|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.888 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.732 |
|
|
\[
{}x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.758 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.232 |
|
|
\[
{}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.934 |
|
|
\[
{}2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.898 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.083 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.991 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.952 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = \cos \left (x \right ) \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.000 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = x^{3}+x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.005 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+2 x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.771 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.819 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.735 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.822 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.226 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}+6 x \right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.840 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}-8\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.250 |
|
|
\[
{}x^{2} y^{\prime \prime }-9 x y^{\prime }+25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.713 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.830 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.886 |
|
|
\[
{}x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.872 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.799 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.624 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.734 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.115 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.713 |
|
|
\[
{}y^{\prime } = y \left (1-y^{2}\right )
\] |
[_quadrature] |
✓ |
3.555 |
|
|
\[
{}\frac {x y^{\prime \prime }}{1-x}+y = \frac {1}{1-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.439 |
|
|
\[
{}\frac {x y^{\prime \prime }}{1-x}+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.929 |
|
|
\[
{}\frac {x y^{\prime \prime }}{1-x}+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.750 |
|
|
\[
{}\frac {x y^{\prime \prime }}{-x^{2}+1}+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.246 |
|
|
\[
{}y^{\prime \prime } = \left (x^{2}+3\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.206 |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.507 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+2 t +1 \\ y^{\prime }=5 x+y+3 t -1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.761 |
|
|
\[
{}y^{\prime \prime }+20 y^{\prime }+500 y = 100000 \cos \left (100 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
97.388 |
|
|
\[
{}y^{\prime \prime } \sin \left (2 x \right )^{2}+y^{\prime } \sin \left (4 x \right )-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.595 |
|
|
\[
{}y^{\prime \prime } = A y^{{2}/{3}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
163.740 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.754 |
|
|
\[
{}y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.230 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.764 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.198 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 6 x^{3} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.999 |
|
|
\[
{}y^{\prime }+y = \frac {1}{x}
\] |
[[_linear, ‘class A‘]] |
✗ |
0.223 |
|
|
\[
{}y^{\prime }+y = \frac {1}{x^{2}}
\] |
[[_linear, ‘class A‘]] |
✗ |
0.259 |
|
|
\[
{}x y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.434 |
|
|
\[
{}y^{\prime } = \frac {1}{x}
\] |
[_quadrature] |
✗ |
0.141 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{x}
\] |
[[_2nd_order, _quadrature]] |
✗ |
0.061 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \frac {1}{x}
\] |
[[_2nd_order, _missing_y]] |
✗ |
0.067 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.066 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \frac {1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.070 |
|
|
\[
{}h^{2}+\frac {2 a h}{\sqrt {1+{h^{\prime }}^{2}}} = b^{2}
\] |
[_quadrature] |
✓ |
18.867 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-24 y = 16-\left (x +2\right ) {\mathrm e}^{4 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.743 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.340 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{a \cos \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.928 |
|
|
\[
{}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.395 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.872 |
|
|
\[
{}x^{2} y^{\prime }+{\mathrm e}^{-y} = 0
\] |
[_separable] |
✓ |
1.179 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{y} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
14.495 |
|
|
\[
{}y^{\prime } = \frac {x y+3 x -2 y+6}{x y-3 x -2 y+6}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.258 |
|
|
\[
{}y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.381 |
|
|
\[
{}y^{\prime } = a
\] |
[_quadrature] |
✓ |
0.347 |
|
|
\[
{}y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.250 |
|
|
\[
{}y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.464 |
|
|
\[
{}y^{\prime } = a x
\] |
[_quadrature] |
✓ |
0.176 |
|
|
\[
{}y^{\prime } = a x y
\] |
[_separable] |
✓ |
0.822 |
|
|
\[
{}y^{\prime } = a x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.685 |
|
|
\[
{}y^{\prime } = a x +b y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.791 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
0.944 |
|
|
\[
{}y^{\prime } = b y
\] |
[_quadrature] |
✓ |
0.691 |
|
|
\[
{}y^{\prime } = a x +b y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.037 |
|
|
\[
{}c y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.389 |
|
|
\[
{}c y^{\prime } = a
\] |
[_quadrature] |
✓ |
0.349 |
|
|
\[
{}c y^{\prime } = a x
\] |
[_quadrature] |
✓ |
0.197 |
|
|
\[
{}c y^{\prime } = a x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.773 |
|
|
\[
{}c y^{\prime } = a x +b y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.802 |
|
|
\[
{}c y^{\prime } = y
\] |
[_quadrature] |
✓ |
0.785 |
|
|
\[
{}c y^{\prime } = b y
\] |
[_quadrature] |
✓ |
0.853 |
|
|
\[
{}c y^{\prime } = a x +b y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.104 |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{r}
\] |
[[_Riccati, _special]] |
✓ |
1.198 |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{r x}
\] |
[_rational, _Riccati] |
✓ |
3.966 |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{r \,x^{2}}
\] |
[_rational, _Riccati] |
✓ |
5.901 |
|
|
\[
{}c y^{\prime } = \frac {a x +b y^{2}}{y}
\] |
[_rational, _Bernoulli] |
✓ |
1.513 |
|
|
\[
{}a \sin \left (x \right ) y x y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.389 |
|
|
\[
{}f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi = 0
\] |
[_quadrature] |
✓ |
0.401 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )+y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.196 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )+y^{2}
\] |
[_Riccati] |
✓ |
2.431 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\frac {y}{x}
\] |
[_linear] |
✓ |
1.137 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+\frac {y^{2}}{x}
\] |
[_Riccati] |
✗ |
4.404 |
|
|
\[
{}y^{\prime } = x +y+b y^{2}
\] |
[_Riccati] |
✓ |
1.191 |
|
|
\[
{}x y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.392 |
|
|
\[
{}5 y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.388 |
|
|
\[
{}{\mathrm e} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.404 |
|
|
\[
{}\pi y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.413 |
|
|
\[
{}\sin \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.427 |
|
|
\[
{}f \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.424 |
|
|
\[
{}x y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.293 |
|
|
\[
{}x y^{\prime } = \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.362 |
|
|
\[
{}\left (x -1\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.381 |
|
|
\[
{}y^{\prime } y = 0
\] |
[_quadrature] |
✓ |
0.382 |
|