|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {y}{x}+2 x +1
\] |
[_linear] |
✓ |
1.004 |
|
|
\[
{}r^{\prime }+r \tan \left (\theta \right ) = \sec \left (\theta \right )
\] |
[_linear] |
✓ |
1.419 |
|
|
\[
{}x y^{\prime }+2 y = \frac {1}{x^{3}}
\] |
[_linear] |
✓ |
1.225 |
|
|
\[
{}t +y+1-y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
0.966 |
|
|
\[
{}y^{\prime } = x^{2} {\mathrm e}^{-4 x}-4 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.464 |
|
|
\[
{}y x^{\prime }+2 x = 5 y^{3}
\] |
[_linear] |
✓ |
1.337 |
|
|
\[
{}x y^{\prime }+3 y+3 x^{2} = \frac {\sin \left (x \right )}{x}
\] |
[_linear] |
✓ |
1.617 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y-x = 0
\] |
[_separable] |
✓ |
1.246 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x^{2} y = \left (x +1\right ) \sqrt {-x^{2}+1}
\] |
[_linear] |
✓ |
2.393 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x \,{\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.345 |
|
|
\[
{}y^{\prime }+4 y-{\mathrm e}^{-x} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
1.389 |
|
|
\[
{}t^{2} x^{\prime }+3 x t = t^{4} \ln \left (t \right )+1
\] |
[_linear] |
✓ |
1.492 |
|
|
\[
{}y^{\prime }+\frac {3 y}{x}+2 = 3 x
\] |
[_linear] |
✓ |
1.451 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y \sin \left (x \right ) = 2 x \cos \left (x \right )^{2}
\] |
[_linear] |
✓ |
2.947 |
|
|
\[
{}\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = x \sin \left (x \right )
\] |
[_linear] |
✓ |
2.340 |
|
|
\[
{}y^{\prime }+y \sqrt {1+\sin \left (x \right )^{2}} = x
\] |
[_linear] |
✓ |
15.873 |
|
|
\[
{}\left ({\mathrm e}^{4 y}+2 x \right ) y^{\prime }-1 = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
4.123 |
|
|
\[
{}y^{\prime }+2 y = \frac {x}{y^{2}}
\] |
[_rational, _Bernoulli] |
✓ |
1.399 |
|
|
\[
{}y^{\prime }+\frac {3 y}{x} = x^{2}
\] |
[_linear] |
✓ |
1.345 |
|
|
\[
{}x^{\prime } = \alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x
\] |
[[_linear, ‘class A‘]] |
✓ |
1.832 |
|
|
\[
{}u^{\prime } = \alpha \left (1-u\right )-\beta u
\] |
[_quadrature] |
✓ |
0.914 |
|
|
\[
{}x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime } = 0
\] |
[_linear] |
✓ |
1.260 |
|
|
\[
{}x^{{10}/{3}}-2 y+x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.358 |
|
|
\[
{}\sqrt {-2 y-y^{2}}+\left (-x^{2}+2 x +3\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.940 |
|
|
\[
{}y \,{\mathrm e}^{x y}+2 x +\left (x \,{\mathrm e}^{x y}-2 y\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.283 |
|
|
\[
{}y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
0.220 |
|
|
\[
{}y^{2}+\left (2 x y+\cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
0.249 |
|
|
\[
{}2 x +y \cos \left (x y\right )+\left (x \cos \left (x y\right )-2 y\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.295 |
|
|
\[
{}\theta r^{\prime }+3 r-\theta -1 = 0
\] |
[_linear] |
✓ |
0.255 |
|
|
\[
{}2 x y+3+\left (x^{2}-1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
0.193 |
|
|
\[
{}2 x +y+\left (x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.316 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )-3 x^{2}+\left ({\mathrm e}^{x} \cos \left (y\right )+\frac {1}{3 y^{{2}/{3}}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.390 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )+2 x -\left (\sin \left (x \right ) \sin \left (y\right )+2 y\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
6.810 |
|
|
\[
{}{\mathrm e}^{t} \left (-t +y\right )+\left ({\mathrm e}^{t}+1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
0.221 |
|
|
\[
{}\frac {t y^{\prime }}{y}+1+\ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
0.287 |
|
|
\[
{}\cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta } = 0
\] |
[_linear] |
✓ |
0.225 |
|
|
\[
{}y \,{\mathrm e}^{x y}-\frac {1}{y}+\left (x \,{\mathrm e}^{x y}+\frac {x}{y^{2}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.281 |
|
|
\[
{}\frac {1}{y}-\left (3 y-\frac {x}{y^{2}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
0.203 |
|
|
\[
{}2 x +y^{2}-\cos \left (x +y\right )+\left (2 x y-\cos \left (x +y\right )-{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
36.481 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x +y}}{y-1}
\] |
[_separable] |
✓ |
1.474 |
|
|
\[
{}y^{\prime }-4 y = 32 x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.036 |
|
|
\[
{}\left (x^{2}-\frac {2}{y^{3}}\right ) y^{\prime }+2 x y-3 x^{2} = 0
\] |
[_exact, _rational] |
✓ |
2.217 |
|
|
\[
{}y^{\prime }+\frac {3 y}{x} = x^{2}-4 x +3
\] |
[_linear] |
✓ |
1.599 |
|
|
\[
{}2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.411 |
|
|
\[
{}t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}} = 0
\] |
[_separable] |
✓ |
