|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
1.082 |
|
|
\[
{}y^{\prime \prime } = -4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.486 |
|
|
\[
{}y^{\prime \prime } = -4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.753 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.471 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.723 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.553 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.713 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.786 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.089 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.894 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.101 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.441 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.303 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.504 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.698 |
|
|
\[
{}y^{\prime }-\sin \left (x +y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.076 |
|
|
\[
{}y^{\prime } = 4 y^{2}-3 y+1
\] |
[_quadrature] |
✓ |
0.480 |
|
|
\[
{}s^{\prime } = t \ln \left (s^{2 t}\right )+8 t^{2}
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.658 |
|
|
\[
{}y^{\prime } = \frac {y \,{\mathrm e}^{x +y}}{x^{2}+2}
\] |
[_separable] |
✓ |
1.669 |
|
|
\[
{}\left (x y^{2}+3 y^{2}\right ) y^{\prime }-2 x = 0
\] |
[_separable] |
✓ |
1.409 |
|
|
\[
{}s^{2}+s^{\prime } = \frac {s+1}{s t}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
0.587 |
|
|
\[
{}y^{\prime } x = \frac {1}{y^{3}}
\] |
[_separable] |
✓ |
1.660 |
|
|
\[
{}x^{\prime } = 3 x t^{2}
\] |
[_separable] |
✓ |
1.042 |
|
|
\[
{}x^{\prime } = \frac {t \,{\mathrm e}^{-t -2 x}}{x}
\] |
[_separable] |
✓ |
1.272 |
|
|
\[
{}y^{\prime } = \frac {x}{y^{2} \sqrt {x +1}}
\] |
[_separable] |
✓ |
1.671 |
|
|
\[
{}x v^{\prime } = \frac {1-4 v^{2}}{3 v}
\] |
[_separable] |
✓ |
3.795 |
|
|
\[
{}y^{\prime } = \frac {\sec \left (y\right )^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
2.130 |
|
|
\[
{}y^{\prime } = 3 x^{2} \left (1+y^{2}\right )^{{3}/{2}}
\] |
[_separable] |
✓ |
94.988 |
|
|
\[
{}x^{\prime }-x^{3} = x
\] |
[_quadrature] |
✓ |
1.535 |
|
|
\[
{}x +x y^{2}+{\mathrm e}^{x^{2}} y y^{\prime } = 0
\] |
[_separable] |
✓ |
2.028 |
|
|
\[
{}\frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right ) = 0
\] |
[_separable] |
✓ |
2.080 |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right )
\] |
[_separable] |
✓ |
3.143 |
|
|
\[
{}y^{\prime } = x^{3} \left (1-y\right )
\] |
[_separable] |
✓ |
1.302 |
|
|
\[
{}\frac {y^{\prime }}{2} = \sqrt {1+y}\, \cos \left (x \right )
\] |
[_separable] |
✓ |
1.947 |
|
|
\[
{}x^{2} y^{\prime } = \frac {4 x^{2}-x -2}{\left (x +1\right ) \left (1+y\right )}
\] |
[_separable] |
✓ |
1.550 |
|
|
\[
{}\frac {y^{\prime }}{\theta } = \frac {y \sin \left (\theta \right )}{y^{2}+1}
\] |
[_separable] |
✓ |
3.867 |
|
|
\[
{}x^{2}+2 y y^{\prime } = 0
\] |
[_separable] |
✓ |
3.229 |
|
|
\[
{}y^{\prime } = 2 t \cos \left (y\right )^{2}
\] |
[_separable] |
✓ |
1.465 |
|
|
\[
{}y^{\prime } = 8 x^{3} {\mathrm e}^{-2 y}
\] |
[_separable] |
✓ |
1.837 |
|
|
\[
{}y^{\prime } = x^{2} \left (1+y\right )
\] |
[_separable] |
✓ |
1.281 |
|
|
\[
{}\sqrt {y}+\left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.715 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.421 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x^{2}}}{y^{2}}
\] |
[_separable] |
✓ |
1.123 |
|
|
\[
{}y^{\prime } = \sqrt {1+\sin \left (x \right )}\, \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
20.115 |
|
|
\[
{}y^{\prime } = 2 y-2 t y
\] |
[_separable] |
✓ |
1.463 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
0.694 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
0.621 |
|
|
\[
{}y^{\prime } = \left (x -3\right ) \left (1+y\right )^{{2}/{3}}
\] |
[_separable] |
✓ |
5.654 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
1.890 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
1.946 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
1.961 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
1.943 |
|
|
\[
{}y^{\prime } = y^{2}-3 y+2
\] |
[_quadrature] |
✓ |
0.813 |
|
|
\[
{}x^{2} y^{\prime }+\sin \left (x \right )-y = 0
\] |
[_linear] |
✓ |
1.819 |
|
|
\[
{}x^{\prime }+x t = {\mathrm e}^{x}
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.474 |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime } = t y-y
\] |
[_separable] |
✓ |
1.355 |
|
|
\[
{}3 t = {\mathrm e}^{t} y^{\prime }+y \ln \left (t \right )
\] |
[_linear] |
✓ |
6.832 |
|
