Number of problems in this table is 917
Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime } = 2 x^{2} y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.164 |
|
|
\[ {}y^{\prime } = x^{2}-y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.438 |
|
|
\[ {}2 x y^{2}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.578 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = \left (y+1\right )^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.967 |
|
|
\[ {}x^{2} y^{\prime } = 1-x^{2}+y^{2}-x^{2} y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.188 |
|
|
\[ {}y^{\prime } = 3 x^{2} \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.2 |
|
|
\[ {}y^{\prime } = 2 x y^{2}+3 x^{2} y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.709 |
|
|
\[ {}x^{2} y^{\prime } = x y+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.517 |
|
|
\[ {}y^{\prime } = \left (4 x +y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.915 |
|
|
\[ {}3 y^{2}+x y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.472 |
|
|
\[ {}x y+y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.591 |
|
|
\[ {}2 x y^{2}+x^{2} y^{\prime } = y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.87 |
|
|
\[ {}2 x y+x^{2} y^{\prime } = y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.942 |
|
|
\[ {}y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.974 |
|
|
\[ {}x^{2} y^{\prime } = x y+3 y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.075 |
|
|
\[ {}y^{\prime } = x^{2}-2 x y+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.438 |
|
|
\[ {}3 x^{5} y^{2}+x^{3} y^{\prime } = 2 y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.846 |
|
|
\[ {}9 x^{2} y^{2}+x^{\frac {3}{2}} y^{\prime } = y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.177 |
|
|
\[ {}\sin \left (x \right ) y^{2}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.796 |
|
|
\[ {}y^{\prime } = \left (1-2 x \right ) y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.166 |
|
|
\[ {}r^{\prime } = \frac {r^{2}}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.269 |
|
|
\[ {}y^{\prime } = \frac {x y^{2}}{\sqrt {x^{2}+1}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.391 |
|
|
\[ {}y^{\prime } = 2 y^{2}+x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.219 |
|
|
\[ {}y^{\prime } = 2 \left (1+x \right ) \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.824 |
|
|
\[ {}y^{\prime } = \frac {t \left (4-y\right ) y}{3} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.697 |
|
|
\[ {}y^{\prime } = \frac {t y \left (4-y\right )}{t +1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.964 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+x y+y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.453 |
|
|
\[ {}x^{2}+3 x y+y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.265 |
|
|
\[ {}y^{\prime } = 2 t y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.711 |
|
|
\[ {}y^{\prime } = t \left (3-y\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.431 |
|
|
\[ {}y^{\prime } = y \left (3-t y\right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.845 |
|
|
\[ {}y^{\prime } = -y \left (3-t y\right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.822 |
|
|
\[ {}y^{\prime } = t -1-y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.582 |
|
|
\[ {}y^{\prime } = 1+2 x +y^{2}+2 x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.109 |
|
|
\[ {}2 y^{\prime }+x \left (y^{2}-1\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.173 |
|
|
\[ {}y^{\prime } = x^{2} \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.995 |
|
|
\[ {}y^{\prime } = x \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.637 |
|
|
\[ {}y^{\prime } = -\frac {y \left (y+1\right )}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.308 |
|
|
\[ {}\frac {y^{\prime }}{\left (y+1\right )^{2}}-\frac {1}{x \left (y+1\right )} = -\frac {3}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
2.29 |
|
|
\[ {}x y^{\prime }+y^{2}+y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.447 |
|
|
\[ {}y^{\prime } = x^{2} \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.918 |
|
|
\[ {}y^{\prime } = \left (-1+x \right ) \left (y-1\right ) \left (y-2\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.982 |
|
|
\[ {}y^{\prime }+x \left (y^{2}+y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.972 |
|
|
\[ {}y^{\prime } \left (x^{2}+2\right ) = 4 x \left (y^{2}+2 y+1\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.424 |
|
|
\[ {}y^{\prime } = \frac {1+y^{2}}{x^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.064 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+y^{2}}{\sin \left (x \right )} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
10.874 |
|
|
\[ {}y^{\prime }-y = x y^{2} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.945 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}+x y-x^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.225 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}+x y-x^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
3.518 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.347 |
|
|
\[ {}x^{2} y^{\prime } = x^{2}+x y+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.52 |
|
|
\[ {}y^{\prime } = \frac {x y+y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.893 |
|
|
\[ {}y^{\prime } = \frac {y^{2}-3 x y-5 x^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
3.981 |
|
|
\[ {}x^{2} y^{\prime } = 2 x^{2}+y^{2}+4 x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
2.976 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}+x y-4 x^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
3.735 |
|
|
\[ {}x^{3} y^{\prime } = 2 y^{2}+2 x^{2} y-2 x^{4} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
3.026 |
|
|
\[ {}y^{\prime } = y^{2} {\mathrm e}^{-x}+4 y+2 \,{\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
1.691 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+y \tan \left (x \right )+\tan \left (x \right )^{2}}{\sin \left (x \right )^{2}} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
55.009 |
|
|
\[ {}x \ln \left (x \right )^{2} y^{\prime } = -4 \ln \left (x \right )^{2}+y \ln \left (x \right )+y^{2} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Riccati] |
✓ |
✓ |
2.782 |
|
|
\[ {}y^{\prime } = 1+x -\left (2 x +1\right ) y+x y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.421 |
|
|
\[ {}-y^{2}+x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.15 |
|
|
\[ {}3 x^{2} y^{2}+2 y+2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.291 |
|
|
\[ {}x^{2} \left (y^{\prime }+y^{2}\right )-x \left (2+x \right ) y+x +2 = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
2.291 |
|
|
\[ {}y^{\prime }+y^{2}+4 x y+4 x^{2}+2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.258 |
|
|
\[ {}\left (2 x +1\right ) \left (y^{\prime }+y^{2}\right )-2 y-2 x -3 = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
4.83 |
|
|
\[ {}\left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-\left (3 x +2\right ) y-6 x +8 = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
5.227 |
|
|
\[ {}x^{2} \left (y^{\prime }+y^{2}\right )+x y+x^{2}-\frac {1}{4} = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
2.25 |
|
|
\[ {}x^{2} \left (y^{\prime }+y^{2}\right )-7 x y+7 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
3.356 |
|
|
\[ {}\left (t^{2}+1\right ) y^{\prime } = 1+y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.366 |
|
|
\[ {}y^{\prime } = 1-t +y^{2}-t y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.581 |
|
|
\[ {}y^{\prime } = y^{2}+\cos \left (t^{2}\right ) \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
3.483 |
|
|
\[ {}y^{\prime } = 1+y+y^{2} \cos \left (t \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
26.26 |
|
|
\[ {}y^{\prime } = t +y^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
1.521 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
1.73 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
0.775 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
0.78 |
|
|
\[ {}y^{\prime } = \frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
14.143 |
|
|
\[ {}y^{\prime } = t^{2}+y^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
1.753 |
|
|
\[ {}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.349 |
|
|
\[ {}x y^{\prime }+y = y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.193 |
|
|
\[ {}x^{2} y^{\prime }+y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.876 |
|
|
\[ {}1+y^{2} = \frac {y^{\prime }}{x^{3} \left (-1+x \right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.212 |
|
|
\[ {}\left (x^{2}+x +1\right ) y^{\prime } = y^{2}+2 y+5 \] |
1 |
0 |
1 |
[_separable] |
✓ |
✓ |
22.352 |
|
|
\[ {}\left (x^{2}-2 x -8\right ) y^{\prime } = y^{2}+y-2 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
8.253 |
|
|
\[ {}x^{2} y+y^{2}+x^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.413 |
|
|
\[ {}y \left (y-x^{2}\right )+x^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.716 |
|
|
\[ {}{\mathrm e}^{x} y^{\prime } = 2 x y^{2}+{\mathrm e}^{x} y \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.677 |
|
|
\[ {}x^{2} y^{\prime }+y^{2} = x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.638 |
|
|
\[ {}x y^{\prime }+y = y^{2} x^{2} \cos \left (x \right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
3.555 |
|
|
\[ {}y^{\prime }+y = y^{2} {\mathrm e}^{-t} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
1.988 |
|
|
\[ {}y-x y^{\prime } = 2 y^{\prime }+2 y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.532 |
|
|
\[ {}x y-y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.412 |
|
|
\[ {}x^{\prime } = x+x^{2} {\mathrm e}^{\theta } \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
2.016 |
|
|
\[ {}4 x y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.096 |
|
|
\[ {}y^{\prime } = x^{2} y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.388 |
|
|
\[ {}x^{2} y^{\prime }+x y^{2} = 4 y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.536 |
|
|
\[ {}y^{\prime } = \frac {4 y^{2}}{x^{2}}-y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.487 |
|
|
\[ {}y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.181 |
|
|
\[ {}y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.727 |
|
|
\[ {}x y^{\prime }+y-\frac {y^{2}}{x^{\frac {3}{2}}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.586 |
|
|
