|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 1-\cot \left (y\right )
\] |
[_quadrature] |
✓ |
1.110 |
|
|
\[
{}y^{\prime } = \left (3 x -y\right )^{{1}/{3}}-1
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.900 |
|
|
\[
{}y^{\prime } = \sin \left (x y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.465 |
|
|
\[
{}y^{\prime } x +y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.255 |
|
|
\[
{}2 y+y^{\prime } = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.092 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x y = 2 x
\] |
[_separable] |
✓ |
1.305 |
|
|
\[
{}y^{\prime } = x +1
\] |
[_quadrature] |
✓ |
0.286 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.897 |
|
|
\[
{}y^{\prime } = y-x
\] |
[[_linear, ‘class A‘]] |
✓ |
0.927 |
|
|
\[
{}y^{\prime } = \frac {x}{2}-y+\frac {3}{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.081 |
|
|
\[
{}y^{\prime } = \left (-1+y\right )^{2}
\] |
[_quadrature] |
✓ |
0.430 |
|
|
\[
{}y^{\prime } = x \left (-1+y\right )
\] |
[_separable] |
✓ |
1.151 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.337 |
|
|
\[
{}y^{\prime } = \cos \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.186 |
|
|
\[
{}y^{\prime } = y-x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.957 |
|
|
\[
{}y^{\prime } = x^{2}+2 x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.002 |
|
|
\[
{}y^{\prime } = \frac {1+y}{x -1}
\] |
[_separable] |
✓ |
1.430 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.414 |
|
|
\[
{}y^{\prime } = 1-x
\] |
[_quadrature] |
✓ |
0.322 |
|
|
\[
{}y^{\prime } = 2 x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.922 |
|
|
\[
{}y^{\prime } = y+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.957 |
|
|
\[
{}y^{\prime } = -\frac {y}{x}
\] |
[_separable] |
✓ |
1.406 |
|
|
\[
{}y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.597 |
|
|
\[
{}y^{\prime } = \frac {1}{x}
\] |
[_quadrature] |
✓ |
0.308 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
0.642 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.407 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
2.306 |
|
|
\[
{}y^{\prime } = x +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
16.418 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.180 |
|
|
\[
{}y^{\prime } = 2 y-2 x^{2}-3
\] |
[[_linear, ‘class A‘]] |
✓ |
1.871 |
|
|
\[
{}y^{\prime } x = 2 x -y
\] |
[_linear] |
✓ |
2.157 |
|
|
\[
{}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.747 |
|
|
\[
{}x y^{\prime } y+1+y^{2} = 0
\] |
[_separable] |
✓ |
2.580 |
|
|
\[
{}y^{\prime } \sin \left (x \right )-\cos \left (x \right ) y = 0
\] |
[_separable] |
✓ |
1.979 |
|
|
\[
{}1+y^{2} = y^{\prime } x
\] |
[_separable] |
✓ |
1.654 |
|
|
\[
{}y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}} = 0
\] |
[_separable] |
✓ |
2.707 |
|
|
\[
{}x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
2.637 |
|
|
\[
{}{\mathrm e}^{-y} y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.678 |
|
|
\[
{}y \ln \left (y\right )+y^{\prime } x = 1
\] |
[_separable] |
✓ |
2.641 |
|
|
\[
{}y^{\prime } = a^{x +y}
\] |
[_separable] |
✓ |
2.616 |
|
|
\[
{}{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right ) = 0
\] |
[_separable] |
✓ |
3.118 |
|
|
\[
{}2 x \sqrt {1-y^{2}} = \left (x^{2}+1\right ) y^{\prime }
\] |
[_separable] |
✓ |
2.547 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )^{3}+\left ({\mathrm e}^{2 x}+1\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
4.190 |
|
|
\[
{}\sin \left (x \right ) y^{2}+\cos \left (x \right )^{2} \ln \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.358 |
|
|
\[
{}y^{\prime } = \sin \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.975 |
|
|
\[
{}y^{\prime } = a x +b y+c
\] |
[[_linear, ‘class A‘]] |
✓ |
0.996 |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
12.774 |
|
|
\[
{}y^{\prime } x +y = a \left (x y+1\right )
\] |
[_linear] |
✓ |
1.183 |
|
|
\[
{}a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
4.159 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.348 |
|
|
\[
{}\cos \left (y^{\prime }\right ) = 0
\] |
[_quadrature] |
✓ |
1.145 |
|
|
\[
{}{\mathrm e}^{y^{\prime }} = 1
\] |
[_quadrature] |
✓ |
0.447 |
|
|
\[
{}\sin \left (y^{\prime }\right ) = x
\] |
[_quadrature] |
✓ |
0.344 |
|
|
\[
{}\ln \left (y^{\prime }\right ) = x