1.424 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-x^{2} y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.642 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.170 |
|
|
\[
{}\left (x^{2}-2\right ) y^{\prime \prime }+2 y^{\prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.739 |
|
|
\[
{}\left (x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }-6 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.307 |
|
|
\[
{}\left (t^{2}-t -2\right ) x^{\prime \prime }+\left (t +1\right ) x^{\prime }-\left (t -2\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.695 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+\left (x^{2}-2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.652 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.589 |
|
|
\[
{}{\mathrm e}^{x} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.012 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-y \ln \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.825 |
|
|
\[
{}y^{\prime }+\left (x +2\right ) y = 0
\] |
[_separable] |
✓ |
0.534 |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.455 |
|
|
\[
{}z^{\prime }-x^{2} z = 0
\] |
[_separable] |
✓ |
0.496 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.576 |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.552 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.636 |
|
|
\[
{}w^{\prime \prime }-x^{2} w^{\prime }+w = 0
\] |
[_Lienard] |
✓ |
0.593 |
|
|
\[
{}\left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.592 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-3 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.693 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-3 y = 0
\] |
[_Hermite] |
✓ |
0.638 |
|
|
\[
{}\left (x^{2}+x +1\right ) y^{\prime \prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.678 |
|
|
\[
{}\left (x^{2}-5 x +6\right ) y^{\prime \prime }-3 x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.666 |
|
|
\[
{}y^{\prime \prime }-\tan \left (x \right ) y^{\prime }+y = 0
\] |
[_Lienard] |
✓ |
1.826 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }-x y^{\prime }+2 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.807 |
|
|
\[
{}y^{\prime }+2 \left (x -1\right ) y = 0
\] |
[_separable] |
✓ |
0.586 |
|
|
\[
{}y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
0.612 |
|
|
\[
{}\left (x^{2}-2 x \right ) y^{\prime \prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.622 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.661 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.686 |
|
|
\[
{}y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.654 |
|
|
\[
{}x^{\prime }+\sin \left (t \right ) x = 0
\] |
[_separable] |
✓ |
0.683 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
0.661 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.947 |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{t} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.732 |
|
|
\[
{}y^{\prime \prime }-{\mathrm e}^{2 x} y^{\prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.143 |
|
|
\[
{}y^{\prime }-x y = \sin \left (x \right )
\] |
[_linear] |
✓ |
0.585 |
|
|
\[
{}w^{\prime }+w x = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
0.605 |
|
|
\[
{}z^{\prime \prime }+x z^{\prime }+z = x^{2}+2 x +1
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.561 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+3 y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.536 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.674 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+2 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.622 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.501 |
|
|
\[
{}y^{\prime \prime }-y \sin \left (x \right ) = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.721 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.734 |
|
|
\[
{}x^{\prime \prime }-\omega ^{2} x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.242 |
|
|
\[
{}x^{\prime \prime \prime }-x^{\prime \prime }+x^{\prime }-x = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}x^{\prime \prime }+42 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.413 |
|
|
\[
{}x^{\prime \prime \prime \prime }+x = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x = F \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.457 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.716 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.641 |
|
|
\[
{}y^{\prime \prime }+16 y = 16 \cos \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.306 |
|
|
\[
{}y^{\prime \prime }-y = \cosh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.792 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.025 |
|
|
\[
{}x^{2} y^{\prime }+2 x y-x +1 = 0
\] |
[_linear] |
✓ |
1.334 |
|