|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.277 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.303 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.562 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.303 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
28.698 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
28.094 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
22.216 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime }+y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.509 |
|
|
\[
{}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.516 |
|
|
\[
{}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.455 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.263 |
|
|
\[
{}x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.183 |
|
|
\[
{}x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.044 |
|
|
\[
{}5 x^{5} y^{\prime \prime \prime \prime }+4 x^{4} y^{\prime \prime \prime }+x^{2} y^{\prime }+y x = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.285 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.680 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = x
\] |
[[_2nd_order, _missing_y]] |
✗ |
396.624 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+x {y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.411 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y {y^{\prime }}^{2} = 0
\] |
[NONE] |
✗ |
0.084 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.507 |
|
|
\[
{}y^{\prime \prime }+\sin \left (y\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.325 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.685 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.581 |
|
|
\[
{}y^{\prime } = 2 x^{2} \sin \left (\frac {y}{x}\right )^{2}+\frac {y}{x}
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
3.497 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 8 \sqrt {x}\, \left (1+\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.878 |
|
|
\[
{}v v^{\prime } = \frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3}
\] |
[_rational, _Bernoulli] |
✓ |
1.449 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.757 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.886 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.827 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.779 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}+x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.864 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.819 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.914 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.876 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.854 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 1+\sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.906 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.928 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \sin \left (x \right )+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.902 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (\cos \left (x \right )-1\right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.068 |
|
|
\[
{}\left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.825 |
|
|
\[
{}\left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.883 |
|
|
\[
{}\left (x +1\right ) \left (3 x -1\right ) y^{\prime \prime }+\cos \left (x \right ) y^{\prime }-3 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.177 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
0.713 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y x = x^{2}+2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.996 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.884 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 y^{\prime } x -y x = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.705 |
|
|
\[
{}y^{\prime \prime }+\left (x -6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.481 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.911 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{2}+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.024 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.009 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{3}+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.052 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{3} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.935 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = x^{3} \cos \left (x \right )+\sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.030 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y = \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.762 |
|
|
\[
{}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.957 |
|
|
\[
{}x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.868 |
|
|
\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.862 |
|
|
\[
{}{y^{\prime }}^{2}+y^{2} = \sec \left (x \right )^{4}
\] |
[‘y=_G(x,y’)‘] |
✓ |
6.923 |
|
|
\[
{}\left (y-2 y^{\prime } x \right )^{2} = {y^{\prime }}^{3}
\] |
unknown |
✗ |
253.040 |
|
|
\[
{}x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.556 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.700 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.781 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.693 |
|
|
\[
{}x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.721 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.173 |
|
|
\[
{}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.921 |
|
|
\[
{}2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.909 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.977 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 y^{\prime } x -y x = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.880 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 y^{\prime } x -y x = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.894 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 y^{\prime } x -y x = \cos \left (x \right ) \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.928 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 y^{\prime } x -y x = x^{3}+x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.890 |
|
|
\[
{}y^{\prime \prime } \cos \left (x \right )+2 y^{\prime } x -y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.829 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.854 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.732 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.788 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.276 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}+6 x \right ) y^{\prime }+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.839 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-8\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.223 |
|
|
\[
{}x^{2} y^{\prime \prime }-9 y^{\prime } x +25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.681 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.810 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.836 |
|
|
\[
{}x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.830 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.780 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.664 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.745 |
|
|
\[
{}x^{2} y^{\prime \prime }-y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.121 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.705 |
|
|
\[
{}y^{\prime } = y \left (1-y^{2}\right )
\] |
[_quadrature] |
✓ |
0.991 |
|
|
\[
{}\frac {x y^{\prime \prime }}{1-x}+y = \frac {1}{1-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.348 |
|
|
\[
{}\frac {x y^{\prime \prime }}{1-x}+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.956 |
|
|
\[
{}\frac {x y^{\prime \prime }}{1-x}+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.438 |
|
|
\[
{}\frac {x y^{\prime \prime }}{-x^{2}+1}+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.220 |
|
|
\[
{}y^{\prime \prime } = \left (x^{2}+3\right ) y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.925 |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.485 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+2 t +1 \\ y^{\prime }=5 x+y+3 t -1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.785 |
|
|
\[
{}y^{\prime \prime }+20 y^{\prime }+500 y = 100000 \cos \left (100 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
55.072 |
|
|
\[
{}y^{\prime \prime } \sin \left (2 x \right )^{2}+y^{\prime } \sin \left (4 x \right )-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.515 |
|
|
\[
{}y^{\prime \prime } = A y^{{2}/{3}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
167.361 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.736 |
|
|
\[
{}y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.156 |
|