|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.102 |
|
|
\[
{}x^{2} \left (2-x \right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.347 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.335 |
|
|
\[
{}x y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.343 |
|
|
\[
{}3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.354 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.345 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.351 |
|
|
\[
{}x^{2} y^{\prime }-x y = \frac {1}{x}
\] |
[_linear] |
✓ |
1.684 |
|
|
\[
{}x \ln \left (y\right ) y^{\prime }-y \ln \left (x \right ) = 0
\] |
[_separable] |
✓ |
1.479 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.080 |
|
|
\[
{}r^{\prime \prime }-6 r^{\prime }+9 r = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.224 |
|
|
\[
{}2 x -y \sin \left (2 x \right ) = \left (\sin \left (x \right )^{2}-2 y\right ) y^{\prime }
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.754 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 10 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.296 |
|
|
\[
{}3 x^{3} y^{2} y^{\prime }-x^{2} y^{3} = 1
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.968 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.839 |
|
|
\[
{}y^{\prime }-2 y-y^{2} {\mathrm e}^{3 x} = 0
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.527 |
|
|
\[
{}u \left (1-v \right )+v^{2} \left (1-u\right ) u^{\prime } = 0
\] |
[_separable] |
✓ |
1.606 |
|
|
\[
{}y+2 x -y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.552 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 4 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.133 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 26 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.697 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.536 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 6 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.401 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.276 |
|
|
\[
{}\left (y+2 x \right ) y^{\prime }-x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.004 |
|
|
\[
{}\left (x \cos \left (y\right )-{\mathrm e}^{-\sin \left (y\right )}\right ) y^{\prime }+1 = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.187 |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime }+\sin \left (x \right )^{2}+\left (x +y\right ) \sin \left (2 x \right ) = 0
\] |
[_linear] |
✓ |
4.606 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
32.594 |
|
|
\[
{}y^{\prime }+x y = \frac {x}{y}
\] |
[_separable] |
✓ |
1.827 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+13 y^{\prime \prime }-18 y^{\prime }+36 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.099 |
|
|
\[
{}\sin \left (\theta \right ) \cos \left (\theta \right ) r^{\prime }-\sin \left (\theta \right )^{2} = r \cos \left (\theta \right )^{2}
\] |
[_linear] |
✓ |
3.130 |
|
|
\[
{}x \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right ) = y y^{\prime }
\] |
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.796 |
|
|
\[
{}3 x^{2} y+x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.752 |
|
|
\[
{}-y+y^{\prime } x = x^{2}
\] |
[_linear] |
✓ |
1.948 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 6
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.806 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2}+4 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.936 |
|
|
\[
{}y^{\prime } x = x y+y
\] |
[_separable] |
✓ |
0.593 |
|
|
\[
{}y^{\prime } x = x y+y
\] |
[_separable] |
✓ |
1.552 |
|
|
\[
{}y^{\prime } = 3 x^{2} y
\] |
[_separable] |
✓ |
0.667 |
|
|
\[
{}y^{\prime } = 3 x^{2} y
\] |
[_separable] |
✓ |
1.615 |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
0.534 |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
1.652 |
|
|
\[
{}y^{\prime \prime } = -4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.617 |
|
|
\[
{}y^{\prime \prime } = -4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.330 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.601 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.292 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.680 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.211 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.846 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.380 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.901 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.167 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.464 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.223 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.589 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.710 |