\] |
[_quadrature] |
✓ |
0.464 |
|
|
\[
{}\tan \left (y^{\prime }\right ) = 0
\] |
[_quadrature] |
✓ |
0.444 |
|
|
\[
{}{\mathrm e}^{y^{\prime }} = x
\] |
[_quadrature] |
✓ |
0.337 |
|
|
\[
{}\tan \left (y^{\prime }\right ) = x
\] |
[_quadrature] |
✓ |
0.419 |
|
|
\[
{}x^{2} y^{\prime } \cos \left (y\right )+1 = 0
\] |
[_separable] |
✗ |
2.336 |
|
|
\[
{}x^{2} y^{\prime }+\cos \left (2 y\right ) = 1
\] |
[_separable] |
✗ |
2.968 |
|
|
\[
{}x^{3} y^{\prime }-\sin \left (y\right ) = 1
\] |
[_separable] |
✓ |
2.929 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2} = 0
\] |
[_separable] |
✓ |
3.309 |
|
|
\[
{}{\mathrm e}^{y} = {\mathrm e}^{4 y} y^{\prime }+1
\] |
[_quadrature] |
✓ |
1.940 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = -1+y
\] |
[_separable] |
✓ |
1.515 |
|
|
\[
{}y^{\prime } = 2 x \left (\pi +y\right )
\] |
[_separable] |
✓ |
1.091 |
|
|
\[
{}x^{2} y^{\prime }+\sin \left (2 y\right ) = 1
\] |
[_separable] |
✗ |
8.095 |
|
|
\[
{}y^{\prime } x = y+x \cos \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.515 |
|
|
\[
{}x -y+y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.384 |
|
|
\[
{}y^{\prime } x = y \left (\ln \left (y\right )-\ln \left (x \right )\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.620 |
|
|
\[
{}x^{2} y^{\prime } = x^{2}-x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.619 |
|
|
\[
{}y^{\prime } x = y+\sqrt {y^{2}-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.931 |
|
|
\[
{}2 x^{2} y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.708 |
|
|
\[
{}4 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.980 |
|
|
\[
{}y-x +\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.641 |
|
|
\[
{}x +y-2+\left (1-x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.187 |
|
|
\[
{}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.016 |
|
|
\[
{}x +y-2+\left (x -y+4\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.245 |
|
|
\[
{}x +y+\left (x -y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.241 |
|
|
\[
{}2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.886 |
|
|
\[
{}8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.981 |
|
|
\[
{}x -2 y-1+\left (3 x -6 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.233 |
|
|
\[
{}x +y+\left (x +y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.581 |
|
|
\[
{}2 x \left (x -y^{2}\right ) y^{\prime }+y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.009 |
|
|
\[
{}4 y^{6}+x^{3} = 6 x y^{5} y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.981 |
|
|
\[
{}y \left (1+\sqrt {x^{2} y^{4}+1}\right )+2 y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.967 |
|
|
\[
{}x +y^{3}+3 \left (y^{3}-x \right ) y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.955 |
|
|
\[
{}2 y+y^{\prime } = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.060 |
|
|
\[
{}x^{2}-y^{\prime } x = y
\] |
[_linear] |
✓ |
1.680 |
|
|
\[
{}y^{\prime }-2 x y = 2 x \,{\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
2.270 |
|
|
\[
{}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
1.387 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }-y \sin \left (x \right ) = 2 x
\] |
[_linear] |
✓ |
2.244 |
|
|
\[
{}y^{\prime } x -2 y = x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.597 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = \frac {1}{\cos \left (x \right )^{3}}
\] |
[_linear] |
✓ |
11.067 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }-y = 3 x^{3} \ln \left (x \right )^{2}
\] |
[_linear] |
✓ |
1.519 |
|
|
\[
{}\left (2 x -y^{2}\right ) y^{\prime } = 2 y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.008 |
|
|
\[
{}y^{\prime }+\cos \left (x \right ) y = \cos \left (x \right )
\] |
[_separable] |
✓ |
1.630 |
|
|
\[
{}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.601 |
|
|
\[
{}\left (\frac {{\mathrm e}^{-y^{2}}}{2}-x y\right ) y^{\prime }-1 = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.728 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 2 x \,{\mathrm e}^{{\mathrm e}^{x}}
\] |
[_linear] |
✓ |
1.455 |
|
|
\[
{}y^{\prime }+y x \,{\mathrm e}^{x} = {\mathrm e}^{{\mathrm e}^{x} \left (1-x \right )}
\] |
[_linear] |
✓ |
1.552 |
|
|
\[
{}y^{\prime }-y \ln \left (2\right ) = 2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.309 |
|