \prime \prime }-x^{\prime \prime }+x^{\prime }-x = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.054 |
|
|
\[
{}x^{\prime \prime }+42 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.285 |
|
|
\[
{}x^{\prime \prime \prime \prime }+x = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.056 |
|
|
\[
{}x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x = F \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
83.747 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.770 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.876 |
|
|
\[
{}y^{\prime \prime }+16 y = 16 \cos \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.226 |
|
|
\[
{}y^{\prime \prime }-y = \cosh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.538 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.345 |
|
|
\[
{}x^{2} y^{\prime }+2 x y-x +1 = 0
\] |
[_linear] |
✓ |
1.714 |
|
|
\[
{}y^{\prime }+y = \left (x +1\right )^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.612 |
|