|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.385 |
|
|
\[
{}y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.500 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.509 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+y = 0
\] |
[_Lienard] |
✓ |
0.615 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+2 y = 0
\] |
[_Hermite] |
✓ |
0.584 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.623 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.618 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.561 |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.616 |
|
|
\[
{}y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.665 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.629 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.710 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.626 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.536 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-\left (2-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.659 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.593 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.618 |
|
|
\[
{}y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.827 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.937 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.414 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.455 |
|
|
\[
{}y^{\prime \prime }-x y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.519 |
|
|
\[
{}y^{\prime \prime }-4 x y^{\prime }-4 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.702 |
|
|
\[
{}x y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.807 |
|
|
\[
{}y^{\prime \prime }+5 x y^{\prime }+\sqrt {x}\, y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.144 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.611 |
|
|
\[
{}y^{\prime \prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.818 |
|
|
\[
{}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
0.120 |
|
|
\[
{}x \left (x +3\right )^{2} y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.529 |
|
|
\[
{}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.880 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.655 |
|
|
\[
{}\left (x^{3}+4 x \right ) y^{\prime \prime }-2 x y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.526 |
|
|
\[
{}x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.773 |
|
|
\[
{}\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (-2+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.805 |
|
|
\[
{}x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.395 |
|
|
\[
{}x^{3} \left (x^{2}-25\right ) \left (-2+x \right )^{2} y^{\prime \prime }+3 x \left (-2+x \right ) y^{\prime }+7 \left (x +5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.151 |
|
|
\[
{}\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.454 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+5 \left (x +1\right ) y^{\prime }+\left (x^{2}-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.875 |
|
|
\[
{}x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.369 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.133 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.829 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.064 |
|
|
\[
{}2 x y^{\prime \prime }+5 y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.832 |
|
|
\[
{}4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.044 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.954 |
|
|
\[
{}3 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.020 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.088 |
|
|
\[
{}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
1.046 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.948 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.145 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.203 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.848 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.973 |
|
|
\[
{}x y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.262 |
|
|
\[
{}y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.181 |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.839 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.837 |
|
|
\[
{}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.118 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.977 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{t}+\lambda y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.919 |
|
|
\[
{}x^{3} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
0.110 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
0.171 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.038 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.936 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.077 |
|
|
\[
{}16 x^{2} y^{\prime \prime }+16 x y^{\prime }+\left (16 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.006 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.859 |
|
|
\[
{}y^{\prime }+x y^{\prime \prime }+\left (x -\frac {4}{x}\right ) y = 0
\] |
[_Bessel] |
✓ |
1.019 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.128 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.807 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.001 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.970 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.862 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.877 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.860 |
|
|
\[
{}x y^{\prime \prime }-5 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.969 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.697 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.895 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.730 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.106 |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.925 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.089 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.839 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.849 |
|
|
\[
{}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.802 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{2}+3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.149 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.058 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.618 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.684 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.567 |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
1.020 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.158 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.606 |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.663 |
|
|
\[
{}\left (1-2 \sin \left (x \right )\right ) y^{\prime \prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.057 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.671 |
|
|
\[
{}x y^{\prime \prime }+\left (1-\cos \left (x \right )\right ) y^{\prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.890 |
|
|
\[
{}\left ({\mathrm e}^{x}-1-x \right ) y^{\prime \prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.889 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 10 x^{3}-2 x +5
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.691 |
|
|
\[
{}y^{\prime }-y = 1
\] |
[_quadrature] |
✓ |
0.293 |
|