|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \cos \left (x \right )+\sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.716 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (\cos \left (x \right )-1\right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.879 |
|
|
\[
{}\left (-2+x \right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.687 |
|
|
\[
{}\left (-2+x \right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.752 |
|
|
\[
{}\left (x +1\right ) \left (3 x -1\right ) y^{\prime \prime }+\cos \left (x \right ) y^{\prime }-3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.192 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.578 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-x y = x^{2}+2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.759 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.704 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.520 |
|
|
\[
{}y^{\prime \prime }+\left (x -6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.343 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.692 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.784 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.781 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{3}+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.872 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{3} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.747 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{3} \cos \left (x \right )+\sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.851 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.653 |
|
|
\[
{}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.776 |
|
|
\[
{}x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.739 |
|
|
\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.687 |
|
|
\[
{}{y^{\prime }}^{2}+y^{2} = \sec \left (x \right )^{4}
\] |
[‘y=_G(x,y’)‘] |
✓ |
35.099 |
|
|
\[
{}\left (y-2 x y^{\prime }\right )^{2} = {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.949 |
|
|
\[
{}x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.405 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.482 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.659 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.483 |
|
|
\[
{}x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.584 |
|
|
\[
{}x \left (-1+x \right ) y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.268 |
|
|
\[
{}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.701 |
|
|
\[
{}2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.694 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.819 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.739 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.720 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = \cos \left (x \right ) \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.759 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = x^{3}+x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.758 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+2 x y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.707 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.630 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.499 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.638 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.258 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}+6 x \right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.647 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}-8\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.265 |
|
|
\[
{}x^{2} y^{\prime \prime }-9 x y^{\prime }+25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.459 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.644 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.640 |
|
|
\[
{}x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.646 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.547 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.432 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.481 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.999 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.558 |
|
|
\[
{}y^{\prime } = y \left (1-y^{2}\right )
\] |
[_quadrature] |
✓ |
4.309 |
|
|
\[
{}\frac {x y^{\prime \prime }}{1-x}+y = \frac {1}{1-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.543 |
|
|
\[
{}\frac {x y^{\prime \prime }}{1-x}+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.706 |
|
|
\[
{}\frac {x y^{\prime \prime }}{1-x}+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.845 |
|
|
\[
{}\frac {x y^{\prime \prime }}{-x^{2}+1}+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.385 |
|
|
\[
{}y^{\prime \prime } = \left (x^{2}+3\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.953 |
|
|
\[
{}y^{\prime \prime }+\left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.329 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+2 t +1 \\ y^{\prime }=5 x+y+3 t -1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.826 |
|
|
\[
{}y^{\prime \prime }+20 y^{\prime }+500 y = 100000 \cos \left (100 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
82.520 |
|
|
\[
{}y^{\prime \prime } \sin \left (2 x \right )^{2}+y^{\prime } \sin \left (4 x \right )-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
4.710 |
|
|
\[
{}y^{\prime \prime } = A y^{{2}/{3}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
124.648 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.511 |
|
|
\[
{}y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.796 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.458 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.828 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y = 6 x^{3} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.800 |
|
|
\[
{}y^{\prime }+y = \frac {1}{x}
\] |
[[_linear, ‘class A‘]] |
✗ |
0.191 |
|
|
\[
{}y^{\prime }+y = \frac {1}{x^{2}}
\] |
[[_linear, ‘class A‘]] |
✗ |
0.270 |
|
|
\[
{}x y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.269 |
|
|
\[
{}y^{\prime } = \frac {1}{x}
\] |
[_quadrature] |
✗ |
0.112 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{x}
\] |
[[_2nd_order, _quadrature]] |
✗ |
0.064 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \frac {1}{x}
\] |
[[_2nd_order, _missing_y]] |
✗ |
0.070 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.067 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \frac {1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.070 |
|
|
\[
{}h^{2}+\frac {2 a h}{\sqrt {1+{h^{\prime }}^{2}}} = b^{2}
\] |
[_quadrature] |
✓ |
2.919 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-24 y = 16-\left (x +2\right ) {\mathrm e}^{4 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.809 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.395 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{a \cos \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.156 |
|
|
\[
{}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.653 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.687 |
|
|
\[
{}x^{2} y^{\prime }+{\mathrm e}^{-y} = 0
\] |
[_separable] |
✓ |
1.632 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{y} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.747 |
|
|
\[
{}y^{\prime } = \frac {x y+3 x -2 y+6}{x y-3 x -2 y+6}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.433 |
|
|
\[
{}y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.428 |
|
|
\[
{}y^{\prime } = a
\] |
[_quadrature] |
✓ |
0.404 |
|
|
\[
{}y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.431 |
|
|
\[
{}y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.782 |
|
|
\[
{}y^{\prime } = a x
\] |
[_quadrature] |
✓ |
0.155 |
|
|
\[
{}y^{\prime } = y a x
\] |
[_separable] |
✓ |
0.816 |
|
|
\[
{}y^{\prime } = a x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.696 |
|
|
\[
{}y^{\prime } = a x +b y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.839 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
1.519 |
|
|
\[
{}y^{\prime } = b y
\] |
[_quadrature] |
✓ |
0.789 |
|
|
\[
{}y^{\prime } = a x +b y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.105 |
|
|
\[
{}c y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.430 |
|
|
\[
{}c y^{\prime } = a
\] |
[_quadrature] |
✓ |
0.359 |
|
|
\[
{}c y^{\prime } = a x
\] |
[_quadrature] |
✓ |
0.168 |
|
|
\[
{}c y^{\prime } = a x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.783 |
|
|
\[
{}c y^{\prime } = a x +b y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.835 |
|