|
\[
{}x x^{\prime }+x t^{2} = \sin \left (t \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.090 |
|
|
\[
{}3 r = r^{\prime }-\theta ^{3}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.179 |
|
|
\[
{}y^{\prime }-y-{\mathrm e}^{3 x} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
0.933 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+2 x +1
\] |
[_linear] |
✓ |
0.898 |
|
|
\[
{}r^{\prime }+r \tan \left (\theta \right ) = \sec \left (\theta \right )
\] |
[_linear] |
✓ |
1.299 |
|
|
\[
{}y^{\prime } x +2 y = \frac {1}{x^{3}}
\] |
[_linear] |
✓ |
1.097 |
|
|
\[
{}t +y+1-y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
0.863 |
|
|
\[
{}y^{\prime } = x^{2} {\mathrm e}^{-4 x}-4 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.365 |
|
|
\[
{}y x^{\prime }+2 x = 5 y^{3}
\] |
[_linear] |
✓ |
1.222 |
|
|
\[
{}y^{\prime } x +3 y+3 x^{2} = \frac {\sin \left (x \right )}{x}
\] |
[_linear] |
✓ |
1.563 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y x -x = 0
\] |
[_separable] |
✓ |
1.149 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x^{2} y = \left (x +1\right ) \sqrt {-x^{2}+1}
\] |
[_linear] |
✓ |
2.981 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x \,{\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.222 |
|
|
\[
{}y^{\prime }+4 y-{\mathrm e}^{-x} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
1.186 |
|
|
\[
{}t^{2} x^{\prime }+3 x t = t^{4} \ln \left (t \right )+1
\] |
[_linear] |
✓ |
1.422 |
|
|
\[
{}y^{\prime }+\frac {3 y}{x}+2 = 3 x
\] |
[_linear] |
✓ |
1.354 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y \sin \left (x \right ) = 2 x \cos \left (x \right )^{2}
\] |
[_linear] |
✓ |
3.486 |
|
|
\[
{}\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = x \sin \left (x \right )
\] |
[_linear] |
✓ |
2.435 |
|
|
\[
{}y^{\prime }+y \sqrt {1+\sin \left (x \right )^{2}} = x
\] |
[_linear] |
✓ |
9.162 |
|
|
\[
{}\left ({\mathrm e}^{4 y}+2 x \right ) y^{\prime }-1 = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
4.026 |
|
|
\[
{}y^{\prime }+2 y = \frac {x}{y^{2}}
\] |
[_rational, _Bernoulli] |
✓ |
1.306 |
|
|
\[
{}y^{\prime }+\frac {3 y}{x} = x^{2}
\] |
[_linear] |
✓ |
1.209 |
|
|
\[
{}x^{\prime } = \alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x
\] |
[[_linear, ‘class A‘]] |
✓ |
1.690 |
|
|
\[
{}u^{\prime } = \alpha \left (1-u\right )-\beta u
\] |
[_quadrature] |
✓ |
0.490 |
|
|
\[
{}x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime } = 0
\] |
[_linear] |
✓ |
1.146 |
|
|
\[
{}x^{{10}/{3}}-2 y+y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.247 |
|
|
\[
{}\sqrt {-2 y-y^{2}}+\left (-x^{2}+2 x +3\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.826 |
|
|
\[
{}y \,{\mathrm e}^{y x}+2 x +\left (x \,{\mathrm e}^{y x}-2 y\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.256 |
|
|
\[
{}y^{\prime }+y x = 0
\] |
[_separable] |
✓ |
0.182 |
|
|
\[
{}y^{2}+\left (2 y x +\cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
0.231 |
|
|
\[
{}2 x +y \cos \left (y x \right )+\left (x \cos \left (y x \right )-2 y\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.276 |
|
|
\[
{}\theta r^{\prime }+3 r-\theta -1 = 0
\] |
[_linear] |
✓ |
0.186 |
|
|
\[
{}2 y x +3+\left (x^{2}-1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
0.159 |
|
|
\[
{}2 x +y+\left (x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.287 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )-3 x^{2}+\left ({\mathrm e}^{x} \cos \left (y\right )+\frac {1}{3 y^{{2}/{3}}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.365 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )+2 x -\left (\sin \left (x \right ) \sin \left (y\right )+2 y\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
10.079 |
|
|
\[
{}{\mathrm e}^{t} \left (y-t \right )+\left (1+{\mathrm e}^{t}\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
0.182 |
|
|
\[
{}\frac {t y^{\prime }}{y}+1+\ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
0.249 |
|
|
\[
{}\cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta } = 0
\] |
[_linear] |
✓ |
0.186 |
|
|
\[
{}y \,{\mathrm e}^{y x}-\frac {1}{y}+\left (x \,{\mathrm e}^{y x}+\frac {x}{y^{2}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.250 |
|
|
\[
{}\frac {1}{y}-\left (3 y-\frac {x}{y^{2}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
0.177 |
|
|
\[
{}2 x +y^{2}-\cos \left (x +y\right )+\left (2 y x -\cos \left (x +y\right )-{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
66.511 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x +y}}{-1+y}
\] |
[_separable] |
✓ |
1.388 |
|