|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-y^{\prime } = -5 \,{\mathrm e}^{-x} \left (\sin \left (x \right )+\cos \left (x \right )\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.398 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 4 \,{\mathrm e}^{x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.613 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = -2 x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.180 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 8 \,{\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.142 |
|
|
\[
{}y^{\prime \prime \prime }-y = 2 x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.169 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 8 \,{\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.202 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.694 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \cos \left (2 x \right )+\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.943 |
|
|
\[
{}y^{\prime \prime }-y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.472 |
|
|
\[
{}y^{\prime \prime }-y = -2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.549 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.261 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 8 \,{\mathrm e}^{x}+9
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.246 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-5 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.993 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
2.800 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.286 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.397 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.227 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.237 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.743 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.808 |
|
|
\[
{}\left (x +2\right )^{2} y^{\prime \prime }+3 \left (x +2\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.110 |
|
|
\[
{}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.027 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.184 |
|
|
\[
{}x^{2} y^{\prime \prime \prime } = 2 y^{\prime }
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.176 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime \prime }-12 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.210 |
|
|
\[
{}\left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.364 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = x \left (6-\ln \left (x \right )\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.638 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = \sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.178 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -3 y = -\frac {16 \ln \left (x \right )}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.687 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -2 y = x^{2}-2 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.124 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x^{m}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.095 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 2 \ln \left (x \right )^{2}+12 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.448 |
|
|
\[
{}\left (x +1\right )^{3} y^{\prime \prime }+3 \left (x +1\right )^{2} y^{\prime }+\left (x +1\right ) y = 6 \ln \left (x +1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.641 |
|
|
\[
{}\left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.462 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.068 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y = 0
\] |
[_Jacobi] |
✓ |
1.237 |
|
|
\[
{}\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (x +1\right ) y^{\prime }+6 y = 6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.480 |
|
|
\[
{}x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.319 |
|
|
\[
{}y^{\prime \prime }+\left (\tan \left (x \right )-2 \cot \left (x \right )\right ) y^{\prime }+2 \cot \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.364 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.402 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -y = 1
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.389 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -3 y = 5 x^{4}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.368 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = \left (x -1\right )^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.429 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+{\mathrm e}^{-2 x} y = {\mathrm e}^{-3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.616 |
|
|
\[
{}\left (x^{4}-x^{3}\right ) y^{\prime \prime }+\left (2 x^{3}-2 x^{2}-x \right ) y^{\prime }-y = \frac {\left (x -1\right )^{2}}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.422 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y = x \,{\mathrm e}^{2 x}-1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.589 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y = x^{2} \left (2 x -3\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.421 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.698 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \frac {1}{{\mathrm e}^{x}+1}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.181 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\cos \left (x \right )^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.158 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.984 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.506 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \frac {{\mathrm e}^{-x}}{\sin \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.536 |
|
|
\[
{}y^{\prime \prime }+y = \frac {2}{\sin \left (x \right )^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.086 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.927 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = \frac {x -1}{x^{3}}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.228 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime } = 4 x^{3} {\mathrm e}^{x^{2}}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.102 |
|
|
\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime } = 1
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.150 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime \prime }-y^{\prime } = \ln \left (x \right )^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.937 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x -1\right ) y^{\prime } = -4 x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.135 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime } = \cos \left (x \right ) \cot \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.237 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.561 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = \frac {x +6}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
53.361 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x = \frac {1}{x^{2}+1}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.583 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y = \left (x -1\right )^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.873 |
|
|
\[
{}2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y = \frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.884 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y = 4 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.393 |
|
|
\[
{}x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x^{2} y^{\prime }+x y = 2 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.734 |
|
|
\[
{}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-2 \left (1-x \right ) y = 2 x -2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.664 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.315 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+6 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.106 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.181 |
|
|
\[
{}x^{\prime \prime }+{x^{\prime }}^{2}+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.834 |
|
|
\[
{}x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.445 |
|
|
\[
{}x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.570 |
|
|
\[
{}x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
2.392 |
|
|
\[
{}x^{\prime \prime }+x {x^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.437 |
|
|
\[
{}x^{\prime \prime }+\left (x+2\right ) x^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.596 |
|
|
\[
{}x^{\prime \prime }-x^{\prime }+x-x^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.506 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.034 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.898 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.228 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.747 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.980 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.010 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.169 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.224 |
|
|
\[
{}y^{\prime \prime }+\alpha y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.152 |
|
|
\[
{}y^{\prime \prime }+\alpha ^{2} y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
6.694 |
|
|
\[
{}y^{\prime \prime }+y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.880 |
|
|
\[
{}y^{\prime \prime }+\lambda ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.879 |
|
|
\[
{}y^{\prime \prime }+\lambda ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.769 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.153 |
|
|
\[
{}y^{\prime \prime \prime \prime }-\lambda ^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.173 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.833 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }+4 x y^{\prime \prime \prime }+2 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.102 |
|
|
\[
{}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.243 |
|
|
\[
{}y^{\prime } = 1-x y
\] |
[_linear] |
✓ |
0.638 |
|
|
\[
{}y^{\prime } = \frac {y-x}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.346 |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
0.762 |
|