\[ {}y^{\prime } = \frac {y^{2}}{x^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.513 |
|
|
\[ {}y^{\prime } = \frac {x \left (y^{2}-1\right )}{2 \left (-2+x \right ) \left (-1+x \right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.073 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.069 |
|
|
\[ {}y^{\prime } = \frac {\left (x +y\right )^{2}}{2 x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.915 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}+3 x y+x^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.714 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x} = 6 x^{4} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.689 |
|
|
\[ {}y^{\prime }+\frac {2 x y}{x^{2}+1} = x y^{2} \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.042 |
|
|
\[ {}y^{\prime } = \left (9 x -y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.585 |
|
|
\[ {}y^{\prime } = \left (4 x +y+2\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.72 |
|
|
\[ {}y^{\prime } = 2 x \left (x +y\right )^{2}-1 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
1.493 |
|
|
\[ {}y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2} = r \left (x \right ) \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
0.925 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x}-y^{2} = -\frac {2}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.568 |
|
|
\[ {}y^{\prime }+\frac {7 y}{x}-3 y^{2} = \frac {3}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
0.924 |
|
|
\[ {}x^{2} y^{\prime } = x \left (y-1\right )+\left (y-1\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
1.263 |
|
|
\[ {}\left (1+x \right ) y^{\prime }-x^{2} y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.686 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+y^{2}}{2 x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.107 |
|
|
\[ {}y^{\prime } = 6 x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.573 |
|
|
\[ {}-y^{2}+x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.083 |
|
|
\[ {}x y^{\prime } = 2 y \left (y-1\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.056 |
|
|
\[ {}2 x y^{\prime } = 1-y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.274 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x} \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.822 |
|
|
\[ {}x^{2} y^{\prime }-2 x y-2 y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.959 |
|
|
\[ {}y^{\prime } = \left (x +y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.807 |
|
|
\[ {}1 = \frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}} \] |
1 |
1 |
1 |
[_exact, _rational, _Riccati] |
✓ |
✓ |
1.38 |
|
|
\[ {}x y^{\prime } = x^{5}+x^{3} y^{2}+y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.711 |
|
|
\[ {}x y^{\prime } = y+x^{2}+9 y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.45 |
|
|
\[ {}y^{\prime } = \left (1+x \right )^{2}+\left (4 y+1\right )^{2}+8 x y+1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.57 |
|
|
\[ {}x^{2}+y+y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.753 |
|
|
\[ {}y^{\prime }+y^{2} = x^{2}+1 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
0.535 |
|
|
\[ {}y^{\prime } = x^{2}-y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.545 |
|
|
\[ {}y^{\prime }+f \left (x \right )^{2} = f^{\prime }\left (x \right )+y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
0.612 |
|
|
\[ {}y^{\prime }+1-x = y \left (x +y\right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.854 |
|
|
\[ {}y^{\prime } = \left (x +y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.727 |
|
|
\[ {}y^{\prime } = \left (x -y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.586 |
|
|
\[ {}y^{\prime } = 3-3 x +3 y+\left (x -y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.682 |
|
|
\[ {}y^{\prime } = 2 x -\left (x^{2}+1\right ) y+y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.368 |
|
|
\[ {}y^{\prime } = x \left (x^{3}+2\right )-\left (2 x^{2}-y\right ) y \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
0.895 |
|
|
\[ {}y^{\prime } = 1+x \left (-x^{3}+2\right )+\left (2 x^{2}-y\right ) y \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
1.597 |
|
|
\[ {}y^{\prime } = \cos \left (x \right )-\left (\sin \left (x \right )-y\right ) y \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.085 |
|
|
\[ {}y^{\prime } = \cos \left (2 x \right )+\left (\sin \left (2 x \right )+y\right ) y \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
8.227 |
|
|
\[ {}y^{\prime } = f \left (x \right )+x f \left (x \right ) y+y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.501 |
|
|
\[ {}y^{\prime } = \left (3+x -4 y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.947 |
|
|
\[ {}y^{\prime } = \left (1+4 x +9 y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.922 |
|
|
\[ {}y^{\prime } = 3 a +3 b x +3 b y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.067 |
|
|
\[ {}y^{\prime } = x a +b y^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
1.648 |
|
|
\[ {}y^{\prime } = a +b x +c y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.926 |
|
|
\[ {}y^{\prime } = a \,x^{n -1}+b \,x^{2 n}+c y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
64.083 |
|
|
\[ {}y^{\prime } = x^{2} a +b y^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
1.826 |
|
|
\[ {}y^{\prime } = f \left (x \right )+a y+b y^{2} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
0.623 |
|
|
\[ {}y^{\prime } = 1+a \left (x -y\right ) y \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.647 |
|
|
\[ {}y^{\prime } = f \left (x \right )+g \left (x \right ) y+a y^{2} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
0.804 |
|
|
\[ {}y^{\prime } = x y \left (3+y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.513 |
|
|
\[ {}y^{\prime } = 1-x -x^{3}+\left (2 x^{2}+1\right ) y-x y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.721 |
|
|
\[ {}y^{\prime } = x \left (2+x^{2} y-y^{2}\right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.99 |
|
|
\[ {}y^{\prime } = x +\left (1-2 x \right ) y-\left (1-x \right ) y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.438 |
|
|
\[ {}y^{\prime } = a x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.592 |
|
|
\[ {}y^{\prime } = x^{n} \left (a +b y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.323 |
|
|
\[ {}y^{\prime } = a \,x^{m}+b \,x^{n} y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.122 |
|
|
\[ {}y^{\prime } = \left (a +b y \cos \left (k x \right )\right ) y \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.233 |
|
|
\[ {}y^{\prime }+4 \csc \left (x \right ) = \left (3-\cot \left (x \right )\right ) y+\sin \left (x \right ) y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
9.078 |
|
|
\[ {}y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.99 |
|
|
\[ {}y^{\prime } = f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{2} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
1.212 |
|
|
\[ {}y^{\prime } = \left (a +b y+c y^{2}\right ) f \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.484 |
|
|
\[ {}x y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
0.814 |
|
|
\[ {}x y^{\prime } = x^{2}+y \left (y+1\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.05 |
|
|
\[ {}x y^{\prime }-y+y^{2} = x^{\frac {2}{3}} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
6.918 |
|
|
\[ {}x y^{\prime } = a +b y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.995 |
|
|
\[ {}x y^{\prime } = x^{2} a +y+b y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.128 |
|
|
\[ {}x y^{\prime } = a \,x^{2 n}+\left (n +b y\right ) y \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.394 |
|
|
\[ {}x y^{\prime } = a \,x^{n}+b y+c y^{2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.53 |
|
|
\[ {}x y^{\prime } = k +a \,x^{n}+b y+c y^{2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.668 |
|
|
\[ {}x y^{\prime }+a +x y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
0.944 |
|
|
\[ {}x y^{\prime }+\left (1-x y\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.727 |
|
|
\[ {}x y^{\prime } = \left (1-x y\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.707 |
|
|
\[ {}x y^{\prime } = \left (1+x y\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.716 |
|
|
\[ {}x y^{\prime } = a \,x^{3} \left (1-x y\right ) y \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.191 |
|
|
\[ {}x y^{\prime } = x^{3}+\left (2 x^{2}+1\right ) y+x y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.095 |
|
|
\[ {}x y^{\prime } = y \left (1+2 x y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.711 |
|
|
\[ {}x y^{\prime }+b x +\left (2+a x y\right ) y = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.043 |
|
|
\[ {}x y^{\prime }+\operatorname {a0} +\operatorname {a1} x +\left (\operatorname {a2} +\operatorname {a3} x y\right ) y = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
3.273 |
|
|
\[ {}x y^{\prime }+a \,x^{2} y^{2}+2 y = b \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.247 |
|
|
\[ {}x y^{\prime }+x^{m}+\frac {\left (n -m \right ) y}{2}+x^{n} y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.462 |
|
|
\[ {}x y^{\prime }+\left (a +b \,x^{n} y\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.899 |
|
|
\[ {}x y^{\prime } = a \,x^{m}-b y-c \,x^{n} y^{2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.053 |
|
|
\[ {}x y^{\prime } = 2 x -y+a \,x^{n} \left (x -y\right )^{2} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
1.286 |
|
|
\[ {}x y^{\prime }+\left (1-a y \ln \left (x \right )\right ) y = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.99 |
|
|
\[ {}x y^{\prime } = y+\left (x^{2}-y^{2}\right ) f \left (x \right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
1.607 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = a y+b x y^{2} \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.895 |
|
|
\[ {}\left (x +a \right ) y^{\prime } = y \left (1-a y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.45 |
|
|
\[ {}2 x y^{\prime }+1 = 4 i x y+y^{2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.587 |
|
|
\[ {}3 x y^{\prime } = 3 x^{\frac {2}{3}}+\left (-3 y+1\right ) y \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.006 |
|
|
\[ {}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.688 |
|
|
\[ {}x^{2} y^{\prime } = \left (1+2 x -y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
1.639 |
|
|
