|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime }+4 y = 8
\] |
[_quadrature] |
✓ |
0.580 |
|
|
\[
{}y^{\prime }+y x = 4 x
\] |
[_separable] |
✓ |
1.253 |
|
|
\[
{}y^{\prime }+4 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.908 |
|
|
\[
{}y^{\prime } = y x -3 x -2 y+6
\] |
[_separable] |
✓ |
1.067 |
|
|
\[
{}y^{\prime } = \sin \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.038 |
|
|
\[
{}y y^{\prime } = {\mathrm e}^{x -3 y^{2}}
\] |
[_separable] |
✓ |
1.399 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
2.631 |
|
|
\[
{}y^{\prime } = y^{2}+9
\] |
[_quadrature] |
✓ |
0.473 |
|
|
\[
{}x y y^{\prime } = y^{2}+9
\] |
[_separable] |
✓ |
2.226 |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
1.677 |
|
|
\[
{}\cos \left (y\right ) y^{\prime } = \sin \left (x \right )
\] |
[_separable] |
✓ |
1.909 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x -3 y}
\] |
[_separable] |
✓ |
1.603 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
3.328 |
|
|
\[
{}y^{\prime } = 2 x -1+2 y x -y
\] |
[_separable] |
✓ |
1.321 |
|
|
\[
{}y y^{\prime } = x y^{2}+x
\] |
[_separable] |
✓ |
1.497 |
|
|
\[
{}y y^{\prime } = 3 \sqrt {x y^{2}+9 x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.177 |
|
|
\[
{}y^{\prime } = y x -4 x
\] |
[_separable] |
✓ |
0.947 |
|
|
\[
{}y^{\prime }-4 y = 2
\] |
[_quadrature] |
✓ |
0.375 |
|
|
\[
{}y y^{\prime } = x y^{2}-9 x
\] |
[_separable] |
✓ |
1.590 |
|
|
\[
{}y^{\prime } = \sin \left (y\right )
\] |
[_quadrature] |
✓ |
0.632 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x +y^{2}}
\] |
[_separable] |
✓ |
1.081 |
|
|
\[
{}y^{\prime } = 200 y-2 y^{2}
\] |
[_quadrature] |
✓ |
0.841 |
|
|
\[
{}y^{\prime } = y x -4 x
\] |
[_separable] |
✓ |
0.993 |
|
|
\[
{}y^{\prime } = y x -3 x -2 y+6
\] |
[_separable] |
✓ |
1.080 |
|
|
\[
{}y^{\prime } = 3 y^{2}-y^{2} \sin \left (x \right )
\] |
[_separable] |
✓ |
1.813 |
|
|
\[
{}y^{\prime } = \tan \left (y\right )
\] |
[_quadrature] |
✓ |
0.519 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.116 |
|
|
\[
{}y^{\prime } = \frac {6 x^{2}+4}{3 y^{2}-4 y}
\] |
[_separable] |
✓ |
1.329 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
1.732 |
|
|
\[
{}\left (-1+y^{2}\right ) y^{\prime } = 4 x y^{2}
\] |
[_separable] |
✓ |
3.197 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-y}
\] |
[_quadrature] |
✓ |
0.403 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-y}+1
\] |
[_quadrature] |
✓ |
0.668 |
|
|
\[
{}y^{\prime } = 3 x y^{3}
\] |
[_separable] |
✓ |
1.669 |
|
|
\[
{}y^{\prime } = \frac {2+\sqrt {x}}{2+\sqrt {y}}
\] |
[_separable] |
✓ |
1.569 |
|
|
\[
{}y^{\prime }-3 x^{2} y^{2} = -3 x^{2}
\] |
[_separable] |
✓ |
1.747 |
|
|
\[
{}y^{\prime }-3 x^{2} y^{2} = 3 x^{2}
\] |
[_separable] |
✓ |
1.806 |
|
|
\[
{}y^{\prime } = 200 y-2 y^{2}
\] |
[_quadrature] |
✓ |
0.887 |
|
|
\[
{}y^{\prime }-2 y = -10
\] |
[_quadrature] |
✓ |
0.589 |
|
|
\[
{}y y^{\prime } = \sin \left (x \right )
\] |
[_separable] |
✓ |
1.421 |
|
|
\[
{}y^{\prime } = 2 x -1+2 y x -y
\] |
[_separable] |
✓ |
1.291 |
|
|
\[
{}y^{\prime } x = y^{2}-y
\] |
[_separable] |
✓ |
2.015 |
|
|
\[
{}y^{\prime } x = y^{2}-y
\] |
[_separable] |
✓ |
1.935 |
|
|
\[
{}y^{\prime } = \frac {-1+y^{2}}{y x}
\] |
[_separable] |
✓ |
2.716 |
|
|
\[
{}\left (-1+y^{2}\right ) y^{\prime } = 4 y x
\] |
[_separable] |
✓ |
1.760 |
|
|
\[
{}x^{2} y^{\prime }+3 x^{2} y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.575 |
|
|
\[
{}y^{2} y^{\prime }+3 x^{2} y = \sin \left (x \right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.502 |
|
|
\[
{}y^{\prime }-x y^{2} = \sqrt {x}
\] |
[_Riccati] |
✓ |
1.608 |
|
|
\[
{}y^{\prime } = 1+\left (y x +3 y\right )^{2}
\] |
[_Riccati] |
✓ |
1.910 |
|
|
\[
{}y^{\prime } = 1+y x +3 y
\] |
[_linear] |
✓ |
1.037 |
|
|
\[
{}y^{\prime } = 4 y+8
\] |
[_quadrature] |
✓ |
0.387 |
|
|
\[
{}y^{\prime }-{\mathrm e}^{2 x} = 0
\] |
[_quadrature] |
✓ |
0.263 |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
1.263 |
|
|
\[
{}y^{\prime }+4 y = y^{3}
\] |
[_quadrature] |
✓ |
1.060 |
|
|
\[
{}y^{\prime } x +\cos \left (x^{2}\right ) = 827 y
\] |
[_linear] |
✓ |
2.012 |
|
|
\[
{}y^{\prime }+2 y = 6
\] |
[_quadrature] |
✓ |
0.573 |
|
|
\[
{}y^{\prime }+2 y = 20 \,{\mathrm e}^{3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.984 |
|
|
\[
{}y^{\prime } = 4 y+16 x
\] |
[[_linear, ‘class A‘]] |
✓ |
0.857 |
|
|
\[
