|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.092 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.076 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+48 y^{\prime \prime }+16 y^{\prime }-96 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.037 |
|
|
\[
{}y^{\prime \prime \prime \prime } = \sin \left (x \right )+24
\] |
[[_high_order, _quadrature]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 10+42 \,{\mathrm e}^{3 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.127 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = 1
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.158 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.119 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.124 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.125 |
|
|
\[
{}x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.184 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.070 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.077 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.826 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.199 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-5 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.655 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.867 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
43.375 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.076 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.163 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
20.288 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
11.091 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+4 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
74.007 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.340 |
|
|
\[
{}y^{\prime \prime }-y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.471 |
|
|
\[
{}y^{\prime \prime } = \tan \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
19.046 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = \ln \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.906 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 2 x -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.081 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.977 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.336 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-y = x \,{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.539 |
|
|
\[
{}y^{\prime \prime }+9 y = \sec \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
27.511 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = x \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.522 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {2}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.802 |
|
|
\[
{}y^{\prime \prime }+4 y = \tan \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.764 |
|
|
\[
{}y^{\prime \prime }-y = 3 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.532 |
|
|
\[
{}y^{\prime \prime }+y = -8 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.735 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{2}+2 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.746 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \frac {x -1}{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.788 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.426 |
|
|
\[
{}y^{\prime \prime }+9 y = -3 \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.545 |
|
|
\[
{}y^{\prime }+y = \cos \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.191 |
|
|
\[
{}y^{\prime \prime } = -3 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
97.530 |
|
|
\[
{}y^{\prime \prime }+\sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.805 |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
0.615 |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
1.156 |
|
|
\[
{}y^{\prime }+y = 1
\] |
[_quadrature] |
✓ |
0.311 |
|
|
\[
{}y^{\prime }+y = 1
\] |
[_quadrature] |
✓ |
0.906 |
|
|
\[
{}y^{\prime }-y = 2
\] |
[_quadrature] |
✓ |
0.526 |
|
|
\[
{}y^{\prime }-y = 2
\] |
[_quadrature] |
✓ |
1.028 |
|
|
\[
{}y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
0.308 |
|
|
\[
{}y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
1.022 |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.533 |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
1.032 |
|
|
\[
{}y^{\prime }-y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.553 |
|
|
\[
{}y^{\prime }-y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.038 |
|
|
\[
{}x y^{\prime } = y
\] |
[_separable] |
✓ |
0.457 |
|
|
\[
{}x y^{\prime } = y
\] |
[_separable] |
✓ |
1.336 |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✗ |
0.090 |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✓ |
1.347 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
0.493 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
1.291 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x
\] |
[_linear] |
✓ |
1.228 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {-x^{2}+1}}
\] |
[_quadrature] |
✓ |
0.356 |
|
|
\[
{}y^{\prime } = y+1
\] |
[_quadrature] |
✓ |
0.309 |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.568 |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.235 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.605 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.651 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }-y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.644 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-x^{2} y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.670 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.677 |
|
|
\[
{}y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.646 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.627 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.610 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.573 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.572 |
|
|
\[
{}y^{\prime \prime }+\left (p +\frac {1}{2}-\frac {x^{2}}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.713 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.503 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.890 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+2 p y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.700 |
|
|
\[
{}x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.131 |
|
|
\[
{}x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.461 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✗ |
0.161 |
|
|
\[
{}\left (3 x +1\right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.562 |
|
|
\[
{}y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.824 |
|
|
\[
{}x y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.879 |
|
|
\[
{}x^{2} y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.308 |
|
|
\[
{}x^{3} y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.894 |
|
|
\[
{}x^{4} y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.176 |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (\cos \left (2 x \right )-1\right ) y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.044 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.089 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.305 |
|
|
\[
{}x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.868 |
|
|
\[
{}4 x y^{\prime \prime }+3 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.051 |
|
|
\[
{}2 x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.017 |
|
|
\[
{}2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.082 |
|