|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
0.318 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.399 |
|
|
\[
{}\cos \left (y\right )-\left (x \sin \left (y\right )-y^{2}\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
0.334 |
|
|
\[
{}x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.773 |
|
|
\[
{}x^{2}-x +y^{2}-\left ({\mathrm e}^{y}-2 x y\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.536 |
|
|
\[
{}2 x +y \cos \left (x \right )+\left (2 y+\sin \left (x \right )-\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.420 |
|
|
\[
{}x \sqrt {x^{2}+y^{2}}-\frac {x^{2} y y^{\prime }}{y-\sqrt {x^{2}+y^{2}}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
0.399 |
|
|
\[
{}4 x^{3}-\sin \left (x \right )+y^{3}-\left (y^{2}+1-3 x y^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.446 |
|
|
\[
{}{\mathrm e}^{x} \left (y^{3}+x y^{3}+1\right )+3 y^{2} \left (x \,{\mathrm e}^{x}-6\right ) y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
0.835 |
|
|
\[
{}\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.117 |
|
|
\[
{}y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.462 |
|
|
\[
{}y^{2}+y-y^{\prime } x = 0
\] |
[_separable] |
✓ |
0.298 |
|
|
\[
{}y \sec \left (x \right )+\sin \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
0.358 |
|
|
\[
{}{\mathrm e}^{x}-\sin \left (y\right )+\cos \left (y\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.380 |
|
|
\[
{}x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
0.338 |
|
|
\[
{}y^{3}+x y^{2}+y+\left (x^{3}+x^{2} y+x \right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
0.585 |
|
|
\[
{}3 y-y^{\prime } x = 0
\] |
[_separable] |
✓ |
0.299 |
|
|
\[
{}y-3 y^{\prime } x = 0
\] |
[_separable] |
✓ |
0.323 |
|
|
\[
{}y \left (2 x^{2} y^{3}+3\right )+x \left (x^{2} y^{3}-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.056 |
|
|
\[
{}2 x y+x^{2}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
0.353 |
|
|
\[
{}x^{2}+y \cos \left (x \right )+\left (y^{3}+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.335 |
|
|
\[
{}x^{2}+y^{2}+x +x y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
0.446 |
|
|
\[
{}x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.366 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.392 |
|
|
\[
{}x^{2}-y^{2}-y-\left (x^{2}-y^{2}-x \right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.566 |
|
|
\[
{}x^{4} y^{2}-y+\left (x^{2} y^{4}-x \right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
0.401 |
|
|
\[
{}y \left (2 x +y^{3}\right )-x \left (2 x -y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
0.398 |
|
|
\[
{}\arctan \left (x y\right )+\frac {x y-2 x y^{2}}{1+x^{2} y^{2}}+\frac {\left (x^{2}-2 x^{2} y\right ) y^{\prime }}{1+x^{2} y^{2}} = 0
\] |
[_exact] |
✓ |
0.513 |
|
|
\[
{}{\mathrm e}^{x} \left (x +1\right )+\left (y \,{\mathrm e}^{y}-x \,{\mathrm e}^{x}\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.421 |
|
|
\[
{}\frac {1+x y}{y}+\frac {\left (2 y-x \right ) y^{\prime }}{y^{2}} = 0
\] |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.437 |
|
|
\[
{}y^{2}-3 x y-2 x^{2}+\left (x y-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.533 |
|
|
\[
{}y \left (2 x +y+1\right )-x \left (x +2 y-1\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.473 |
|
|
\[
{}y \left (2 x -y-1\right )+x \left (2 y-x -1\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.461 |
|
|
\[
{}y^{2}+12 x^{2} y+\left (2 x y+4 x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.488 |
|
|
\[
{}3 \left (x +y\right )^{2}+x \left (2 x +3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.540 |
|
|
\[
{}y-\left (y^{2}+x^{2}+x \right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.217 |
|
|
\[
{}2 x y+\left (x^{2}+y^{2}+a \right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
0.203 |
|
|
\[
{}2 x y+x^{2}+b +\left (x^{2}+y^{2}+a \right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
0.227 |
|
|
\[
{}y^{\prime } x +y = x^{3}
\] |
[_linear] |
✓ |
1.599 |
|
|
\[
{}y^{\prime }+a y = b
\] |
[_quadrature] |
✓ |
0.694 |
|
|
\[
{}y^{\prime } x +y = y^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
2.102 |
|
|
\[
{}x^{\prime }+2 y x = {\mathrm e}^{-y^{2}}
\] |
[_linear] |
✓ |
1.624 |
|
|
\[
{}r^{\prime } = \left (r+{\mathrm e}^{-\theta }\right ) \tan \left (\theta \right )
\] |
[_linear] |
✓ |
1.924 |
|
|
\[
{}y^{\prime }-\frac {2 x y}{x^{2}+1} = 1
\] |
[_linear] |
✓ |
1.710 |
|
|
\[
{}y^{\prime }+y = x y^{3}
\] |
[_Bernoulli] |
✓ |
0.517 |
|
|
\[
{}\left (-x^{3}+1\right ) y^{\prime }-2 \left (x +1\right ) y = y^{{5}/{2}}
\] |
[_rational, _Bernoulli] |
✓ |
7.625 |
|
|
\[
{}\tan \left (\theta \right ) r^{\prime }-r = \tan \left (\theta \right )^{2}
\] |
[_linear] |
✓ |
1.720 |
|
|
\[
{}y^{\prime }+2 y = 3 \,{\mathrm e}^{-2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.247 |
|
|
\[
{}y^{\prime }+2 y = \frac {3 \,{\mathrm e}^{-2 x}}{4}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.390 |
|
|
\[
{}y^{\prime }+2 y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.408 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = {\mathrm e}^{2 x}
