|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {y}{x -1}+x^{2}
\] |
[_linear] |
✓ |
1.188 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\sin \left (x^{2}\right )
\] |
[_linear] |
✓ |
1.796 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}+{\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.820 |
|
|
\[
{}y^{\prime } = y \cot \left (x \right )+\sin \left (x \right )
\] |
[_linear] |
✓ |
1.897 |
|
|
\[
{}x -y y^{\prime } = 0
\] |
[_separable] |
✓ |
3.075 |
|
|
\[
{}y-x y^{\prime } = 0
\] |
[_separable] |
✓ |
1.271 |
|
|
\[
{}x^{2}-y+x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.146 |
|
|
\[
{}x y \left (1-y\right )-2 y^{\prime } = 0
\] |
[_separable] |
✓ |
1.921 |
|
|
\[
{}x \left (1-y^{3}\right )-3 y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.398 |
|
|
\[
{}y \left (2 x -1\right )+x \left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.377 |
|
|
\[
{}y^{\prime } = \frac {1}{x -1}
\] |
[_quadrature] |
✓ |
0.405 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.165 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.465 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.496 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
2.510 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
1.990 |
|
|
\[
{}y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x}
\] |
[_linear] |
✓ |
2.543 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.151 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.158 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.176 |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
1.695 |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
1.229 |
|
|
\[
{}y^{\prime } = y^{3}
\] |
[_quadrature] |
✓ |
1.716 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
2.868 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
3.101 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
2.480 |
|
|
\[
{}y^{\prime } = -\frac {3 x^{2}}{2 y}
\] |
[_separable] |
✓ |
3.056 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.563 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.372 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.508 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
2.625 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
138.292 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
17.552 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
115.734 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
11.371 |
|
|
\[
{}y^{\prime } = 3 x y^{{1}/{3}}
\] |
[_separable] |
✓ |
49.743 |
|
|
\[
{}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )}
\] |
[_quadrature] |
✓ |
20.224 |
|
|
\[
{}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )}
\] |
[_quadrature] |
✓ |
4.022 |
|
|
\[
{}y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )}
\] |
[_quadrature] |
✓ |
99.625 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.039 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.798 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.936 |
|
|
\[
{}y^{\prime } = \frac {y}{y-x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.952 |
|
|
\[
{}y^{\prime } = \frac {x y}{y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.925 |
|
|
\[
{}y^{\prime } = \frac {x y}{y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.095 |
|
|
\[
{}y^{\prime } = \frac {x y}{y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.897 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
4.363 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
84.505 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
7.842 |
|
|
\[
{}y^{\prime } = x \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
3.222 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.685 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.385 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.521 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.984 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.334 |
|
|
\[
{}3 y^{\prime \prime }-2 y^{\prime }+4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
20.174 |
|
|
\[
{}x y^{\prime \prime \prime }+x y^{\prime } = 4
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.682 |
|
|
\[
{}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.561 |
|
|
\[
{}x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.973 |
|
|
\[
{}\sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.704 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right ) = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.257 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.989 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.903 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.169 |
|
|
\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_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]] |
✓ |
2.521 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.092 |
|
|
\[
{}y^{\prime \prime }-4 y = 31
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.191 |
|
|
\[
{}y^{\prime \prime }+9 y = 27 x +18
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.226 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = -3 x -\frac {3}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.049 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.845 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+6 y^{\prime }-4 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.082 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.091 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.082 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35 y^{\prime \prime }+16 y^{\prime }-52 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.087 |
|
|
\[
{}y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.111 |
|
|
\[
{}y^{\prime \prime }+\alpha y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.705 |
|
|
\[
{}y^{\prime \prime \prime }+\left (-3-4 i\right ) y^{\prime \prime }+\left (-4+12 i\right ) y^{\prime }+12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.095 |
|
|
\[
{}y^{\prime \prime \prime \prime }+\left (-3-i\right ) y^{\prime \prime \prime }+\left (4+3 i\right ) y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.090 |
|
|
\[
{}y^{\prime }-i y = 0
\] |
[_quadrature] |
✓ |
1.165 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.174 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 24 x^{2}-6 x +14+32 \cos \left (2 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.641 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3+\cos \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.182 |
|
|
\[
{}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 6 x -20-120 \,{\mathrm e}^{x} x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.173 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y = 36 \,{\mathrm e}^{2 x} \sin \left (3 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.555 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = \left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.273 |
|
|
\[
{}y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y = {\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.272 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.158 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.155 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 2 \,{\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.143 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 x +4
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.146 |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.177 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.230 |
|
|
\[
{}y^{\prime }+2 y = 4
\] |
[_quadrature] |
✓ |
0.199 |
|
|
\[
{}y^{\prime \prime }-9 y = 2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.246 |
|