\[ {}x^{2} y^{\prime } = a +b y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.772 |
|
|
\[ {}x^{2} y^{\prime } = \left (a y+x \right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.651 |
|
|
\[ {}x^{2} y^{\prime } = \left (x a +b y\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.786 |
|
|
\[ {}x^{2} y^{\prime }+x^{2} a +b x y+c y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.764 |
|
|
\[ {}x^{2} y^{\prime } = a +b \,x^{n}+x^{2} y^{2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.918 |
|
|
\[ {}x^{2} y^{\prime }+2+x y \left (4+x y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.003 |
|
|
\[ {}x^{2} y^{\prime }+2+a x \left (1-x y\right )-x^{2} y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.275 |
|
|
\[ {}x^{2} y^{\prime } = a +b \,x^{2} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
1.735 |
|
|
\[ {}x^{2} y^{\prime } = a +b \,x^{n}+c \,x^{2} y^{2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.972 |
|
|
\[ {}x^{2} y^{\prime } = a +b x y+c \,x^{2} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
2.024 |
|
|
\[ {}x^{2} y^{\prime } = a +b x y+c \,x^{4} y^{2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.576 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.555 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = 1-y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.515 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = 1-\left (2 x -y\right ) y \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.006 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = n \left (1-2 x y+y^{2}\right ) \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.596 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.104 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = x y \left (1+a y\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.698 |
|
|
\[ {}\left (-x^{2}+4\right ) y^{\prime }+4 y = \left (2+x \right ) y^{2} \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.651 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right ) = 0 \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.622 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime } = a^{2}+3 x y-2 y^{2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
3.102 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime }+x y+b x y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.346 |
|
|
\[ {}x \left (x +a \right ) y^{\prime } = \left (b +c y\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.375 |
|
|
\[ {}\left (x -a \right )^{2} y^{\prime }+k \left (x +y-a \right )^{2}+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
1.631 |
|
|
\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime } = c y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.829 |
|
|
\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.154 |
|
|
\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
2.243 |
|
|
\[ {}2 x^{2} y^{\prime }+1+2 x y-x^{2} y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
0.979 |
|
|
\[ {}2 x^{2} y^{\prime } = 2 x y+\left (1-x \cot \left (x \right )\right ) \left (x^{2}-y^{2}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
1.714 |
|
|
\[ {}x \left (1-2 x \right ) y^{\prime } = 4 x -\left (1+4 x \right ) y+y^{2} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.909 |
|
|
\[ {}2 x \left (1-x \right ) y^{\prime }+x +\left (1-x \right ) y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.364 |
|
|
\[ {}a \,x^{2} y^{\prime } = x^{2}+a x y+b^{2} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.956 |
|
|
\[ {}\left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.681 |
|
|
\[ {}x^{3} y^{\prime } = x^{4}+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
0.602 |
|
|
\[ {}x^{3} y^{\prime } = y \left (y+x^{2}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.691 |
|
|
\[ {}x^{3} y^{\prime } = x^{2} \left (y-1\right )+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.47 |
|
|
\[ {}x^{3} y^{\prime } = \left (1+x \right ) y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.538 |
|
|
\[ {}x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.165 |
|
|
\[ {}x^{3} y^{\prime }+3+\left (3-2 x \right ) x^{2} y-x^{6} y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.024 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime }+x^{2}+\left (-x^{2}+1\right ) y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.477 |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime } = \left (2-x \right ) x y-y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.813 |
|
|
\[ {}x \left (c \,x^{2}+b x +a \right ) y^{\prime }+x^{2}-\left (c \,x^{2}+b x +a \right ) y = y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.576 |
|
|
\[ {}x^{4} y^{\prime } = \left (x^{3}+y\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.574 |
|
|
\[ {}x^{4} y^{\prime }+a^{2}+x^{4} y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
1.111 |
|
|
\[ {}\left (-x^{4}+1\right ) y^{\prime } = 2 x \left (1-y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.381 |
|
|
\[ {}x \left (-x^{3}+1\right ) y^{\prime } = x^{2}+\left (1-2 x y\right ) y \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.112 |
|
|
\[ {}x^{2} \left (-x^{2}+1\right ) y^{\prime } = \left (x -3 x^{3} y\right ) y \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
0.868 |
|
|
\[ {}\left (c \,x^{2}+b x +a \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
3.77 |
|
|
\[ {}x \left (-x^{4}+1\right ) y^{\prime } = 2 x \left (x^{2}-y^{2}\right )+\left (-x^{4}+1\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.354 |
|
|
\[ {}x^{n} y^{\prime } = x^{2 n -1}-y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.288 |
|
|
\[ {}x^{n} y^{\prime }+x^{2 n -2}+y^{2}+\left (-n +1\right ) x^{n -1} = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
12.794 |
|
|
\[ {}x^{n} y^{\prime } = a^{2} x^{2 n -2}+b^{2} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
3.025 |
|
|
\[ {}x^{n} y^{\prime } = x^{n -1} \left (a \,x^{2 n}+n y-b y^{2}\right ) \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.429 |
|
|
\[ {}y^{\prime } \sqrt {-x^{2}+1} = 1+y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.656 |
|
|
\[ {}x^{\frac {3}{2}} y^{\prime } = a +b \,x^{\frac {3}{2}} y^{2} \] |
1 |
1 |
1 |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
1.547 |
|
|
\[ {}y^{\prime } \left (a +\cos \left (\frac {x}{2}\right )^{2}\right ) = y \tan \left (\frac {x}{2}\right ) \left (1+a +\cos \left (\frac {x}{2}\right )^{2}-y\right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
10.263 |
|
|
\[ {}y+x y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.744 |
|
|
\[ {}\left (-x^{2}+1\right ) z^{\prime }-x z = a x z^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.239 |
|
|
\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.004 |
|
|
\[ {}\frac {x^{n} y^{\prime }}{b y^{2}-c \,x^{2 a}}-\frac {a y x^{a -1}}{b y^{2}-c \,x^{2 a}}+x^{a -1} = 0 \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
40.685 |
|
|
\[ {}x y^{\prime }-a y+y^{2} = x^{-2 a} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
0.6 |
|
|
\[ {}x y^{\prime }-a y+y^{2} = x^{-\frac {2 a}{3}} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.211 |
|
|
\[ {}u^{\prime }+u^{2} = \frac {c}{x^{\frac {4}{3}}} \] |
1 |
1 |
1 |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
0.856 |
|
|
\[ {}u^{\prime }+b u^{2} = \frac {c}{x^{4}} \] |
1 |
1 |
1 |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
0.313 |
|
|
\[ {}u^{\prime }-u^{2} = \frac {2}{x^{\frac {8}{3}}} \] |
1 |
1 |
1 |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
1.391 |
|
|
\[ {}x y-y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.472 |
|
|
\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.133 |
|
|
\[ {}x y^{\prime }+x y^{2}-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.94 |
|
|
\[ {}x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right ) = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.199 |
|
|
\[ {}x^{2} \left (-1+x \right ) y^{\prime }-y^{2}-x \left (-2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.212 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = \frac {y^{2}}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.67 |
|
|
\[ {}y^{\prime } = x^{3}+\frac {2 y}{x}-\frac {y^{2}}{x} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.318 |
|
|
\[ {}y^{\prime } = 2 \tan \left (x \right ) \sec \left (x \right )-\sin \left (x \right ) y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.563 |
|
|
\[ {}y^{\prime } = \frac {1}{x^{2}}-\frac {y}{x}-y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
2.769 |
|
|
\[ {}y^{\prime } = 1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
3.303 |
|
|
\[ {}x^{2} y+y^{2}+x^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.845 |
|
|
\[ {}x y^{\prime }+y = x^{2} \left (1+{\mathrm e}^{x}\right ) y^{2} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.166 |
|
|
\[ {}y^{\prime } = \left (x +y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.852 |
|
|
\[ {}x y^{\prime }-y^{2}+1 = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.028 |
|
|
\[ {}x^{3} y^{\prime }-y^{2}-x^{2} y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.043 |
|
|
\[ {}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.434 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+x y-3 x y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
6.486 |
|
|
\[ {}y^{\prime } = a x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.365 |
|
|
\[ {}y^{\prime } = \frac {1+y^{2}}{x^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.748 |
|
|
\[ {}y^{\prime }+y^{2} = \frac {a^{2}}{x^{4}} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.376 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.135 |
|
|
\[ {}y^{\prime } = x y^{2}-\frac {2 y}{x}-\frac {1}{x^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.128 |
|
|
\[ {}y^{\prime } = \frac {2 y^{2}}{x}+\frac {y}{x}-2 x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.372 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{-x} y^{2}+y-{\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
0.921 |
|
|
\[ {}y^{\prime }-2 y-y^{2} {\mathrm e}^{3 x} = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
0.631 |
|
|
\[ {}\frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.726 |
|
|
\[ {}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.17 |
|
|
\[ {}y^{\prime } = \sqrt {\sin \left (x \right )+1}\, \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
76.019 |
|
|