{}y^{\prime }-2 y x = x
\] |
[_separable] |
✓ |
0.982 |
|
|
\[
{}y^{\prime } x +3 y-10 x^{2} = 0
\] |
[_linear] |
✓ |
1.206 |
|
|
\[
{}x^{2} y^{\prime }+2 y x = \sin \left (x \right )
\] |
[_linear] |
✓ |
1.160 |
|
|
\[
{}y^{\prime } x = \sqrt {x}+3 y
\] |
[_linear] |
✓ |
1.297 |
|
|
\[
{}y^{\prime } \cos \left (x \right )+y \sin \left (x \right ) = \cos \left (x \right )^{2}
\] |
[_linear] |
✓ |
2.505 |
|
|
\[
{}y^{\prime } x +\left (5 x +2\right ) y = \frac {20}{x}
\] |
[_linear] |
✓ |
2.159 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime }+y = 2 x \,{\mathrm e}^{-\sqrt {x}}
\] |
[_linear] |
✓ |
3.557 |
|
|
\[
{}y^{\prime }-3 y = 6
\] |
[_quadrature] |
✓ |
0.625 |
|
|
\[
{}y^{\prime }-3 y = 6
\] |
[_quadrature] |
✓ |
0.438 |
|
|
\[
{}y^{\prime }+5 y = {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.211 |
|
|
\[
{}3 y+y^{\prime } x = 20 x^{2}
\] |
[_linear] |
✓ |
1.531 |
|
|
\[
{}y^{\prime } x = y+x^{2} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.450 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (3+3 x^{2}-y\right )
\] |
[_linear] |
✓ |
3.912 |
|
|
\[
{}y^{\prime }+6 y x = \sin \left (x \right )
\] |
[_linear] |
✓ |
1.486 |
|
|
\[
{}x^{2} y^{\prime }+y x = \sqrt {x}\, \sin \left (x \right )
\] |
[_linear] |
✓ |
1.842 |
|
|
\[
{}-y+y^{\prime } x = x^{2} {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
1.384 |
|
|
\[
{}y^{\prime } = \frac {1}{\left (3 x +3 y+2\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
5.211 |
|
|
\[
{}y^{\prime } = \frac {\left (3 x -2 y\right )^{2}+1}{3 x -2 y}+\frac {3}{2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
10.772 |
|
|
\[
{}\cos \left (-4 y+8 x -3\right ) y^{\prime } = 2+2 \cos \left (-4 y+8 x -3\right )
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
147.949 |
|
|
\[
{}y^{\prime } = 1+\left (-x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
2.734 |
|
|
\[
{}x^{2} y^{\prime }-y x = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.877 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\frac {x}{y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.238 |
|
|
\[
{}\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right ) = 1+\sin \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.867 |
|
|
\[
{}y^{\prime } = \frac {x -y}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.519 |
|
|
\[
{}y^{\prime }+3 y = 3 y^{3}
\] |
[_quadrature] |
✓ |
1.138 |
|
|
\[
{}y^{\prime }-\frac {3 y}{x} = \frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.651 |
|
|
\[
{}y^{\prime }+3 \cot \left (x \right ) y = 6 \cos \left (x \right ) y^{{2}/{3}}
\] |
[_Bernoulli] |
✓ |
3.525 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = \frac {1}{y}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.466 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\frac {x^{2}}{y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.375 |
|
|
\[
{}3 y^{\prime } = -2+\sqrt {2 x +3 y+4}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.279 |
|
|
\[
{}3 y^{\prime }+\frac {2 y}{x} = 4 \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.355 |
|
|
\[
{}y^{\prime } = 4+\frac {1}{\sin \left (4 x -y\right )}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
72.263 |
|
|
\[
{}\left (-x +y\right ) y^{\prime } = 1
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.177 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.082 |
|
|
\[
{}\left (2 y x +2 x^{2}\right ) y^{\prime } = x^{2}+2 y x +2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
69.645 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x^{2} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.264 |
|
|
\[
{}y^{\prime } = 2 \sqrt {2 x +y-3}-2
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.155 |
|
|
\[
{}y^{\prime } = 2 \sqrt {2 x +y-3}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.374 |
|
|
\[
{}-y+y^{\prime } x = \sqrt {y x +x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
7.698 |
|
|
\[
{}y^{\prime }+3 y = \frac {28 \,{\mathrm e}^{2 x}}{y^{3}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
2.551 |
|
|
\[
{}y^{\prime } = \left (x -y+3\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
3.119 |
|
|
\[
{}y^{\prime }+2 x = 2 \sqrt {y+x^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.948 |
|
|
\[
{}\cos \left (y\right ) y^{\prime } = {\mathrm e}^{-x}-\sin \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.058 |
|