|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (y+1\right ) y^{\prime } = y
\] |
[_quadrature] |
✓ |
2.299 |
|
|
\[
{}y^{\prime }-x y = x
\] |
[_separable] |
✓ |
1.917 |
|
|
\[
{}2 y^{\prime } = 3 \left (y-2\right )^{{1}/{3}}
\] |
[_quadrature] |
✓ |
2.159 |
|
|
\[
{}\left (x +x y\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
2.239 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.248 |
|
|
\[
{}x^{2} y^{\prime }+3 x y = 1
\] |
[_linear] |
✓ |
0.224 |
|
|
\[
{}y^{\prime }+2 x y-x \,{\mathrm e}^{-x^{2}} = 0
\] |
[_linear] |
✓ |
0.263 |
|
|
\[
{}2 x y^{\prime }+y = 2 x^{{5}/{2}}
\] |
[_linear] |
✓ |
0.205 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y = \cos \left (x \right )^{2}
\] |
[_linear] |
✓ |
0.489 |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {x^{2}+1}} = \frac {1}{x +\sqrt {x^{2}+1}}
\] |
[_linear] |
✓ |
0.251 |
|
|
\[
{}\left ({\mathrm e}^{x}+1\right ) y^{\prime }+2 y \,{\mathrm e}^{x} = \left ({\mathrm e}^{x}+1\right ) {\mathrm e}^{x}
\] |
[_linear] |
✓ |
0.277 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }+y = \ln \left (x \right )
\] |
[_linear] |
✓ |
0.129 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = x y+2 x \sqrt {-x^{2}+1}
\] |
[_linear] |
✓ |
0.236 |
|
|
\[
{}y^{\prime }+y \tanh \left (x \right ) = 2 \,{\mathrm e}^{x}
\] |
[_linear] |
✓ |
0.314 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
0.330 |
|
|
\[
{}x^{\prime } = \cos \left (y \right )-x \tan \left (y \right )
\] |
[_linear] |
✓ |
0.285 |
|
|
\[
{}x^{\prime }+x-{\mathrm e}^{y} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
0.247 |
|
|
\[
{}x^{\prime } = \frac {3 y^{{2}/{3}}-x}{3 y}
\] |
[_linear] |
✓ |
0.210 |
|
|
\[
{}y^{\prime }+y = x y^{{2}/{3}}
\] |
[_Bernoulli] |
✓ |
1.273 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = 2 x^{{3}/{2}} \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
11.735 |
|
|
\[
{}3 x y^{2} y^{\prime }+3 y^{3} = 1
\] |
[_separable] |
✓ |
3.418 |
|
|
\[
{}2 x \,{\mathrm e}^{3 y}+{\mathrm e}^{x}+\left (3 x^{2} {\mathrm e}^{3 y}-y^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.849 |
|
|
\[
{}\left (x -y\right ) y^{\prime }+y+x +1 = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.432 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )+\sin \left (x \right )^{2}-\left (\sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right )^{2}\right ) y^{\prime } = 0
\] |
unknown |
✓ |
43.244 |
|
|
\[
{}x^{2} y^{\prime }+y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.464 |
|
|
\[
{}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.005 |
|
|
\[
{}x y+\left (y^{2}-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
16.866 |
|
|
\[
{}y^{2}-x y+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
86.082 |
|
|
\[
{}y^{\prime } = \cos \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.284 |
|
|
\[
{}y^{\prime } = \frac {y}{x}-\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.918 |
|
|
\[
{}\left (-1+x \right ) y^{\prime }+y-\frac {1}{x^{2}}+\frac {2}{x^{3}} = 0
\] |
[_linear] |
✓ |
2.978 |
|
|
\[
{}y^{\prime } = x y^{2}-\frac {2 y}{x}-\frac {1}{x^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.960 |
|
|
\[
{}y^{\prime } = \frac {2 y^{2}}{x}+\frac {y}{x}-2 x
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.003 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-x} y^{2}+y-{\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
1.589 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.857 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.954 |
|
|
\[
{}y^{\prime \prime }+9 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.923 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.951 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.014 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.175 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.842 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.878 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.656 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.858 |
|
|
\[
{}y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.445 |
|
|
\[
{}y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.444 |
|
|
\[
{}y^{\prime \prime \prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.059 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-6 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.049 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }-5 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.111 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.059 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = 10
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.966 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 16
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.096 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.105 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 24 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.105 |
|
|
\[
{}y^{\prime \prime }+y = 2 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.836 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 12 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.197 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.156 |
|
|
\[
{}y^{\prime \prime }-16 y = 40 \,{\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.191 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.100 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 6 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.178 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 100 \cos \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
43.473 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+12 y = 80 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
76.241 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.483 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+25 y = 120 \sin \left (5 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
49.121 |
|
|
\[
{}5 y^{\prime \prime }+12 y^{\prime }+20 y = 120 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
47.579 |
|
|
\[
{}y^{\prime \prime }+9 y = 30 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.635 |
|
|
\[
{}y^{\prime \prime }+16 y = 16 \cos \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.646 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+17 y = 60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
50.113 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+5 y = 40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
15.592 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+8 y = 30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
38.030 |
|
|
\[
{}5 y^{\prime \prime }+6 y^{\prime }+2 y = x^{2}+6 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
39.657 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime } = 2 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.179 |
|
|
\[
{}y^{\prime \prime }+y = 2 x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.856 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 12 x \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.233 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 16 x^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.218 |
|
|
\[
{}y^{\prime \prime }+y = 8 x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.507 |
|
|
\[
{}y^{\prime \prime }+y = x^{3}-1+2 \cos \left (x \right )+\left (2-4 x \right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.265 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{x}+6 x -5
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.213 |
|
|
\[
{}y^{\prime \prime }-y = \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.616 |
|
|
\[
{}y^{\prime \prime }+y = 2 \sin \left (x \right )+4 x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.381 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 4 \,{\mathrm e}^{x}+\left (1-x \right ) \left ({\mathrm e}^{2 x}-1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.464 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.553 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.964 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.670 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.514 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.226 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.727 |
|
|
\[
{}2 y y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.371 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }+{y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.418 |
|
|
\[
{}{y^{\prime \prime }}^{2} = k^{2} \left (1+{y^{\prime }}^{2}\right )
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.868 |
|
|
\[
{}k = \frac {y^{\prime \prime }}{\left (y^{\prime }+1\right )^{{3}/{2}}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear]] |
✓ |
2.670 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.896 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.837 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.901 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.405 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 8 x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.794 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = x -\frac {1}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.362 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 2 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.610 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 6 x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.614 |
|
|
\[
{}x^{2} y^{\prime \prime }+y = 3 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.141 |
|