\[ {}y^{\prime }+x y = x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.536 |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime } = 1+y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.693 |
|
|
\[ {}x y^{\prime }+3 y = x^{2} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.606 |
|
|
\[ {}y^{\prime }-\cot \left (x \right ) y = y^{2} \sec \left (x \right )^{2} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
2.363 |
|
|
\[ {}y^{\prime }+x +x y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.891 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = x y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.179 |
|
|
\[ {}y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.185 |
|
|
\[ {}y^{2}+x y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
28.431 |
|
|
\[ {}y^{\prime } = -2 \left (2 x +3 y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.867 |
|
|
\[ {}y \left (x -2 y\right )-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.345 |
|
|
\[ {}y+y^{\prime } = y^{2} {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
0.582 |
|
|
\[ {}y^{\prime } = \left (1+x +y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.776 |
|
|
\[ {}y^{\prime } = x^{2} \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.74 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.875 |
|
|
\[ {}y^{\prime } = -\frac {2}{t}+\frac {y}{t}+\frac {y^{2}}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.951 |
|
|
\[ {}y^{\prime } = -\frac {y}{t}-1-y^{2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.099 |
|
|
\[ {}\phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right ) = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.227 |
|
|
\[ {}\left (\phi ^{\prime }-\frac {\phi ^{2}}{2}\right ) \sin \left (\theta \right )^{2}-\phi \sin \left (\theta \right ) \cos \left (\theta \right ) = \frac {\cos \left (2 \theta \right )}{2}+1 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
3.698 |
|
|
\[ {}-y+x y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.256 |
|
|
\[ {}y^{\prime } = x^{2} y^{2}-4 x^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.866 |
|
|
\[ {}y^{\prime } = \frac {\left (x +y-1\right )^{2}}{2 \left (2+x \right )^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
2.06 |
|
|
\[ {}x y^{\prime } = y+x^{2}+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.287 |
|
|
\[ {}x y^{\prime }+y = x y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.415 |
|
|
\[ {}\frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}} = 1 \] |
1 |
1 |
1 |
[_exact, _rational, _Riccati] |
✓ |
✓ |
2.265 |
|
|
\[ {}\frac {x y^{\prime }+y}{1-x^{2} y^{2}}+x = 0 \] |
1 |
1 |
1 |
[_exact, _rational, _Riccati] |
✓ |
✓ |
2.368 |
|
|
\[ {}y^{\prime } = -x +y^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
10.51 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.919 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x} = 6 x^{4} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.166 |
|
|
\[ {}y^{\prime } = \frac {5 x^{2}-x y+y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
2.058 |
|
|
\[ {}x y^{\prime }-2 y+b y^{2} = c \,x^{4} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.987 |
|
|
\[ {}x y^{\prime }-y+y^{2} = x^{\frac {2}{3}} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
22.616 |
|
|
\[ {}u^{\prime }+u^{2} = \frac {1}{x^{\frac {4}{5}}} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
0.265 |
|
|
\[ {}y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
1.315 |
|
|
\[ {}y^{\prime } = x^{2}+y^{2}-1 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.411 |
|
|
\[ {}y^{\prime }-y^{2}-x -x^{2} = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
9.154 |
|
|
\[ {}y^{\prime } = x a +b y^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
2.091 |
|
|
\[ {}c y^{\prime } = x a +b y^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
2.31 |
|
|
\[ {}c y^{\prime } = \frac {x a +b y^{2}}{r} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
2.399 |
|
|
\[ {}c y^{\prime } = \frac {x a +b y^{2}}{r x} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.359 |
|
|
\[ {}c y^{\prime } = \frac {x a +b y^{2}}{r \,x^{2}} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.62 |
|
|
\[ {}y^{\prime } = \sin \left (x \right )+y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
6.935 |
|
|
\[ {}y^{\prime } = \cos \left (x \right )+\frac {y^{2}}{x} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
6.023 |
|
|
\[ {}y^{\prime } = x +y+b y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.653 |
|
|
\[ {}y^{\prime } = x -y^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
1.388 |
|
|
\[ {}y^{\prime }+y^{2}-x a -b = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.892 |
|
|
\[ {}y^{\prime }+y^{2}+a \,x^{m} = 0 \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
2.517 |
|
|
\[ {}y^{\prime }+y^{2}-2 x^{2} y+x^{4}-2 x -1 = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
1.682 |
|
|
\[ {}y^{\prime }+y^{2}+\left (x y-1\right ) f \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.187 |
|
|
\[ {}y^{\prime }-y^{2}-x y-x +1 = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.724 |
|
|
\[ {}y^{\prime }-\left (x +y\right )^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.865 |
|
|
\[ {}y^{\prime }-y^{2}+\left (x^{2}+1\right ) y-2 x = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.007 |
|
|
\[ {}y^{\prime }-y^{2}+y \sin \left (x \right )-\cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.408 |
|
|
\[ {}y^{\prime }-y^{2}-y \sin \left (2 x \right )-\cos \left (2 x \right ) = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
8.329 |
|
|
\[ {}y^{\prime }+a y^{2}-b \,x^{\nu } = 0 \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
2.557 |
|
|
\[ {}y^{\prime }+a y^{2}-b \,x^{2 \nu }-c \,x^{\nu -1} = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
37.242 |
|
|
\[ {}y^{\prime }+a y \left (y-x \right )-1 = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.786 |
|
|
\[ {}y^{\prime }+x y^{2}-x^{3} y-2 x = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.886 |
|
|
\[ {}y^{\prime }-x y^{2}-3 x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.435 |
|
|
\[ {}y^{\prime }+x^{-a -1} y^{2}-x^{a} = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.22 |
|
|
\[ {}y^{\prime }-a \,x^{n} \left (1+y^{2}\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.48 |
|
|
\[ {}y^{\prime }+\sin \left (x \right ) y^{2}-\frac {2 \sin \left (x \right )}{\cos \left (x \right )^{2}} = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
6.928 |
|
|
\[ {}y^{\prime }-\frac {y^{2} f^{\prime }\left (x \right )}{g \left (x \right )}+\frac {g^{\prime }\left (x \right )}{f \left (x \right )} = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.881 |
|
|
\[ {}y^{\prime }+f \left (x \right ) y^{2}+g \left (x \right ) y = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.957 |
|
|
\[ {}y^{\prime }+f \left (x \right ) \left (y^{2}+2 a y+b \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.998 |
|
|
\[ {}2 y^{\prime }-3 y^{2}-4 a y-b -c \,{\mathrm e}^{-2 x a} = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.635 |
|
|
\[ {}x y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.49 |
|
|
\[ {}x y^{\prime }-y^{2}+1 = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.039 |
|
|
\[ {}x y^{\prime }+a y^{2}-y+b \,x^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.899 |
|
|
\[ {}x y^{\prime }+a y^{2}-b y+c \,x^{2 b} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.335 |
|
|
\[ {}x y^{\prime }+a y^{2}-b y-c \,x^{\beta } = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.734 |
|
|
\[ {}x y^{\prime }+x y^{2}+a = 0 \] |
1 |
1 |
1 |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
1.539 |
|
|
\[ {}x y^{\prime }+x y^{2}-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.065 |
|
|
\[ {}x y^{\prime }+x y^{2}-y-a \,x^{3} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
3.173 |
|
|
\[ {}x y^{\prime }+x y^{2}-\left (2 x^{2}+1\right ) y-x^{3} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
3.859 |
|
|
\[ {}x y^{\prime }+a x y^{2}+2 y+b x = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.866 |
|
|
\[ {}x y^{\prime }+a x y^{2}+b y+c x +d = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
6.303 |
|
|
\[ {}x y^{\prime }+x^{a} y^{2}+\frac {\left (-b +a \right ) y}{2}+x^{b} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.518 |
|
|
\[ {}x y^{\prime }+a \,x^{\alpha } y^{2}+b y-c \,x^{\beta } = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
4.059 |
|
|
\[ {}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.306 |
|
|
\[ {}x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right ) = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.316 |
|
|
\[ {}x y^{\prime }+f \left (x \right ) \left (-x^{2}+y^{2}\right ) = 0 \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
1.879 |
|
|
\[ {}\left (1+x \right ) y^{\prime }+y \left (y-x \right ) = 0 \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.158 |
|
|
\[ {}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.293 |
|
|
\[ {}x^{2} y^{\prime }-y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.117 |
|
|
\[ {}x^{2} y^{\prime }-y^{2}-x y-x^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.257 |
|
|
\[ {}x^{2} \left (y^{\prime }+y^{2}\right )+a \,x^{k}-b \left (b -1\right ) = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
3.506 |
|
|
\[ {}x^{2} \left (y^{\prime }+y^{2}\right )+4 x y+2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.753 |
|
|
\[ {}x^{2} \left (y^{\prime }+y^{2}\right )+a x y+b = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
2.507 |
|
|
\[ {}x^{2} \left (y^{\prime }-y^{2}\right )-a \,x^{2} y+x a +2 = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.374 |
|
|
\[ {}x^{2} \left (y^{\prime }+a y^{2}\right )-b = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
2.336 |
|
|
\[ {}x^{2} \left (y^{\prime }+a y^{2}\right )+b \,x^{\alpha }+c = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
3.549 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+y^{2}-2 x y+1 = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.912 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }-y \left (y-x \right ) = 0 \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.102 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+a \left (1-2 x y+y^{2}\right ) = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.945 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+a x y^{2}+x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.3 |
