|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = y-x
\] |
[[_linear, ‘class A‘]] |
✓ |
1.537 |
|
|
\[
{}y^{\prime } = \frac {x}{2}-y+\frac {3}{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.653 |
|
|
\[
{}y^{\prime } = \left (y-1\right )^{2}
\] |
[_quadrature] |
✓ |
1.131 |
|
|
\[
{}y^{\prime } = \left (y-1\right ) x
\] |
[_separable] |
✓ |
1.528 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.217 |
|
|
\[
{}y^{\prime } = \cos \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.460 |
|
|
\[
{}y^{\prime } = y-x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.342 |
|
|
\[
{}y^{\prime } = x^{2}+2 x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.317 |
|
|
\[
{}y^{\prime } = \frac {y+1}{-1+x}
\] |
[_separable] |
✓ |
1.843 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
39.825 |
|
|
\[
{}y^{\prime } = 1-x
\] |
[_quadrature] |
✓ |
0.464 |
|
|
\[
{}y^{\prime } = 2 x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.258 |
|
|
\[
{}y^{\prime } = y+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.299 |
|
|
\[
{}y^{\prime } = -\frac {y}{x}
\] |
[_separable] |
✓ |
2.198 |
|
|
\[
{}y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.853 |
|
|
\[
{}y^{\prime } = \frac {1}{x}
\] |
[_quadrature] |
✓ |
0.430 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
1.574 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.954 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.540 |
|
|
\[
{}y^{\prime } = x +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
15.151 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.554 |
|
|
\[
{}y^{\prime } = 2 y-2 x^{2}-3
\] |
[[_linear, ‘class A‘]] |
✓ |
1.541 |
|
|
\[
{}x y^{\prime } = 2 x -y
\] |
[_linear] |
✓ |
3.442 |
|
|
\[
{}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.799 |
|
|
\[
{}1+y^{2}+x y y^{\prime } = 0
\] |
[_separable] |
✓ |
3.755 |
|
|
\[
{}\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
2.714 |
|
|
\[
{}1+y^{2} = x y^{\prime }
\] |
[_separable] |
✓ |
2.038 |
|
|
\[
{}x \sqrt {1+y^{2}}+y y^{\prime } \sqrt {x^{2}+1} = 0
\] |
[_separable] |
✓ |
5.135 |
|
|
\[
{}x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
13.860 |
|
|
\[
{}{\mathrm e}^{-y} y^{\prime } = 1
\] |
[_quadrature] |
✓ |
1.428 |
|
|
\[
{}y \ln \left (y\right )+x y^{\prime } = 1
\] |
[_separable] |
✓ |
1.766 |
|
|
\[
{}y^{\prime } = a^{x +y}
\] |
[_separable] |
✓ |
2.476 |
|
|
\[
{}{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right ) = 0
\] |
[_separable] |
✓ |
3.415 |
|
|
\[
{}2 x \sqrt {1-y^{2}} = \left (x^{2}+1\right ) y^{\prime }
\] |
[_separable] |
✓ |
7.696 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )^{3}+\left (1+{\mathrm e}^{2 x}\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
4.732 |
|
|
\[
{}y^{2} \sin \left (x \right )+\cos \left (x \right )^{2} \ln \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.877 |
|
|
\[
{}y^{\prime } = \sin \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.631 |
|
|
\[
{}y^{\prime } = a x +b y+c
\] |
[[_linear, ‘class A‘]] |
✓ |
0.845 |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
5.282 |
|
|
\[
{}x y^{\prime }+y = a \left (1+x y\right )
\] |
[_linear] |
✓ |
1.138 |
|
|
\[
{}a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
3.638 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.273 |
|
|
\[
{}\cos \left (y^{\prime }\right ) = 0
\] |
[_quadrature] |
✓ |
1.130 |
|
|
\[
{}{\mathrm e}^{y^{\prime }} = 1
\] |
[_quadrature] |
✓ |
0.591 |
|
|
\[
{}\sin \left (y^{\prime }\right ) = x
\] |
[_quadrature] |
✓ |
0.404 |
|
|
\[
{}\ln \left (y^{\prime }\right ) = x
\] |
[_quadrature] |
✓ |
0.490 |
|
|
\[
{}\tan \left (y^{\prime }\right ) = 0
\] |
[_quadrature] |
✓ |
0.598 |
|
|
\[
{}{\mathrm e}^{y^{\prime }} = x
\] |
[_quadrature] |
✓ |
0.405 |
|
|
\[
{}\tan \left (y^{\prime }\right ) = x
\] |
[_quadrature] |
✓ |
0.522 |
|
|
\[
{}x^{2} y^{\prime } \cos \left (y\right )+1 = 0
\] |
[_separable] |
✗ |
3.674 |
|
|
\[
{}x^{2} y^{\prime }+\cos \left (2 y\right ) = 1
\] |
[_separable] |
✗ |
4.326 |
|
|
\[
{}x^{3} y^{\prime }-\sin \left (y\right ) = 1
\] |
[_separable] |
✓ |
5.253 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2} = 0
\] |
[_separable] |
✓ |
16.628 |
|
|
\[
{}{\mathrm e}^{y} = {\mathrm e}^{4 y} y^{\prime }+1
\] |
[_quadrature] |
✓ |
2.669 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = y-1
