|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y = y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right )
\] |
[_separable] |
✓ |
2.917 |
|
|
\[
{}2 y^{\prime \prime } = \frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
0.582 |
|
|
\[
{}y^{\prime \prime \prime } = \sqrt {1-{y^{\prime \prime }}^{2}}
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
0.398 |
|
|
\[
{}x y^{\prime \prime \prime }-y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.197 |
|
|
\[
{}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.450 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.196 |
|
|
\[
{}y^{\prime \prime } = \sqrt {1-{y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.411 |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.400 |
|
|
\[
{}y^{\prime \prime } = \sqrt {1+y^{\prime }}
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.396 |
|
|
\[
{}y^{\prime \prime } = y^{\prime } \ln \left (y^{\prime }\right )
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.237 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+2 = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.682 |
|
|
\[
{}y^{\prime \prime } = y^{\prime } \left (1+y^{\prime }\right )
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.528 |
|
|
\[
{}3 y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.833 |
|
|
\[
{}y^{\prime \prime \prime }+{y^{\prime \prime }}^{2} = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
0.147 |
|
|
\[
{}y y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.250 |
|
|
\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.831 |
|
|
\[
{}3 y^{\prime } y^{\prime \prime } = 2 y
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.862 |
|
|
\[
{}2 y^{\prime \prime } = 3 y^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.861 |
|
|
\[
{}{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.414 |
|
|
\[
{}y y^{\prime \prime } = y^{\prime }+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.285 |
|
|
\[
{}y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.099 |
|
|
\[
{}2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.194 |
|
|
\[
{}y^{3} y^{\prime \prime } = -1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.990 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.487 |
|
|
\[
{}y^{\prime \prime } = {\mathrm e}^{2 y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
25.229 |
|
|
\[
{}2 y y^{\prime \prime }-3 {y^{\prime }}^{2} = 4 y^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
5.277 |
|
|
\[
{}y^{\prime \prime \prime } = 3 y y^{\prime }
\] |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
0.051 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.103 |
|
|
\[
{}3 y^{\prime \prime }-2 y^{\prime }-8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.879 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.138 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.868 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.490 |
|
|
\[
{}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.047 |
|
|
\[
{}y^{\left (6\right )}+2 y^{\left (5\right )}+y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.075 |
|
|
\[
{}4 y^{\prime \prime }-8 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.611 |
|
|
\[
{}y^{\prime \prime \prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.080 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+10 y^{\prime \prime }+12 y^{\prime }+5 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.081 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.514 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.062 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }-5 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-6 y^{\prime }-4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.084 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}y^{\left (5\right )} = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.041 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.075 |
|
|
\[
{}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.131 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 3
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.701 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime } = \left (x -1\right )^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.694 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.540 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime } = {\mathrm e}^{-7 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.560 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+16 y = \left (1-x \right ) {\mathrm e}^{4 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.129 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.063 |
|
|
\[
{}4 y^{\prime \prime }-3 y^{\prime } = x \,{\mathrm e}^{\frac {3 x}{4}}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.661 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = x \,{\mathrm e}^{4 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.645 |
|
|
\[
{}y^{\prime \prime }+25 y = \cos \left (5 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.829 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )-\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.915 |
|
|
\[
{}y^{\prime \prime }+16 y = \sin \left (4 x +\alpha \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.067 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.246 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )-\cos \left (2 x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
14.924 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = {\mathrm e}^{-3 x} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
13.425 |
|
|
\[
{}y^{\prime \prime }+k^{2} y = k \sin \left (k x +\alpha \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.039 |
|
|
\[
{}y^{\prime \prime }+k^{2} y = k
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.885 |
|
|
\[
{}y^{\prime \prime \prime }+y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.121 |
|
|
\[
{}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 1
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.107 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = 2
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.101 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = 3
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.099 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.108 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime } = 2
\] |
[[_high_order, _missing_x]] |
✓ |
0.121 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime } = 3
\] |
[[_high_order, _missing_x]] |
✓ |
0.105 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime } = 4
\] |
[[_high_order, _missing_x]] |
✓ |
0.107 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime } = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.110 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{4 x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.122 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{-x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.127 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{-x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.144 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.174 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.161 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = x \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.204 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y = a \sin \left (n x +\alpha \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.165 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 n^{2} y^{\prime \prime }+n^{4} y = \cos \left (n x +\alpha \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.186 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.145 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = x \,{\mathrm e}^{x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.151 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = -2
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.007 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = -2
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.744 |
|
|
\[
{}y^{\prime \prime }+9 y = 9
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.431 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = 1
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.102 |
|
|
\[
{}5 y^{\prime \prime \prime }-7 y^{\prime \prime } = 3
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.104 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime } = -6
\] |
[[_high_order, _missing_x]] |
✓ |
0.119 |
|
|
\[
{}3 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime } = 2
\] |
[[_high_order, _missing_x]] |
✓ |
0.108 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.083 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime } = 8 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.694 |
|
|
\[
{}y^{\prime \prime }-2 k y^{\prime }+k^{2} y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.922 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 8 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.100 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 9 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.238 |
|
|
\[
{}7 y^{\prime \prime }-y^{\prime } = 14 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.590 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 3 x \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.649 |
|