|
|
\[ {}\left (x^{2}-4\right ) y^{\prime }+\left (2+x \right ) y^{2}-4 y = 0 \] |
1 |
1 |
1 |
[_rational, _Bernoulli] |
✓ |
✓ |
1.078 |
|
|
\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
5.833 |
|
|
\[ {}2 x^{2} y^{\prime }-2 y^{2}-x y+2 x \,a^{2} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.762 |
|
|
\[ {}2 x^{2} y^{\prime }-2 y^{2}-3 x y+2 x \,a^{2} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.631 |
|
|
\[ {}x \left (2 x -1\right ) y^{\prime }+y^{2}-\left (1+4 x \right ) y+4 x = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
3.405 |
|
|
\[ {}2 x \left (-1+x \right ) y^{\prime }+\left (-1+x \right ) y^{2}-x = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.408 |
|
|
\[ {}3 x^{2} y^{\prime }-7 y^{2}-3 x y-x^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.614 |
|
|
\[ {}3 \left (x^{2}-4\right ) y^{\prime }+y^{2}-x y-3 = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.335 |
|
|
\[ {}x^{3} y^{\prime }-y^{2}-x^{4} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.056 |
|
|
\[ {}x^{3} y^{\prime }-y^{2}-x^{2} y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.181 |
|
|
\[ {}x^{3} y^{\prime }-x^{4} y^{2}+x^{2} y+20 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.99 |
|
|
\[ {}x^{3} y^{\prime }-x^{6} y^{2}-\left (2 x -3\right ) x^{2} y+3 = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.912 |
|
|
\[ {}x \left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right ) y^{2}-x^{2} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.658 |
|
|
\[ {}x^{2} \left (-1+x \right ) y^{\prime }-y^{2}-x \left (-2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.302 |
|
|
\[ {}2 x \left (x^{2}-1\right ) y^{\prime }+2 \left (x^{2}-1\right ) y^{2}-\left (3 x^{2}-5\right ) y+x^{2}-3 = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.309 |
|
|
\[ {}3 x \left (x^{2}-1\right ) y^{\prime }+x y^{2}-\left (x^{2}+1\right ) y-3 x = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
3.339 |
|
|
\[ {}\left (x^{2} a +b x +c \right ) \left (-y+x y^{\prime }\right )-y^{2}+x^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
2.892 |
|
|
\[ {}x^{4} \left (y^{\prime }+y^{2}\right )+a = 0 \] |
1 |
1 |
1 |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
2.418 |
|
|
\[ {}x \left (x^{3}-1\right ) y^{\prime }-2 x y^{2}+y+x^{2} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.973 |
|
|
|
||||||||
|
\[ {}\left (x^{2} a +b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
5.824 |
|
|
\[ {}x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{2 n -2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
2.357 |
|
|
\[ {}x^{n} y^{\prime }-a y^{2}-b \,x^{2 n -2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
5.237 |
|
|
\[ {}x y^{\prime } \ln \left (x \right )-y^{2} \ln \left (x \right )-\left (2 \ln \left (x \right )^{2}+1\right ) y-\ln \left (x \right )^{3} = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.189 |
|
|
\[ {}y^{\prime } \sin \left (x \right )-y^{2} \sin \left (x \right )^{2}+\left (\cos \left (x \right )-3 \sin \left (x \right )\right ) y+4 = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
15.024 |
|
|
\[ {}2 f \left (x \right ) y^{\prime }+2 f \left (x \right ) y^{2}-f^{\prime }\left (x \right ) y-2 f \left (x \right )^{2} = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
0.951 |
|
|
\[ {}y^{\prime } = \frac {\left (-1+y \ln \left (x \right )\right )^{2}}{x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.95 |
|
|
\[ {}y^{\prime } = \frac {\left (2 y \ln \left (x \right )-1\right )^{2}}{x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.034 |
|
|
\[ {}y^{\prime } = \frac {y+x^{3} a \,{\mathrm e}^{x}+a \,x^{4}+a \,x^{3}-x y^{2} {\mathrm e}^{x}-x^{2} y^{2}-x y^{2}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
1.763 |
|
|
\[ {}y^{\prime } = \frac {y+x^{3} a \ln \left (1+x \right )+a \,x^{4}+a \,x^{3}-x y^{2} \ln \left (1+x \right )-x^{2} y^{2}-x y^{2}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
1.858 |
|
|
\[ {}y^{\prime } = \frac {y+x^{3} \ln \left (x \right )+x^{4}+x^{3}+7 x y^{2} \ln \left (x \right )+7 x^{2} y^{2}+7 x y^{2}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
1.745 |
|
|
\[ {}y^{\prime } = \frac {y+x^{3} b \ln \left (\frac {1}{x}\right )+x^{4} b +b \,x^{3}+x a y^{2} \ln \left (\frac {1}{x}\right )+a \,x^{2} y^{2}+a x y^{2}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
1.874 |
|
|
\[ {}y^{\prime } = \frac {y \left (-1+\ln \left (\left (1+x \right ) x \right ) y x^{4}-\ln \left (\left (1+x \right ) x \right ) x^{3}\right )}{x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
3.632 |
|
|
\[ {}y^{\prime } = \frac {y+\ln \left (\left (-1+x \right ) \left (1+x \right )\right ) x^{3}+7 \ln \left (\left (-1+x \right ) \left (1+x \right )\right ) x y^{2}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
1.882 |
|
|
\[ {}y^{\prime } = \frac {y-\ln \left (\frac {1+x}{-1+x}\right ) x^{3}+\ln \left (\frac {1+x}{-1+x}\right ) x y^{2}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
2.185 |
|
|
\[ {}y^{\prime } = \frac {y+{\mathrm e}^{\frac {1+x}{-1+x}} x^{3}+{\mathrm e}^{\frac {1+x}{-1+x}} x y^{2}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
3.069 |
|
|
\[ {}y^{\prime } = \frac {x y-y-{\mathrm e}^{1+x} x^{3}+{\mathrm e}^{1+x} x y^{2}}{\left (-1+x \right ) x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
2.608 |
|
|
\[ {}y^{\prime } = \frac {y \ln \left (-1+x \right )+x^{4}+x^{3}+x^{2} y^{2}+x y^{2}}{\ln \left (-1+x \right ) x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
1.908 |
|
|
\[ {}y^{\prime } = \frac {y \ln \left (-1+x \right )+{\mathrm e}^{1+x} x^{3}+7 \,{\mathrm e}^{1+x} x y^{2}}{\ln \left (-1+x \right ) x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
2.854 |
|
|
\[ {}y^{\prime } = \frac {2 x \,{\mathrm e}^{x}-2 x -\ln \left (x \right )-1+x^{4} \ln \left (x \right )+x^{4}-2 y x^{2} \ln \left (x \right )-2 x^{2} y+y^{2} \ln \left (x \right )+y^{2}}{{\mathrm e}^{x}-1} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
17.087 |
|
|
\[ {}y^{\prime } = \frac {-{\mathrm e}^{x} y+x y-x^{3} \ln \left (x \right )-x^{3}-x y^{2} \ln \left (x \right )-x y^{2}}{\left (-{\mathrm e}^{x}+x \right ) x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
2.129 |
|
|
\[ {}y^{\prime } = \frac {y \left (1-x +y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-1+x \right ) x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.721 |
|
|
\[ {}y^{\prime } = \frac {y \ln \left (x \right ) x -y+2 x^{5} b +2 x^{3} a y^{2}}{\left (x \ln \left (x \right )-1\right ) x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
2.013 |
|
|
\[ {}y^{\prime } = \frac {-\ln \left (x \right )+{\mathrm e}^{\frac {1}{x}}+4 x^{2} y+2 x +2 x y^{2}+2 x^{3}}{\ln \left (x \right )-{\mathrm e}^{\frac {1}{x}}} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
10.543 |
|
|
\[ {}y^{\prime } = -\frac {y \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}+y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right ) x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.694 |
|
|
\[ {}y^{\prime } = \frac {y \left (-{\mathrm e}^{x}+\ln \left (2 x \right ) x^{2} y-\ln \left (2 x \right ) x \right ) {\mathrm e}^{-x}}{x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.566 |
|
|
\[ {}y^{\prime } = \frac {\left (18 x^{\frac {3}{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
4.141 |
|
|
\[ {}y^{\prime } = \frac {-\ln \left (x \right )+2 \ln \left (2 x \right ) x y+\ln \left (2 x \right )+\ln \left (2 x \right ) y^{2}+\ln \left (2 x \right ) x^{2}}{\ln \left (x \right )} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
3.72 |
|
|
\[ {}y^{\prime } = \frac {2 x \sin \left (x \right )-\ln \left (2 x \right )+\ln \left (2 x \right ) x^{4}-2 \ln \left (2 x \right ) x^{2} y+\ln \left (2 x \right ) y^{2}}{\sin \left (x \right )} \] |
1 |
0 |
0 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✗ |
N/A |
81.822 |
|
|
\[ {}y^{\prime } = \frac {2 x^{2}+2 x +x^{4}-2 x^{2} y-1+y^{2}}{1+x} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
2.947 |
|
|
\[ {}y^{\prime } = -\frac {y \left (\tan \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tan \left (x \right )} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
37.084 |
|
|
\[ {}y^{\prime } = \frac {y \left (-1-\ln \left (\frac {\left (-1+x \right ) \left (1+x \right )}{x}\right )+\ln \left (\frac {\left (-1+x \right ) \left (1+x \right )}{x}\right ) x y\right )}{x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
12.734 |
|
|
\[ {}y^{\prime } = \frac {y \left (-\ln \left (x \right )-x \ln \left (\frac {\left (-1+x \right ) \left (1+x \right )}{x}\right )+\ln \left (\frac {\left (-1+x \right ) \left (1+x \right )}{x}\right ) x^{2} y\right )}{x \ln \left (x \right )} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
5.017 |
|
|
\[ {}y^{\prime } = \frac {y \left (-\ln \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \ln \left (\frac {1}{x}\right )} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
5.582 |
|
|
\[ {}y^{\prime } = \frac {y \left (-\tanh \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \tanh \left (\frac {1}{x}\right )} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
36.352 |
|
|
\[ {}y^{\prime } = -\frac {y \left (\tanh \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tanh \left (x \right )} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
14.089 |
|
|
\[ {}y^{\prime } = \frac {-\sinh \left (x \right )+\ln \left (x \right ) x^{2}+2 y \ln \left (x \right ) x +\ln \left (x \right )+y^{2} \ln \left (x \right )}{\sinh \left (x \right )} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
41.107 |
|
|
\[ {}y^{\prime } = -\frac {\ln \left (x \right )-\sinh \left (x \right ) x^{2}-2 \sinh \left (x \right ) x y-\sinh \left (x \right )-\sinh \left (x \right ) y^{2}}{\ln \left (x \right )} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
79.651 |
|
|
\[ {}y^{\prime } = \frac {y \ln \left (x \right )+\cosh \left (x \right ) x a y^{2}+\cosh \left (x \right ) x^{3} b}{x \ln \left (x \right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
4.746 |
|
|
\[ {}y^{\prime } = -\frac {y \left (\ln \left (-1+x \right )+\coth \left (1+x \right ) x -\coth \left (1+x \right ) x^{2} y\right )}{x \ln \left (-1+x \right )} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
46.734 |
|
|