\] |
[_linear] |
✓ |
2.174 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
2.338 |
|
|
\[
{}y^{\prime } x +y = x \sin \left (x \right )
\] |
[_linear] |
✓ |
1.377 |
|
|
\[
{}-y+y^{\prime } x = x^{2} \sin \left (x \right )
\] |
[_linear] |
✓ |
1.514 |
|
|
\[
{}y^{\prime } x +x y^{2}-y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.132 |
|
|
\[
{}y^{\prime } x -y \left (2 y \ln \left (x \right )-1\right ) = 0
\] |
[_Bernoulli] |
✓ |
2.205 |
|
|
\[
{}x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.262 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.481 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \frac {y^{2}}{x}
\] |
[_separable] |
✓ |
3.310 |
|
|
\[
{}2 \cos \left (x \right ) y^{\prime } = y \sin \left (x \right )-y^{3}
\] |
[_Bernoulli] |
✓ |
15.018 |
|
|
\[
{}\left (x -\cos \left (y\right )\right ) y^{\prime }+\tan \left (y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
4.822 |
|
|
\[
{}y^{\prime } = x^{3}+\frac {2 y}{x}-\frac {y^{2}}{x}
\] |
[_rational, _Riccati] |
✓ |
1.529 |
|
|
\[
{}y^{\prime } = 2 \tan \left (x \right ) \sec \left (x \right )-y^{2} \sin \left (x \right )
\] |
[_Riccati] |
✓ |
4.276 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}}-\frac {y}{x}-y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
2.115 |
|
|
\[
{}y^{\prime } = 1+\frac {y}{x}-\frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.726 |
|
|
\[
{}2 x y y^{\prime }+\left (x +1\right ) y^{2} = {\mathrm e}^{x}
\] |
[_Bernoulli] |
✓ |
1.866 |
|
|
\[
{}\cos \left (y\right ) y^{\prime }+\sin \left (y\right ) = x^{2}
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.110 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-1-y = \left (x +1\right ) \sqrt {1+y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.959 |
|
|
\[
{}{\mathrm e}^{y} \left (1+y^{\prime }\right ) = {\mathrm e}^{x}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.638 |
|
|
\[
{}y^{\prime } \sin \left (y\right )+\sin \left (x \right ) \cos \left (y\right ) = \sin \left (x \right )
\] |
[_separable] |
✓ |
40.861 |
|
|
\[
{}\left (x -y\right )^{2} y^{\prime } = 4
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.636 |
|
|
\[
{}-y+y^{\prime } x = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.686 |
|
|
\[
{}\left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2 = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.627 |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.051 |
|
|
\[
{}y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.315 |
|
|
\[
{}x^{2} y+y^{2}+x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.077 |
|
|
\[
{}y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
35.582 |
|
|
\[
{}y^{\prime } = \left (x^{2}+2 y-1\right )^{{2}/{3}}-x
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.504 |
|
|
\[
{}y^{\prime } x +y = x^{2} \left (1+{\mathrm e}^{x}\right ) y^{2}
\] |
[_Bernoulli] |
✓ |
2.943 |
|
|
\[
{}2 y-x y \ln \left (x \right )-2 x \ln \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.023 |
|
|
\[
{}y^{\prime }+a y = k \,{\mathrm e}^{b x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.972 |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.840 |
|
|
\[
{}y^{\prime }+8 x^{3} y^{3}+2 x y = 0
\] |
[_Bernoulli] |
✓ |
1.314 |
|
|
\[
{}\left (x y \sqrt {x^{2}-y^{2}}+x \right ) y^{\prime } = y-x^{2} \sqrt {x^{2}-y^{2}}
\] |
[NONE] |
✗ |
50.216 |
|
|
\[
{}y^{\prime }+a y = b \sin \left (k x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.272 |
|
|
\[
{}y^{\prime } x -y^{2}+1 = 0
\] |
[_separable] |
✓ |
1.865 |
|
|
\[
{}\left (y^{2}+a \sin \left (x \right )\right ) y^{\prime } = \cos \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.926 |
|
|
\[
{}y^{\prime } x = x \,{\mathrm e}^{\frac {y}{x}}+x +y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
9.584 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = {\mathrm e}^{-\sin \left (x \right )}
\] |
[_linear] |
✓ |
1.700 |
|
|
\[
{}y^{\prime } x -y \left (\ln \left (x y\right )-1\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.906 |
|
|
\[
{}x^{3} y^{\prime }-y^{2}-x^{2} y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.154 |
|
|
\[
{}y^{\prime } x +a y+b \,x^{n} = 0
\] |
[_linear] |
✓ |
1.023 |
|
|
\[
{}y^{\prime } x -y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.863 |
|
|
\[
{}y^{2}-3 x y-2 x^{2}+\left (x y-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.878 |
|
|
\[
{}\left (6 x y+x^{2}+3\right ) y^{\prime }+3 y^{2}+2 x y+2 x = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.432 |
|
|
\[
{}x^{2} y^{\prime }+y^{2}+x y+x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.203 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y-\cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
2.642 |
|
|
\[
{}\left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1 = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.353 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+x y-3 x y^{2} = 0
\] |
[_separable] |
✓ |
2.881 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
2.391 |
|