|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y = x \left (x +1\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.713 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = \left (1-x \right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.740 |
|
|
\[
{}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = x^{2} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.391 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.619 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.582 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.510 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.342 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.339 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.378 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.435 |
|
|
\[
{}y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.372 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.345 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.366 |
|
|
\[
{}y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.895 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.360 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}y^{\prime \prime \prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.084 |
|
|
\[
{}y^{\prime \prime \prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.080 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.076 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.081 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.110 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.081 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+48 y^{\prime \prime }+16 y^{\prime }-96 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.043 |
|
|
\[
{}y^{\prime \prime \prime \prime } = \sin \left (x \right )+24
\] |
[[_high_order, _quadrature]] |
✓ |
0.152 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 10+42 \,{\mathrm e}^{3 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.140 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = 1
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.212 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.125 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.132 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.137 |
|
|
\[
{}x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.278 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.446 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.506 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.259 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.529 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-5 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.006 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.303 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
40.220 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.332 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.689 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
22.090 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
12.430 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+4 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.774 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.698 |
|
|
\[
{}y^{\prime \prime }-y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.494 |
|
|
\[
{}y^{\prime \prime } = \tan \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
22.459 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = \ln \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.849 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 2 x -1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.341 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.338 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.786 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-y = x \,{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.038 |
|
|
\[
{}y^{\prime \prime }+9 y = \sec \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
30.182 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = x \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.970 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \frac {2}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.970 |
|
|
\[
{}y^{\prime \prime }+4 y = \tan \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.603 |
|
|
\[
{}y^{\prime \prime }-y = 3 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.656 |
|
|
\[
{}y^{\prime \prime }+y = -8 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.819 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{2}+2 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.002 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \frac {x -1}{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.895 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.458 |
|
|
\[
{}y^{\prime \prime }+9 y = -3 \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.087 |
|
|
\[
{}y^{\prime }+y = \cos \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.438 |
|
|
\[
{}y^{\prime \prime } = -3 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
97.720 |
|
|
\[
{}y^{\prime \prime }+\sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.068 |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
0.731 |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
1.626 |
|
|
\[
{}y^{\prime }+y = 1
\] |
[_quadrature] |
✓ |
0.415 |
|
|
\[
{}y^{\prime }+y = 1
\] |
[_quadrature] |
✓ |
1.242 |
|
|
\[
{}y^{\prime }-y = 2
\] |
[_quadrature] |
✓ |
0.625 |
|
|
\[
{}y^{\prime }-y = 2
\] |
[_quadrature] |
✓ |
1.144 |
|
|
\[
{}y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
0.389 |
|
|
\[
{}y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
1.394 |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.619 |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
1.378 |
|
|
\[
{}y^{\prime }-y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.616 |
|
|
\[
{}y^{\prime }-y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.319 |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
0.528 |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
1.621 |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✗ |
0.098 |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✓ |
1.744 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
0.574 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
1.665 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x
\] |
[_linear] |
✓ |
1.634 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {-x^{2}+1}}
\] |
[_quadrature] |
✓ |
0.432 |
|
|
\[
{}y^{\prime } = 1+y
\] |
[_quadrature] |
✓ |
0.410 |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.669 |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.509 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.693 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.751 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x -y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.708 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-x^{2} y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.762 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.765 |
|
|
\[
{}y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.698 |
|