|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}{y^{\prime }}^{4} = 1
\] |
[_quadrature] |
✓ |
1.079 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.208 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.245 |
|
|
\[
{}y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.441 |
|
|
\[
{}{y^{\prime }}^{2}+y y^{\prime \prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.286 |
|
|
\[
{}y^{\prime \prime \prime \prime } = x
\] |
[[_high_order, _quadrature]] |
✓ |
0.122 |
|
|
\[
{}y^{\prime \prime \prime } = x +\cos \left (x \right )
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.155 |
|
|
\[
{}y^{\prime \prime } \left (x +2\right )^{5} = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.962 |
|
|
\[
{}y^{\prime \prime } = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.945 |
|
|
\[
{}y^{\prime \prime } = 2 x \ln \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.246 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.021 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.884 |
|
|
\[
{}x y^{\prime \prime } = \left (2 x^{2}+1\right ) y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.929 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }+x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.172 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.822 |
|
|
\[
{}x y = y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right )
\] |
[_separable] |
✓ |
2.915 |
|
|
\[
{}2 y^{\prime \prime } = \frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
0.607 |
|
|
\[
{}y^{\prime \prime \prime } = \sqrt {1-{y^{\prime \prime }}^{2}}
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
1.899 |
|
|
\[
{}x y^{\prime \prime \prime }-y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.177 |
|
|
\[
{}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.382 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.310 |
|
|
\[
{}y^{\prime \prime } = \sqrt {1-{y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.046 |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.630 |
|
|
\[
{}y^{\prime \prime } = \sqrt {1+y^{\prime }}
\] |
[[_2nd_order, _missing_x]] |
✓ |
80.868 |
|
|
\[
{}y^{\prime \prime } = y^{\prime } \ln \left (y^{\prime }\right )
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.602 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+2 = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.334 |
|
|
\[
{}y^{\prime \prime } = y^{\prime } \left (1+y^{\prime }\right )
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.744 |
|
|
\[
{}3 y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
6.066 |
|
|
\[
{}y^{\prime \prime \prime }+{y^{\prime \prime }}^{2} = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
0.287 |
|
|
\[
{}y y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.273 |
|
|
\[
{}y^{\prime \prime } = 2 y^{\prime } y
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.965 |
|
|
\[
{}3 y^{\prime } y^{\prime \prime } = 2 y
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.912 |
|
|
\[
{}2 y^{\prime \prime } = 3 y^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.865 |
|
|
\[
{}{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.465 |
|
|
\[
{}y y^{\prime \prime } = y^{\prime }+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.304 |
|
|
\[
{}y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.152 |
|
|
\[
{}2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.245 |
|
|
\[
{}y^{3} y^{\prime \prime } = -1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.074 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.510 |
|
|
\[
{}y^{\prime \prime } = {\mathrm e}^{2 y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
26.429 |
|
|
\[
{}2 y y^{\prime \prime }-3 {y^{\prime }}^{2} = 4 y^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
5.263 |
|
|
\[
{}y^{\prime \prime \prime } = 3 y^{\prime } y
\] |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
0.061 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.301 |
|
|
\[
{}3 y^{\prime \prime }-2 y^{\prime }-8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.161 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.257 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.757 |
|
|
\[
{}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.091 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.378 |
|
|
\[
{}y^{\left (6\right )}+2 y^{\left (5\right )}+y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.095 |
|
|
\[
{}4 y^{\prime \prime }-8 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.920 |
|
|
\[
{}y^{\prime \prime \prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.095 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+10 y^{\prime \prime }+12 y^{\prime }+5 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.098 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.460 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.234 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }-5 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.099 |
|
|
\[
{}y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-6 y^{\prime }-4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.105 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.087 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.091 |
|
|
\[
{}y^{\left (5\right )} = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.055 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.080 |
|
|
\[
{}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.138 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 3
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.398 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime } = \left (x -1\right )^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.508 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.277 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime } = {\mathrm e}^{-7 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.250 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+16 y = \left (1-x \right ) {\mathrm e}^{4 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.507 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.472 |
|
|
\[
{}4 y^{\prime \prime }-3 y^{\prime } = x \,{\mathrm e}^{\frac {3 x}{4}}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.455 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = x \,{\mathrm e}^{4 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.479 |
|
|
\[
{}y^{\prime \prime }+25 y = \cos \left (5 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.199 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )-\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.321 |
|
|
\[
{}y^{\prime \prime }+16 y = \sin \left (4 x +\alpha \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.578 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
15.847 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )-\cos \left (2 x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
26.360 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = {\mathrm e}^{-3 x} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
21.930 |
|
|
\[
{}y^{\prime \prime }+k^{2} y = k \sin \left (k x +\alpha \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.548 |
|
|
\[
{}y^{\prime \prime }+k^{2} y = k
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.131 |
|
|
\[
{}y^{\prime \prime \prime }+y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 1
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.111 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = 2
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.100 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = 3
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.098 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.108 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime } = 2
\] |
[[_high_order, _missing_x]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime } = 3
\] |
[[_high_order, _missing_x]] |
✓ |
0.124 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime } = 4
\] |
[[_high_order, _missing_x]] |
✓ |
0.120 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime } = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.114 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{4 x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.123 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{-x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.128 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{-x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.142 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.170 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.156 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = x \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.209 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y = a \sin \left (n x +\alpha \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.174 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 n^{2} y^{\prime \prime }+n^{4} y = \cos \left (n x +\alpha \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.195 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.156 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.149 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = x \,{\mathrm e}^{x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.155 |
|