|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.906 |
|
|
\[
{}x^{2} \left (2-x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.106 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.091 |
|
|
\[
{}x y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.105 |
|
|
\[
{}3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.107 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.105 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.115 |
|
|
\[
{}x^{2} y^{\prime }-x y = \frac {1}{x}
\] |
[_linear] |
✓ |
1.658 |
|
|
\[
{}x \ln \left (y\right ) y^{\prime }-y \ln \left (x \right ) = 0
\] |
[_separable] |
✓ |
1.634 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.053 |
|
|
\[
{}r^{\prime \prime }-6 r^{\prime }+9 r = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.976 |
|
|
\[
{}2 x -y \sin \left (2 x \right ) = \left (\sin \left (x \right )^{2}-2 y\right ) y^{\prime }
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.767 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 10 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
19.058 |
|
|
\[
{}3 x^{3} y^{2} y^{\prime }-x^{2} y^{3} = 1
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.098 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.680 |
|
|
\[
{}y^{\prime }-2 y-y^{2} {\mathrm e}^{3 x} = 0
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.793 |
|
|
\[
{}u \left (1-v \right )+v^{2} \left (1-u\right ) u^{\prime } = 0
\] |
[_separable] |
✓ |
1.655 |
|
|
\[
{}y+2 x -x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.641 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 4 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.915 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 26 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
13.431 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.374 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 6 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.150 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.118 |
|
|
\[
{}\left (y+2 x \right ) y^{\prime }-x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.547 |
|
|
\[
{}\left (x \cos \left (y\right )-{\mathrm e}^{-\sin \left (y\right )}\right ) y^{\prime }+1 = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.448 |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime }+\sin \left (x \right )^{2}+\left (x +y\right ) \sin \left (2 x \right ) = 0
\] |
[_linear] |
✓ |
5.441 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
43.627 |
|
|
\[
{}y^{\prime }+x y = \frac {x}{y}
\] |
[_separable] |
✓ |
2.124 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+13 y^{\prime \prime }-18 y^{\prime }+36 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}\sin \left (\theta \right ) \cos \left (\theta \right ) r^{\prime }-\sin \left (\theta \right )^{2} = r \cos \left (\theta \right )^{2}
\] |
[_linear] |
✓ |
3.382 |
|
|
\[
{}x \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right ) = y y^{\prime }
\] |
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.098 |
|
|
\[
{}3 x^{2} y+x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.646 |
|
|
\[
{}-y+x y^{\prime } = x^{2}
\] |
[_linear] |
✓ |
1.845 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 6
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.525 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2}+4 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.654 |
|
|
\[
{}x y^{\prime } = x y+y
\] |
[_separable] |
✓ |
0.401 |
|
|
\[
{}x y^{\prime } = x y+y
\] |
[_separable] |
✓ |
1.664 |
|
|
\[
{}y^{\prime } = 3 x^{2} y
\] |
[_separable] |
✓ |
0.435 |
|
|
\[
{}y^{\prime } = 3 x^{2} y
\] |
[_separable] |
✓ |
1.641 |
|
|
\[
{}x y^{\prime } = y
\] |
[_separable] |
✓ |
0.269 |
|
|
\[
{}x y^{\prime } = y
\] |
[_separable] |
✓ |
1.610 |
|
|
\[
{}y^{\prime \prime } = -4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.378 |
|
|
\[
{}y^{\prime \prime } = -4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.175 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.362 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.005 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.487 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.935 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.602 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.021 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.702 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.961 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.275 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.034 |
