|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {1}{x -1}
\] |
[_quadrature] |
✓ |
0.661 |
|
|
\[
{}y^{\prime } = \frac {1}{x -1}
\] |
[_quadrature] |
✓ |
0.596 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}-1}
\] |
[_quadrature] |
✓ |
0.625 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}-1}
\] |
[_quadrature] |
✓ |
0.738 |
|
|
\[
{}y^{\prime } = \tan \left (x \right )
\] |
[_quadrature] |
✓ |
1.083 |
|
|
\[
{}y^{\prime } = \tan \left (x \right )
\] |
[_quadrature] |
✓ |
0.713 |
|
|
\[
{}y^{\prime } = 3 y
\] |
[_quadrature] |
✓ |
1.730 |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
1.132 |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
1.381 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{y-x^{2}}
\] |
[_separable] |
✓ |
2.090 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.918 |
|
|
\[
{}y^{\prime } = \frac {2 x}{y}
\] |
[_separable] |
✓ |
5.420 |
|
|
\[
{}y^{\prime } = -2 y+y^{2}
\] |
[_quadrature] |
✓ |
2.258 |
|
|
\[
{}y^{\prime } = x y+x
\] |
[_separable] |
✓ |
1.770 |
|
|
\[
{}x \,{\mathrm e}^{y}+y^{\prime } = 0
\] |
[_separable] |
✓ |
2.621 |
|
|
\[
{}y-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.658 |
|
|
\[
{}2 y y^{\prime } = 1
\] |
[_quadrature] |
✓ |
1.683 |
|
|
\[
{}2 x y y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
2.219 |
|
|
\[
{}y^{\prime } = \frac {1-x y}{x^{2}}
\] |
[_linear] |
✓ |
1.173 |
|
|
\[
{}y^{\prime } = -\frac {y \left (2 x +y\right )}{x \left (2 y+x \right )}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.483 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{1-x y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.563 |
|
|
\[
{}y^{\prime } = 4 y+1
\] |
[_quadrature] |
✓ |
1.487 |
|
|
\[
{}y^{\prime } = x y+2
\] |
[_linear] |
✓ |
1.308 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.865 |
|
|
\[
{}y^{\prime } = \frac {y}{x -1}+x^{2}
\] |
[_linear] |
✓ |
1.390 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\sin \left (x^{2}\right )
\] |
[_linear] |
✓ |
2.044 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}+{\mathrm e}^{x}
\] |
[_linear] |
✓ |
2.097 |
|
|
\[
{}y^{\prime } = \cot \left (x \right ) y+\sin \left (x \right )
\] |
[_linear] |
✓ |
1.978 |
|
|
\[
{}x -y y^{\prime } = 0
\] |
[_separable] |
✓ |
3.570 |
|
|
\[
{}y-y^{\prime } x = 0
\] |
[_separable] |
✓ |
1.636 |
|
|
\[
{}x^{2}-y+y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.529 |
|
|
\[
{}x y \left (1-y\right )-2 y^{\prime } = 0
\] |
[_separable] |
✓ |
2.179 |
|
|
\[
{}x \left (1-y^{3}\right )-3 y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.474 |
|
|
\[
{}y \left (2 x -1\right )+x \left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.723 |
|
|
\[
{}y^{\prime } = \frac {1}{x -1}
\] |
[_quadrature] |
✓ |
0.588 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.454 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.866 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.880 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
2.210 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
1.859 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
2.319 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.508 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.481 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.562 |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
1.999 |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
1.560 |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
1.997 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
3.094 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
3.384 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
2.768 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
3.229 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.619 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.544 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.713 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.934 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
133.155 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
16.715 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
115.042 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
10.308 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
48.593 |
|
|
\[
{}y^{\prime } = \sqrt {\left (y+2\right ) \left (-1+y\right )}
\] |
[_quadrature] |
✓ |
19.529 |
|
|
\[
{}y^{\prime } = \sqrt {\left (y+2\right ) \left (-1+y\right )}
\] |
[_quadrature] |
✓ |
4.035 |
|
|
\[
{}y^{\prime } = \sqrt {\left (y+2\right ) \left (-1+y\right )}
\] |
[_quadrature] |
✓ |
92.622 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.283 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.148 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.191 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.365 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.824 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.246 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.788 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
4.084 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
82.032 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
7.519 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
3.162 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.753 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.451 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.646 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
3.039 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.498 |
|
|
\[
{}3 y^{\prime \prime }-2 y^{\prime }+4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
19.395 |
|
|
\[
{}x y^{\prime \prime \prime }+y^{\prime } x = 4
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.782 |
|
|
\[
{}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.469 |
|
|
\[
{}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.709 |
|
|
\[
{}\sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.703 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right ) = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.379 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.207 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.165 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.086 |
|
|
\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.323 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.716 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.076 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.901 |
|
|
\[
{}y^{\prime \prime }-4 y = 31
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.210 |
|
|
\[
{}y^{\prime \prime }+9 y = 27 x +18
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.268 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = -3 x -\frac {3}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.641 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.043 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+6 y^{\prime }-4 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.071 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.082 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.089 |
|