\] |
[_separable] |
✓ |
1.944 |
|
|
\[
{}y^{\prime } = 2 x \left (\pi +y\right )
\] |
[_separable] |
✓ |
1.565 |
|
|
\[
{}x^{2} y^{\prime }+\sin \left (2 y\right ) = 1
\] |
[_separable] |
✗ |
16.709 |
|
|
\[
{}x y^{\prime } = y+x \cos \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.271 |
|
|
\[
{}x -y+x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.783 |
|
|
\[
{}x y^{\prime } = y \left (\ln \left (y\right )-\ln \left (x \right )\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.986 |
|
|
\[
{}x^{2} y^{\prime } = y^{2}-x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.293 |
|
|
\[
{}x y^{\prime } = y+\sqrt {y^{2}-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.702 |
|
|
\[
{}2 x^{2} y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.277 |
|
|
\[
{}4 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.710 |
|
|
\[
{}y-x +\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.352 |
|
|
\[
{}x +y-2+\left (1-x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.496 |
|
|
\[
{}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.567 |
|
|
\[
{}x +y-2+\left (x -y+4\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.445 |
|
|
\[
{}x +y+\left (x -y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.572 |
|
|
\[
{}2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.234 |
|
|
\[
{}8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.137 |
|
|
\[
{}x -2 y-1+\left (3 x -6 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.191 |
|
|
\[
{}x +y+\left (x +y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.898 |
|
|
\[
{}2 x y^{\prime } \left (x -y^{2}\right )+y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.092 |
|
|
\[
{}4 y^{6}+x^{3} = 6 x y^{5} y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.439 |
|
|
\[
{}y \left (1+\sqrt {x^{2} y^{4}+1}\right )+2 x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.343 |
|
|
\[
{}x +y^{3}+3 \left (y^{3}-x \right ) y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.734 |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.575 |
|
|
\[
{}x^{2}-x y^{\prime } = y
\] |
[_linear] |
✓ |
2.393 |
|
|
\[
{}y^{\prime }-2 x y = 2 x \,{\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
3.275 |
|
|
\[
{}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
2.091 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }-y \sin \left (x \right ) = 2 x
\] |
[_linear] |
✓ |
2.579 |
|
|
\[
{}x y^{\prime }-2 y = x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.960 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = \frac {1}{\cos \left (x \right )^{3}}
\] |
[_linear] |
✓ |
11.954 |
|
|
\[
{}y^{\prime } x \ln \left (x \right )-y = 3 x^{3} \ln \left (x \right )^{2}
\] |
[_linear] |
✓ |
1.548 |
|
|
\[
{}\left (2 x -y^{2}\right ) y^{\prime } = 2 y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.316 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \cos \left (x \right )
\] |
[_separable] |
✓ |
2.062 |
|
|
\[
{}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.731 |
|
|
\[
{}\left (\frac {{\mathrm e}^{-y^{2}}}{2}-x y\right ) y^{\prime }-1 = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.636 |
|
|
\[
{}y^{\prime }-y \,{\mathrm e}^{x} = 2 x \,{\mathrm e}^{{\mathrm e}^{x}}
\] |
[_linear] |
✓ |
1.734 |
|
|
\[
{}y^{\prime }+x y \,{\mathrm e}^{x} = {\mathrm e}^{\left (1-x \right ) {\mathrm e}^{x}}
\] |
[_linear] |
✓ |
1.654 |
|
|
\[
{}y^{\prime }-y \ln \left (2\right ) = 2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.614 |
|
|
\[
{}y^{\prime }-y = -2 \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.323 |
|
|
\[
{}\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = -\frac {\sin \left (x \right )^{2}}{x^{2}}
\] |
[_linear] |
✓ |
4.746 |
|
|
\[
{}x^{2} y^{\prime } \cos \left (\frac {1}{x}\right )-y \sin \left (\frac {1}{x}\right ) = -1
\] |
[_linear] |
✓ |
3.000 |
|
|
\[
{}2 x y^{\prime }-y = 1-\frac {2}{\sqrt {x}}
\] |
[_linear] |
✓ |
1.901 |
|
|
\[
{}x^{2} y^{\prime }+y = \left (x^{2}+1\right ) {\mathrm e}^{x}
\] |
[_linear] |
✓ |
2.369 |
|
|
\[
{}x y^{\prime }+y = 2 x
\] |
[_linear] |
✓ |
3.421 |
|
|
\[
{}\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 1
\] |
[_linear] |
✓ |
2.411 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }-y \sin \left (x \right ) = -\sin \left (2 x \right )
\] |
[_linear] |
✓ |
3.372 |
|