|
|
\[
{}y^{\prime }-\sin \left (x +y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.608 |
|
|
\[
{}y^{\prime } = 4 y^{2}-3 y+1
\] |
[_quadrature] |
✓ |
1.333 |
|
|
\[
{}s^{\prime } = t \ln \left (s^{2 t}\right )+8 t^{2}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.813 |
|
|
\[
{}y^{\prime } = \frac {y \,{\mathrm e}^{x +y}}{x^{2}+2}
\] |
[_separable] |
✓ |
1.954 |
|
|
\[
{}\left (x y^{2}+3 y^{2}\right ) y^{\prime }-2 x = 0
\] |
[_separable] |
✓ |
1.877 |
|
|
\[
{}s^{2}+s^{\prime } = \frac {s+1}{s t}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
0.952 |
|
|
\[
{}y^{\prime } x = \frac {1}{y^{3}}
\] |
[_separable] |
✓ |
2.358 |
|
|
\[
{}x^{\prime } = 3 x t^{2}
\] |
[_separable] |
✓ |
1.625 |
|
|
\[
{}x^{\prime } = \frac {t \,{\mathrm e}^{-t -2 x}}{x}
\] |
[_separable] |
✓ |
1.603 |
|
|
\[
{}y^{\prime } = \frac {x}{y^{2} \sqrt {x +1}}
\] |
[_separable] |
✓ |
2.068 |
|
|
\[
{}x v^{\prime } = \frac {1-4 v^{2}}{3 v}
\] |
[_separable] |
✓ |
4.391 |
|
|
\[
{}y^{\prime } = \frac {\sec \left (y\right )^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
2.520 |
|
|
\[
{}y^{\prime } = 3 x^{2} \left (1+y^{2}\right )^{{3}/{2}}
\] |
[_separable] |
✓ |
105.077 |
|
|
\[
{}x^{\prime }-x^{3} = x
\] |
[_quadrature] |
✓ |
4.315 |
|
|
\[
{}x +x y^{2}+{\mathrm e}^{x^{2}} y y^{\prime } = 0
\] |
[_separable] |
✓ |
2.402 |
|
|
\[
{}\frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right ) = 0
\] |
[_separable] |
✓ |
2.416 |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right )
\] |
[_separable] |
✓ |
4.038 |
|
|
\[
{}y^{\prime } = x^{3} \left (1-y\right )
\] |
[_separable] |
✓ |
1.765 |
|
|
\[
{}\frac {y^{\prime }}{2} = \sqrt {1+y}\, \cos \left (x \right )
\] |
[_separable] |
✓ |
2.254 |
|
|
\[
{}x^{2} y^{\prime } = \frac {4 x^{2}-x -2}{\left (x +1\right ) \left (1+y\right )}
\] |
[_separable] |
✓ |
3.906 |
|
|
\[
{}\frac {y^{\prime }}{\theta } = \frac {y \sin \left (\theta \right )}{y^{2}+1}
\] |
[_separable] |
✓ |
3.844 |
|
|
\[
{}x^{2}+2 y y^{\prime } = 0
\] |
[_separable] |
✓ |
5.741 |
|
|
\[
{}y^{\prime } = 2 t \cos \left (y\right )^{2}
\] |
[_separable] |
✓ |
1.818 |
|
|
\[
{}y^{\prime } = 8 x^{3} {\mathrm e}^{-2 y}
\] |
[_separable] |
✓ |
2.420 |
|
|
\[
{}y^{\prime } = x^{2} \left (1+y\right )
\] |
[_separable] |
✓ |
1.843 |
|
|
\[
{}\sqrt {y}+\left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.943 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.726 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x^{2}}}{y^{2}}
\] |
[_separable] |
✓ |
3.047 |
|
|
\[
{}y^{\prime } = \sqrt {1+\sin \left (x \right )}\, \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
81.235 |
|
|
\[
{}y^{\prime } = 2 y-2 t y
\] |
[_separable] |
✓ |
2.168 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
1.790 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
2.016 |
|
|
\[
{}y^{\prime } = \left (x -3\right ) \left (1+y\right )^{{2}/{3}}
\] |
[_separable] |
✓ |
6.367 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
2.555 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
4.148 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
4.454 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
4.453 |
|
|
\[
{}y^{\prime } = y^{2}-3 y+2
\] |
[_quadrature] |
✓ |
1.933 |
|
|
\[
{}x^{2} y^{\prime }+\sin \left (x \right )-y = 0
\] |
[_linear] |
✓ |
2.091 |
|
|
\[
{}x^{\prime }+t x = {\mathrm e}^{x}
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.983 |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime } = t y-y
\] |
[_separable] |
✓ |
2.013 |
|
|
\[
{}3 t = {\mathrm e}^{t} y^{\prime }+y \ln \left (t \right )
\] |
[_linear] |
✓ |
4.582 |
|
|
\[
{}x x^{\prime }+x t^{2} = \sin \left (t \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.406 |
|
|
\[
{}3 r = r^{\prime }-\theta ^{3}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.562 |
|
|
\[
{}y^{\prime }-y-{\mathrm e}^{3 x} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
1.312 |
|