|
|
\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.357 |
|
|
\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.579 |
|
|
\[
{}y^{\prime }-\sin \left (x +y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.266 |
|
|
\[
{}y^{\prime } = 4 y^{2}-3 y+1
\] |
[_quadrature] |
✓ |
1.442 |
|
|
\[
{}s^{\prime } = t \ln \left (s^{2 t}\right )+8 t^{2}
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.081 |
|
|
\[
{}y^{\prime } = \frac {y \,{\mathrm e}^{x +y}}{x^{2}+2}
\] |
[_separable] |
✓ |
2.053 |
|
|
\[
{}\left (x y^{2}+3 y^{2}\right ) y^{\prime }-2 x = 0
\] |
[_separable] |
✓ |
2.108 |
|
|
\[
{}s^{2}+s^{\prime } = \frac {s+1}{s t}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
0.962 |
|
|
\[
{}x y^{\prime } = \frac {1}{y^{3}}
\] |
[_separable] |
✓ |
3.823 |
|
|
\[
{}x^{\prime } = 3 x t^{2}
\] |
[_separable] |
✓ |
1.678 |
|
|
\[
{}x^{\prime } = \frac {t \,{\mathrm e}^{-t -2 x}}{x}
\] |
[_separable] |
✓ |
1.701 |
|
|
\[
{}y^{\prime } = \frac {x}{y^{2} \sqrt {x +1}}
\] |
[_separable] |
✓ |
2.416 |
|
|
\[
{}x v^{\prime } = \frac {1-4 v^{2}}{3 v}
\] |
[_separable] |
✓ |
5.043 |
|
|
\[
{}y^{\prime } = \frac {\sec \left (y\right )^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
2.823 |
|
|
\[
{}y^{\prime } = 3 x^{2} \left (1+y^{2}\right )^{{3}/{2}}
\] |
[_separable] |
✓ |
108.181 |
|
|
\[
{}x^{\prime }-x^{3} = x
\] |
[_quadrature] |
✓ |
5.010 |
|
|
\[
{}x +x y^{2}+{\mathrm e}^{x^{2}} y y^{\prime } = 0
\] |
[_separable] |
✓ |
2.895 |
|
|
\[
{}\frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right ) = 0
\] |
[_separable] |
✓ |
2.552 |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right )
\] |
[_separable] |
✓ |
3.900 |
|
|
\[
{}y^{\prime } = x^{3} \left (1-y\right )
\] |
[_separable] |
✓ |
1.836 |
|
|
\[
{}\frac {y^{\prime }}{2} = \sqrt {y+1}\, \cos \left (x \right )
\] |
[_separable] |
✓ |
2.579 |
|
|
\[
{}x^{2} y^{\prime } = \frac {4 x^{2}-x -2}{\left (x +1\right ) \left (y+1\right )}
\] |
[_separable] |
✓ |
5.376 |
|
|
\[
{}\frac {y^{\prime }}{\theta } = \frac {y \sin \left (\theta \right )}{y^{2}+1}
\] |
[_separable] |
✓ |
4.131 |
|
|
\[
{}x^{2}+2 y y^{\prime } = 0
\] |
[_separable] |
✓ |
11.428 |
|
|
\[
{}y^{\prime } = 2 t \cos \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.033 |
|
|
\[
{}y^{\prime } = 8 x^{3} {\mathrm e}^{-2 y}
\] |
[_separable] |
✓ |
2.548 |
|
|
\[
{}y^{\prime } = x^{2} \left (y+1\right )
\] |
[_separable] |
✓ |
1.963 |
|
|
\[
{}\sqrt {y}+\left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.592 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.769 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x^{2}}}{y^{2}}
\] |
[_separable] |
✓ |
3.842 |
|
|
\[
{}y^{\prime } = \sqrt {\sin \left (x \right )+1}\, \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
81.429 |
|
|
\[
{}y^{\prime } = 2 y-2 t y
\] |
[_separable] |
✓ |
3.052 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
2.469 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
2.318 |
|
|
\[
{}y^{\prime } = \left (x -3\right ) \left (y+1\right )^{{2}/{3}}
\] |
[_separable] |
✓ |
7.220 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
3.519 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
3.776 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
3.788 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
3.856 |
|
|
\[
{}y^{\prime } = y^{2}-3 y+2
\] |
[_quadrature] |
✓ |
2.462 |
|
|
\[
{}x^{2} y^{\prime }+\sin \left (x \right )-y = 0
\] |
[_linear] |
✓ |
1.906 |
|
|
\[
{}x^{\prime }+t x = {\mathrm e}^{x}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.149 |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime } = t y-y
\] |
[_separable] |
✓ |
2.121 |
|
|
\[
{}3 t = {\mathrm e}^{t} y^{\prime }+y \ln \left (t \right )
\] |
[_linear] |
✓ |
4.354 |
|
|
\[
{}x x^{\prime }+x t^{2} = \sin \left (t \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.802 |
|
|
\[
{}3 r = r^{\prime }-\theta ^{3}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.634 |
|
|
\[
{}y^{\prime }-y-{\mathrm e}^{3 x} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
1.335 |
|