|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = x \,{\mathrm e}^{y-x^{2}}
\] |
[_separable] |
✓ |
2.094 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.853 |
|
|
\[
{}y^{\prime } = \frac {2 x}{y}
\] |
[_separable] |
✓ |
6.438 |
|
|
\[
{}y^{\prime } = -2 y+y^{2}
\] |
[_quadrature] |
✓ |
2.103 |
|
|
\[
{}y^{\prime } = x y+x
\] |
[_separable] |
✓ |
1.774 |
|
|
\[
{}x \,{\mathrm e}^{y}+y^{\prime } = 0
\] |
[_separable] |
✓ |
2.185 |
|
|
\[
{}y-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.673 |
|
|
\[
{}2 y^{\prime } y = 1
\] |
[_quadrature] |
✓ |
1.656 |
|
|
\[
{}2 x y y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
2.207 |
|
|
\[
{}y^{\prime } = \frac {1-x y}{x^{2}}
\] |
[_linear] |
✓ |
1.200 |
|
|
\[
{}y^{\prime } = -\frac {y \left (2 x +y\right )}{x \left (2 y+x \right )}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.724 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{1-x y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.524 |
|
|
\[
{}y^{\prime } = 4 y+1
\] |
[_quadrature] |
✓ |
1.494 |
|
|
\[
{}y^{\prime } = x y+2
\] |
[_linear] |
✓ |
1.305 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.921 |
|
|
\[
{}y^{\prime } = \frac {y}{x -1}+x^{2}
\] |
[_linear] |
✓ |
1.411 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\sin \left (x^{2}\right )
\] |
[_linear] |
✓ |
2.055 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}+{\mathrm e}^{x}
\] |
[_linear] |
✓ |
2.060 |
|
|
\[
{}y^{\prime } = \cot \left (x \right ) y+\sin \left (x \right )
\] |
[_linear] |
✓ |
2.004 |
|
|
\[
{}x -y^{\prime } y = 0
\] |
[_separable] |
✓ |
3.499 |
|
|
\[
{}y-y^{\prime } x = 0
\] |
[_separable] |
✓ |
1.646 |
|
|
\[
{}x^{2}-y+y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.508 |
|
|
\[
{}x y \left (1-y\right )-2 y^{\prime } = 0
\] |
[_separable] |
✓ |
2.118 |
|
|
\[
{}x \left (1-y^{3}\right )-3 y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.176 |
|
|
\[
{}y \left (2 x -1\right )+x \left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.700 |
|
|
\[
{}y^{\prime } = \frac {1}{x -1}
\] |
[_quadrature] |
✓ |
0.600 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.420 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.858 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.816 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
2.346 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
1.923 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
2.341 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.542 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.518 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.535 |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
1.991 |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
1.617 |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
2.000 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
3.626 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
3.539 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
2.936 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
3.809 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.615 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.519 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.629 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.929 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
133.704 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
8.617 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
114.345 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
11.530 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
14.012 |
|
|
\[
{}y^{\prime } = \sqrt {\left (2+y\right ) \left (-1+y\right )}
\] |
[_quadrature] |
✓ |
19.111 |
|
|
\[
{}y^{\prime } = \sqrt {\left (2+y\right ) \left (-1+y\right )}
\] |
[_quadrature] |
✓ |
3.829 |
|
|
\[
{}y^{\prime } = \sqrt {\left (2+y\right ) \left (-1+y\right )}
\] |
[_quadrature] |
✓ |
61.680 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.569 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.072 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.919 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.243 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.011 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.389 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.907 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
4.109 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
84.826 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
7.483 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
3.225 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.750 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.522 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.593 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
3.022 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.497 |
|
|
\[
{}3 y^{\prime \prime }-2 y^{\prime }+4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
19.648 |
|
|
\[
{}x y^{\prime \prime \prime }+y^{\prime } x = 4
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.793 |
|
|
\[
{}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.460 |
|
|
\[
{}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.729 |
|
|
\[
{}\sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.837 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right ) = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.357 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.168 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.148 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.063 |
|
|
\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.339 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.747 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.092 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.928 |
|
|
\[
{}y^{\prime \prime }-4 y = 31
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.275 |
|
|
\[
{}y^{\prime \prime }+9 y = 27 x +18
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.242 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = -3 x -\frac {3}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.710 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.064 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+6 y^{\prime }-4 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.081 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.098 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.099 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.093 |
|
|
\[
{}y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.095 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35 y^{\prime \prime }+16 y^{\prime }-52 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.100 |
|
|
\[
{}y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.116 |
|
|
\[
{}y^{\prime \prime }+\alpha y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
38.749 |
|
|
\[
{}y^{\prime \prime \prime }+\left (-3-4 i\right ) y^{\prime \prime }+\left (-4+12 i\right ) y^{\prime }+12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.106 |
|
|
\[
{}y^{\prime \prime \prime \prime }+\left (-3-i\right ) y^{\prime \prime \prime }+\left (4+3 i\right ) y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.090 |
|
|
\[
{}y^{\prime }-i y = 0
\] |
[_quadrature] |
✓ |
1.190 |
|