\[ {}y^{\prime } = -\frac {\ln \left (-1+x \right )-\coth \left (1+x \right ) x^{2}-2 \coth \left (1+x \right ) x y-\coth \left (1+x \right )-\coth \left (1+x \right ) y^{2}}{\ln \left (-1+x \right )} \] |
1 |
1 |
0 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
93.694 |
|
|
\[ {}y^{\prime } = \frac {2 x \ln \left (\frac {1}{-1+x}\right )-\coth \left (\frac {1+x}{-1+x}\right )+\coth \left (\frac {1+x}{-1+x}\right ) y^{2}-2 \coth \left (\frac {1+x}{-1+x}\right ) x^{2} y+\coth \left (\frac {1+x}{-1+x}\right ) x^{4}}{\ln \left (\frac {1}{-1+x}\right )} \] |
1 |
0 |
0 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✗ |
N/A |
93.109 |
|
|
\[ {}y^{\prime } = \frac {2 x^{2} \cosh \left (\frac {1}{-1+x}\right )-2 x \cosh \left (\frac {1}{-1+x}\right )-1+y^{2}-2 x^{2} y+x^{4}-x +x y^{2}-2 x^{3} y+x^{5}}{\left (-1+x \right ) \cosh \left (\frac {1}{-1+x}\right )} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✗ |
N/A |
87.348 |
|
|
\[ {}y^{\prime } = \frac {y \left (-\cosh \left (\frac {1}{1+x}\right ) x +\cosh \left (\frac {1}{1+x}\right )-x +x^{2} y-x^{2}+x^{3} y\right )}{x \left (-1+x \right ) \cosh \left (\frac {1}{1+x}\right )} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
18.688 |
|
|
\[ {}y^{\prime } = \frac {y \left (-1-\cosh \left (\frac {1+x}{-1+x}\right ) x +\cosh \left (\frac {1+x}{-1+x}\right ) x^{2} y-\cosh \left (\frac {1+x}{-1+x}\right ) x^{2}+\cosh \left (\frac {1+x}{-1+x}\right ) x^{3} y\right )}{x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
34.423 |
|
|
\[ {}y^{\prime } = \frac {y \left (-1-{\mathrm e}^{\frac {1+x}{-1+x}} x +x^{2} {\mathrm e}^{\frac {1+x}{-1+x}} y-x^{2} {\mathrm e}^{\frac {1+x}{-1+x}}+x^{3} {\mathrm e}^{\frac {1+x}{-1+x}} y\right )}{x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
5.467 |
|
|
\[ {}y^{\prime } = \frac {x +y+y^{2}-2 y \ln \left (x \right ) x +x^{2} \ln \left (x \right )^{2}}{x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
2.726 |
|
|
\[ {}y^{\prime } = \frac {\left (4 \,{\mathrm e}^{-x^{2}}-4 x^{2} {\mathrm e}^{-x^{2}}+4 y^{2}-4 x^{2} {\mathrm e}^{-x^{2}} y+x^{4} {\mathrm e}^{-2 x^{2}}\right ) x}{4} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
4.315 |
|
|
\[ {}y^{\prime } = \frac {30 x^{3}+25 \sqrt {x}+25 y^{2}-20 x^{3} y-100 y \sqrt {x}+4 x^{6}+40 x^{\frac {7}{2}}+100 x}{25 x} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
33.944 |
|
|
\[ {}y^{\prime } = \frac {y+x^{2} \ln \left (x \right )^{3}+2 x^{2} \ln \left (x \right )^{2} y+x^{2} \ln \left (x \right ) y^{2}}{x \ln \left (x \right )} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
10.425 |
|
|
\[ {}y^{\prime } = \frac {y+x^{3} \ln \left (x \right )^{3}+2 x^{3} \ln \left (x \right )^{2} y+x^{3} \ln \left (x \right ) y^{2}}{x \ln \left (x \right )} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
5.578 |
|
|
\[ {}y^{\prime } = \frac {2 x y^{2}+4 y \ln \left (2 x +1\right ) x +2 \ln \left (2 x +1\right )^{2} x +y^{2}-2+\ln \left (2 x +1\right )^{2}+2 y \ln \left (2 x +1\right )}{2 x +1} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
3.367 |
|
|
\[ {}y^{\prime } = \frac {-2 \cos \left (x \right ) x +2 \sin \left (x \right ) x^{2}+2 x +2 y^{2}+4 y \cos \left (x \right ) x -4 x y+x^{2} \cos \left (2 x \right )+3 x^{2}-4 x^{2} \cos \left (x \right )}{2 x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
9.873 |
|
|
\[ {}y^{\prime } = \frac {2 x^{2} \cos \left (x \right )+2 \sin \left (x \right ) x^{3}-2 x \sin \left (x \right )+2 x +2 x^{2} y^{2}-4 y \sin \left (x \right ) x +4 y \cos \left (x \right ) x^{2}+4 x y+3-\cos \left (2 x \right )-2 \sin \left (2 x \right ) x -4 \sin \left (x \right )+x^{2} \cos \left (2 x \right )+x^{2}+4 \cos \left (x \right ) x}{2 x^{3}} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
22.888 |
|
|
\[ {}y^{\prime } = \frac {y \left (-1-x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2}-x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} \ln \left (x \right )+x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y+2 x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y \ln \left (x \right )+x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} x^{2} y \ln \left (x \right )^{2}\right )}{\left (1+\ln \left (x \right )\right ) x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
11.429 |
|
|
\[ {}y^{\prime } = \frac {y \left (-1-x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}}-x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} \ln \left (x \right )+x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y+2 x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y \ln \left (x \right )+x^{3} x^{\frac {2}{1+\ln \left (x \right )}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{1+\ln \left (x \right )}} y \ln \left (x \right )^{2}\right )}{\left (1+\ln \left (x \right )\right ) x} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
10.642 |
|
|
\[ {}y^{\prime } = -F \left (x \right ) \left (-x^{2} a +y^{2}\right )+\frac {y}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
3.55 |
|
|
\[ {}y^{\prime } = -F \left (x \right ) \left (-x^{2}-2 x y+y^{2}\right )+\frac {y}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
2.852 |
|
|
\[ {}y^{\prime } = -F \left (x \right ) \left (-a y^{2}-b \,x^{2}\right )+\frac {y}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
2.964 |
|
|
\[ {}y^{\prime } = -F \left (x \right ) \left (-y^{2}+2 x^{2} y+1-x^{4}\right )+2 x \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
3.02 |
|
|
\[ {}y^{\prime } = -F \left (x \right ) \left (x^{2}+2 x y-y^{2}\right )+\frac {y}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
2.735 |
|
|
\[ {}y^{\prime } = -F \left (x \right ) \left (-7 x y^{2}-x^{3}\right )+\frac {y}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
2.915 |
|
|
\[ {}y^{\prime } = -F \left (x \right ) \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{\ln \left (x \right ) x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.082 |
|
|
\[ {}y^{\prime } = -x^{3} \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{\ln \left (x \right ) x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.876 |
|
|
\[ {}y^{\prime } = \left (y-{\mathrm e}^{x}\right )^{2}+{\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
2.679 |
|
|
\[ {}y^{\prime } = \frac {\left (y-\operatorname {Si}\left (x \right )\right )^{2}+\sin \left (x \right )}{x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
3.821 |
|
|
\[ {}y^{\prime } = \left (y+\cos \left (x \right )\right )^{2}+\sin \left (x \right ) \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
3.0 |
|
|
\[ {}y^{\prime } = \frac {\left (y-\ln \left (x \right )-\operatorname {Ci}\left (x \right )\right )^{2}+\cos \left (x \right )}{x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
4.853 |
|
|
\[ {}y^{\prime } = \frac {\left (y-x +\ln \left (1+x \right )\right )^{2}+x}{1+x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
2.306 |
|
|
\[ {}y^{\prime } = \frac {2 x^{2} y+x^{3}+y \ln \left (x \right ) x -y^{2}-x y}{x^{2} \left (x +\ln \left (x \right )\right )} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.15 |
|
|
\[ {}y^{\prime } = a y^{2}+b x +c \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.483 |
|
|
\[ {}y^{\prime } = y^{2}-a^{2} x^{2}+3 a \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.68 |
|
|
\[ {}y^{\prime } = y^{2}+a^{2} x^{2}+b x +c \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
14.279 |
|
|
\[ {}y^{\prime } = a y^{2}+b \,x^{n} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
2.231 |
|
|
\[ {}y^{\prime } = y^{2}+a n \,x^{n -1}-a^{2} x^{2 n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
118.678 |
|
|
\[ {}y^{\prime } = a y^{2}+b \,x^{2 n}+c \,x^{n -1} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
36.872 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}+b \,x^{-n -2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
2.179 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.477 |
|
|
\[ {}y^{\prime } = y^{2}+k \left (x a +b \right )^{n} \left (c x +d \right )^{-n -4} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
5.879 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{n +2 m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
128.141 |
|
|
\[ {}y^{\prime } = \left (a \,x^{2 n}+b \,x^{n -1}\right ) y^{2}+c \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
90.599 |
|
|
\[ {}\left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} x +b_{0} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
94.806 |
|
|
\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
4.039 |
|
|
\[ {}x^{2} y^{\prime } = x^{2} y^{2}-a^{2} x^{4}+a \left (1-2 b \right ) x^{2}-b \left (b +1\right ) \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
3.519 |
|
|
\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b \,x^{n}+c \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
4.32 |
|
|
\[ {}x^{2} y^{\prime } = x^{2} y^{2}+a \,x^{2 m} \left (b \,x^{m}+c \right )^{n}-\frac {n^{2}}{4}+\frac {1}{4} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
3.649 |
|
|
\[ {}\left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
143.639 |
|
|
\[ {}x^{4} y^{\prime } = -x^{4} y^{2}-a^{2} \] |
1 |
1 |
1 |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
2.489 |
|
|
\[ {}a \,x^{2} \left (-1+x \right )^{2} \left (y^{\prime }+\lambda y^{2}\right )+b \,x^{2}+c x +s = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✗ |
7.046 |
|
|
\[ {}\left (x^{2} a +b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
6.493 |
|
|
\[ {}x^{n +1} y^{\prime } = a \,x^{2 n} y^{2}+c \,x^{m}+d \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
5.091 |
|
|
\[ {}\left (a \,x^{n}+b \right ) y^{\prime } = b y^{2}+a \,x^{n -2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
5.682 |
|
|
\[ {}\left (a \,x^{n}+b \,x^{m}+c \right ) \left (y^{\prime }-y^{2}\right )+a n \left (n -1\right ) x^{n -2}+b m \left (m -1\right ) x^{m -2} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
7.027 |
|
|
\[ {}y^{\prime } = a y^{2}+b y+c x +k \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.887 |
|
|
\[ {}y^{\prime } = y^{2}+a \,x^{n} y+a \,x^{n -1} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
130.475 |
|
|
\[ {}y^{\prime } = y^{2}+a \,x^{n} y+b \,x^{n -1} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
7.266 |
|
|
\[ {}y^{\prime } = y^{2}+\left (\alpha x +\beta \right ) y+x^{2} a +b x +c \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
67.095 |
|
|
\[ {}y^{\prime } = y^{2}+a \,x^{n} y-a b \,x^{n}-b^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.001 |
|
|
\[ {}y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+a \,x^{1+m +n}-a \,x^{m} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
5.684 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m} y+b c \,x^{m}-a \,c^{2} x^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.307 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}-a \,x^{n} \left (b \,x^{m}+c \right ) y+b m \,x^{m -1} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
5.657 |
|
|
\[ {}y^{\prime } = -a n \,x^{n -1} y^{2}+c \,x^{m} \left (a \,x^{n}+b \right ) y-c \,x^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
31.73 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m} y+c k \,x^{k -1}-b c \,x^{m +k}-a \,c^{2} x^{n +2 k} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
9.673 |
|
|
\[ {}x y^{\prime } = a y^{2}+b y+c \,x^{2 b} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.538 |
|
|
\[ {}x y^{\prime } = a y^{2}+b y+c \,x^{n} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
3.43 |
|
|
\[ {}x y^{\prime } = a y^{2}+\left (n +b \,x^{n}\right ) y+c \,x^{2 n} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
4.291 |
|
|
\[ {}x y^{\prime } = x y^{2}+a y+b \,x^{n} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
4.086 |
|
|
\[ {}x y^{\prime }+a_{3} x y^{2}+a_{2} y+a_{1} x +a_{0} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
7.144 |
|
|
\[ {}x y^{\prime } = a \,x^{n} y^{2}+b y+c \,x^{-n} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
3.868 |
|
|
\[ {}x y^{\prime } = a \,x^{n} y^{2}+m y-a \,b^{2} x^{n +2 m} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.948 |
|
|
\[ {}x y^{\prime } = x^{2 n} y^{2}+\left (m -n \right ) y+x^{2 m} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.868 |
|
|
\[ {}x y^{\prime } = a \,x^{n} y^{2}+b y+c \,x^{m} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
4.839 |
|
|
\[ {}x y^{\prime } = a \,x^{2 n} y^{2}+\left (b \,x^{n}-n \right ) y+c \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
3.958 |
|
|
\[ {}x y^{\prime } = a \,x^{2 n +m} y^{2}+\left (b \,x^{m +n}-n \right ) y+c \,x^{m} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
5.187 |
|
|
\[ {}\left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (a_{1} x +b_{1} \right ) y+a_{0} x +b_{0} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
33.569 |
|
|
\[ {}\left (x a +c \right ) y^{\prime } = \alpha \left (b x +a y\right )^{2}+\beta \left (b x +a y\right )-b x +\gamma \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
5.273 |
|
|
\[ {}2 x^{2} y^{\prime } = 2 y^{2}+x y-2 x \,a^{2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
2.02 |
|
|
\[ {}2 x^{2} y^{\prime } = 2 y^{2}+3 x y-2 x \,a^{2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
3.115 |
|
|
\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b x y+c \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
4.879 |
|
|
\[ {}x^{2} y^{\prime } = c \,x^{2} y^{2}+\left (x^{2} a +b x \right ) y+\alpha \,x^{2}+\beta x +\gamma \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
123.02 |
|
|
\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b x y+c \,x^{n}+s \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
5.068 |
|
|
\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b x y+c \,x^{2 n}+s \,x^{n} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
7.152 |
|
|
\[ {}x^{2} y^{\prime } = c \,x^{2} y^{2}+\left (a \,x^{n}+b \right ) x y+\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
161.362 |
|
|
\[ {}x^{2} y^{\prime } = \left (\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \right ) y^{2}+\left (a \,x^{n}+b \right ) x y+c \,x^{2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✗ |
70.098 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+\lambda \left (1-2 x y+y^{2}\right ) = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
3.589 |
|
|
\[ {}\left (x^{2} a +b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\frac {b \left (a +\beta \right )}{\alpha } = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
3.492 |
|
|
\[ {}\left (x^{2} a +b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\gamma = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
57.786 |
|
|
\[ {}\left (x^{2} a +b \right ) y^{\prime }+y^{2}-2 x y+\left (1-a \right ) x^{2}-b = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
4.773 |
|
|
\[ {}\left (x^{2} a +b x +c \right ) y^{\prime } = y^{2}+\left (2 \lambda x +b \right ) y+\lambda \left (\lambda -a \right ) x^{2}+\mu \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
6.681 |
|
|
\[ {}\left (x^{2} a +b x +c \right ) y^{\prime } = y^{2}+\left (x a +\mu \right ) y-\lambda ^{2} x^{2}+\lambda \left (b -\mu \right ) x +c \lambda \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✗ |
145.468 |
|
|
\[ {}\left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime } = y^{2}+\left (a_{1} x +b_{1} \right ) y-\lambda \left (\lambda +a_{1} -a_{2} \right ) x^{2}+\lambda \left (b_{2} -b_{1} \right ) x +\lambda c_{2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✗ |
158.893 |
|
|
\[ {}\left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime } = y^{2}+\left (a_{1} x +b_{1} \right ) y+a_{0} x^{2}+b_{0} x +c_{0} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✗ |
157.181 |
|
|
\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
5.77 |
|
|
\[ {}\left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (b_{1} x +a_{1} \right ) y+a_{0} = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✗ |
35.999 |
|
|
\[ {}x^{3} y^{\prime } = x^{3} a y^{2}+\left (b \,x^{2}+c \right ) y+s x \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
35.645 |
|
|
\[ {}x^{3} y^{\prime } = x^{3} a y^{2}+x \left (b x +c \right ) y+\alpha x +\beta \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
83.606 |
|
|
\[ {}x \left (x^{2}+a \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (b \,x^{2}+c \right ) y+s x = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
4.635 |
|
|
\[ {}x^{2} \left (x +a \right ) \left (y^{\prime }+\lambda y^{2}\right )+x \left (b x +c \right ) y+\alpha x +\beta = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✗ |
6.953 |
|
|
\[ {}\left (x^{2} a +b x +e \right ) \left (-y+x y^{\prime }\right )-y^{2}+x^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
2.059 |
|
|
\[ {}x^{2} \left (x^{2}+a \right ) \left (y^{\prime }+\lambda y^{2}\right )+x \left (b \,x^{2}+c \right ) y+s = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✗ |
7.855 |
|
|
\[ {}a \left (x^{2}-1\right ) \left (y^{\prime }+\lambda y^{2}\right )+b x \left (x^{2}-1\right ) y+c \,x^{2}+d x +s = 0 \] |
1 |
1 |
0 |
[_rational, _Riccati] |
✓ |
✓ |
3.535 |
|
|
\[ {}x^{n +1} y^{\prime } = a \,x^{2 n} y^{2}+b \,x^{n} y+c \,x^{m}+d \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.516 |
|
|
\[ {}x \left (a \,x^{k}+b \right ) y^{\prime } = \alpha \,x^{n} y^{2}+\left (\beta -a n \,x^{k}\right ) y+\gamma \,x^{-n} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
5.438 |
|
|
\[ {}x^{2} \left (a \,x^{n}-1\right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (p \,x^{n}+q \right ) x y+r \,x^{n}+s = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✗ |
15.242 |
|
|
\[ {}\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime } = c y^{2}-b \,x^{m -1} y+a \,x^{n -2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
94.876 |
|
|
\[ {}\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime } = a \,x^{n -2} y^{2}+b \,x^{m -1} y+c \] |
1 |
1 |
0 |
[_rational, _Riccati] |
✓ |
✓ |
83.819 |
|
|
\[ {}\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime } = \alpha \,x^{k} y^{2}+\beta \,x^{s} y-\alpha \,\lambda ^{2} x^{k}+\beta \lambda \,x^{s} \] |
1 |
0 |
1 |
[_rational, _Riccati] |
✗ |
N/A |
105.711 |
|
|
\[ {}\left (a \,x^{n}+b \,x^{m}+c \right ) \left (-y+x y^{\prime }\right )+s \,x^{k} \left (y^{2}-\lambda \,x^{2}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
3.273 |
|
|
\[ {}y^{\prime } = a y^{2}+b \,{\mathrm e}^{\lambda x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.061 |
|
|
\[ {}y^{\prime } = y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.118 |
|
|
\[ {}y^{\prime } = \sigma y^{2}+a +b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 \lambda x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
9.621 |
|
|
\[ {}y^{\prime } = \sigma y^{2}+a y+b \,{\mathrm e}^{x}+c \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.375 |
|
|
\[ {}y^{\prime } = y^{2}+b y+a \left (\lambda -b \right ) {\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.973 |
|
|
\[ {}y^{\prime } = y^{2}+a \,{\mathrm e}^{\lambda x} y-a b \,{\mathrm e}^{\lambda x}-b^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.715 |
|
|
\[ {}y^{\prime } = y^{2}+a \,{\mathrm e}^{2 \lambda x} \left ({\mathrm e}^{\lambda x}+b \right )^{n}-\frac {\lambda ^{2}}{4} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
106.799 |
|
|
\[ {}y^{\prime } = y^{2}+a \,{\mathrm e}^{8 \lambda x}+b \,{\mathrm e}^{6 \lambda x}+c \,{\mathrm e}^{4 \lambda x}-\lambda ^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✗ |
8.615 |
|
|
\[ {}y^{\prime } = a \,{\mathrm e}^{k x} y^{2}+b \,{\mathrm e}^{s x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.537 |
|
|
\[ {}y^{\prime } = b \,{\mathrm e}^{\mu x} y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} b \,{\mathrm e}^{\left (\mu +2 \lambda \right ) x} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
2.774 |
|
|
\[ {}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+b y+c \,{\mathrm e}^{-\lambda x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
2.21 |
|
|
\[ {}y^{\prime } = a \,{\mathrm e}^{\mu x} y^{2}+\lambda y-a \,b^{2} {\mathrm e}^{\left (\mu +2 \lambda \right ) x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.217 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\mu x} y+a \lambda \,{\mathrm e}^{\left (\mu -\lambda \right ) x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.423 |
|
|
\[ {}y^{\prime } = -\lambda \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\mu x} y-a \,{\mathrm e}^{\left (\mu -\lambda \right ) x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.789 |
|
|
\[ {}y^{\prime } = a \,{\mathrm e}^{\mu x} y^{2}+a b \,{\mathrm e}^{x \left (\lambda +\mu \right )} y-b \lambda \,{\mathrm e}^{\lambda x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
110.655 |
|
|
\[ {}y^{\prime } = a \,{\mathrm e}^{k x} y^{2}+b y+c \,{\mathrm e}^{s x}+d \,{\mathrm e}^{-k x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.636 |
|
|
\[ {}y^{\prime } = a \,{\mathrm e}^{\left (\mu +2 \lambda \right ) x} y^{2}+\left (b \,{\mathrm e}^{x \left (\lambda +\mu \right )}-\lambda \right ) y+c \,{\mathrm e}^{\mu x} \] |
1 |
0 |
1 |
[_Riccati] |
✗ |
N/A |
2.656 |
|
|
\[ {}y^{\prime } = a \,{\mathrm e}^{k x} y^{2}+b y+c \,{\mathrm e}^{k n x}+d \,{\mathrm e}^{k \left (1+2 n \right ) x} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
3.434 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{\mu x} \left (y-b \,{\mathrm e}^{\lambda x}\right )^{2}+b \lambda \,{\mathrm e}^{\lambda x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.938 |
|
|
\[ {}\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime } = y^{2}+k \,{\mathrm e}^{x \nu } y-m^{2}+k m \,{\mathrm e}^{x \nu } \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
80.895 |
|
|
\[ {}\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{\mu x}+c \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} {\mathrm e}^{\lambda x}+b \,\mu ^{2} {\mathrm e}^{\mu x} = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.68 |
|
|
\[ {}y^{\prime } = y^{2}+a x \,{\mathrm e}^{\lambda x} y+{\mathrm e}^{\lambda x} a \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.27 |
|
|
\[ {}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+b \,{\mathrm e}^{-\lambda x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
2.273 |
|
|
\[ {}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+b n \,x^{n -1}-a \,b^{2} {\mathrm e}^{\lambda x} x^{2 n} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
4.69 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{\lambda x} y^{2}+a \,x^{n} y+a \lambda \,x^{n} {\mathrm e}^{-\lambda x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.981 |
|
|
\[ {}y^{\prime } = -\lambda \,{\mathrm e}^{\lambda x} y^{2}+a \,x^{n} {\mathrm e}^{\lambda x} y-a \,x^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.862 |
|
|
\[ {}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}-a b \,x^{n} {\mathrm e}^{\lambda x} y+b n \,x^{n -1} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.889 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}+b \lambda \,{\mathrm e}^{\lambda x}-a \,b^{2} x^{n} {\mathrm e}^{2 \lambda x} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
4.379 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}+\lambda y-a \,b^{2} x^{n} {\mathrm e}^{2 \lambda x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.848 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}-a b \,x^{n} {\mathrm e}^{\lambda x} y+b \lambda \,{\mathrm e}^{\lambda x} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
3.435 |
|
|
\[ {}y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} {\mathrm e}^{\lambda x} y-{\mathrm e}^{\lambda x} a \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
5.784 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}-a \,x^{n} \left (b \,{\mathrm e}^{\lambda x}+c \right ) y+c \,x^{n} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
5.43 |
|
|
\[ {}y^{\prime } = a \,x^{n} {\mathrm e}^{2 \lambda x} y^{2}+\left (b \,x^{n} {\mathrm e}^{\lambda x}-\lambda \right ) y+c \,x^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
10.79 |
|
|
\[ {}y^{\prime } = a \,{\mathrm e}^{\lambda x} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
2.992 |
|
|
\[ {}x y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+k y+a \,b^{2} x^{2 k} {\mathrm e}^{\lambda x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.052 |
|
|
\[ {}x y^{\prime } = a \,x^{2 n} {\mathrm e}^{\lambda x} y^{2}+\left (b \,x^{n} {\mathrm e}^{\lambda x}-n \right ) y+c \,{\mathrm e}^{\lambda x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.039 |
|
|
\[ {}y^{\prime } = y^{2}+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} {\mathrm e}^{2 \lambda \,x^{2}} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
2.316 |
|
|
\[ {}y^{\prime } = a \,{\mathrm e}^{-\lambda \,x^{2}} y^{2}+\lambda x y+a \,b^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.102 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}+\lambda x y+a \,b^{2} x^{n} {\mathrm e}^{\lambda \,x^{2}} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.352 |
|
|
\[ {}x^{4} \left (y^{\prime }-y^{2}\right ) = a +b \,{\mathrm e}^{\frac {k}{x}}+c \,{\mathrm e}^{\frac {2 k}{x}} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
25.376 |
|
|
\[ {}y^{\prime } = y^{2}-a^{2}+a \lambda \sinh \left (\lambda x \right )-a^{2} \sinh \left (\lambda x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
9.966 |
|
|
\[ {}y^{\prime } = y^{2}+a \sinh \left (\beta x \right ) y+a b \sinh \left (\beta x \right )-b^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.682 |
|
|
\[ {}y^{\prime } = y^{2}+a x \sinh \left (b x \right )^{m} y+a \sinh \left (b x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
13.319 |
|
|
\[ {}y^{\prime } = \lambda \sinh \left (\lambda x \right ) y^{2}-\lambda \sinh \left (\lambda x \right )^{3} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
5.879 |
|
|
\[ {}y^{\prime } = \left (a \sinh \left (\lambda x \right )^{2}-\lambda \right ) y^{2}-a \sinh \left (\lambda x \right )^{2}+\lambda -a \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
13.552 |
|
|
\[ {}\left (a \sinh \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \sinh \left (\mu x \right ) y-d^{2}+c d \sinh \left (\mu x \right ) \] |
1 |
0 |
1 |
[_Riccati] |
✗ |
N/A |
109.078 |
|
|
\[ {}\left (a \sinh \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} \sinh \left (\lambda x \right ) = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
5.491 |
|
|
\[ {}y^{\prime } = \alpha y^{2}+\beta +\gamma \cosh \left (x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.461 |
|
|
\[ {}y^{\prime } = y^{2}+a \cosh \left (\beta x \right ) y+a b \cosh \left (\beta x \right )-b^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
5.974 |
|
|
\[ {}y^{\prime } = y^{2}+a x \cosh \left (b x \right )^{m} y+a \cosh \left (b x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
9.689 |
|
|
\[ {}y^{\prime } = \left (a \cosh \left (\lambda x \right )^{2}-\lambda \right ) y^{2}+a +\lambda -a \cosh \left (\lambda x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
11.165 |
|
|
\[ {}2 y^{\prime } = \left (a -\lambda +a \cosh \left (\lambda x \right )\right ) y^{2}+a +\lambda -a \cosh \left (\lambda x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
17.17 |
|
|
|
||||||||
|
\[ {}y^{\prime } = y^{2}-\lambda ^{2}+a \cosh \left (\lambda x \right )^{n} \sinh \left (\lambda x \right )^{-n -4} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
27.444 |
|
|
\[ {}y^{\prime } = a \sinh \left (\lambda x \right ) y^{2}+b \sinh \left (\lambda x \right ) \cosh \left (\lambda x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
8.098 |
|
|
\[ {}y^{\prime } = a \cosh \left (\lambda x \right ) y^{2}+b \cosh \left (\lambda x \right ) \sinh \left (\lambda x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
11.575 |
|
|
\[ {}\left (a \cosh \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \cosh \left (\mu x \right ) y-d^{2}+c d \cosh \left (\mu x \right ) \] |
1 |
0 |
1 |
[_Riccati] |
✗ |
N/A |
155.652 |
|
|
\[ {}\left (a \cosh \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} \cosh \left (\lambda x \right ) = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.684 |
|
|
\[ {}y^{\prime } = y^{2}+a \lambda -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
6.315 |
|
|
\[ {}y^{\prime } = y^{2}+3 a \lambda -\lambda ^{2}-a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
6.465 |
|
|
\[ {}y^{\prime } = y^{2}+a x \tanh \left (b x \right )^{m} y+a \tanh \left (b x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
7.38 |
|
|
\[ {}\left (a \tanh \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \tanh \left (\mu x \right ) y-d^{2}+c d \tanh \left (\mu x \right ) \] |
1 |
0 |
1 |
[_Riccati] |
✗ |
N/A |
87.704 |
|
|
\[ {}y^{\prime } = y^{2}+a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
6.385 |
|
|
\[ {}y^{\prime } = y^{2}-\lambda ^{2}+3 a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
6.603 |
|
|
\[ {}y^{\prime } = y^{2}+a x \coth \left (b x \right )^{m} y+a \coth \left (b x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
7.881 |
|
|
\[ {}\left (a \coth \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \coth \left (\mu x \right ) y-d^{2}+c d \coth \left (\mu x \right ) \] |
1 |
0 |
1 |
[_Riccati] |
✗ |
N/A |
109.109 |
|
|
\[ {}y^{\prime } = y^{2}-2 \lambda ^{2} \tanh \left (\lambda x \right )^{2}-2 \lambda ^{2} \coth \left (\lambda x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
19.498 |
|
|
\[ {}y^{\prime } = y^{2}+a \lambda +b \lambda -2 a b -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2}-b \left (b +\lambda \right ) \coth \left (\lambda x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
38.283 |
|
|
\[ {}y^{\prime } = a \ln \left (x \right )^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{2 m} \ln \left (x \right )^{n} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
4.673 |
|
|
\[ {}x y^{\prime } = a y^{2}+b \ln \left (x \right )+c \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.865 |
|
|
\[ {}x y^{\prime } = a y^{2}+b \ln \left (x \right )^{k}+c \ln \left (x \right )^{2 k +2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
32.25 |
|
|
\[ {}x y^{\prime } = x y^{2}-a^{2} x \ln \left (\beta x \right )^{2}+a \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
2.323 |
|
|
\[ {}x y^{\prime } = x y^{2}-a^{2} x \ln \left (\beta x \right )^{2 k}+a k \ln \left (\beta x \right )^{k -1} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
3.624 |
|
|
\[ {}x y^{\prime } = a \,x^{n} y^{2}+b -a \,b^{2} x^{n} \ln \left (x \right )^{2} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
3.071 |
|
|
\[ {}x^{2} y^{\prime } = x^{2} y^{2}+a \ln \left (x \right )^{2}+b \ln \left (x \right )+c \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
8.459 |
|
|
\[ {}x^{2} y^{\prime } = x^{2} y^{2}+a \left (b \ln \left (x \right )+c \right )^{n}+\frac {1}{4} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
2.644 |
|
|
\[ {}x^{2} \ln \left (x a \right ) \left (y^{\prime }-y^{2}\right ) = 1 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.682 |
|
|
\[ {}y^{\prime } = y^{2}+a \ln \left (\beta x \right ) y-a b \ln \left (\beta x \right )-b^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.299 |
|
|
\[ {}y^{\prime } = y^{2}+a x \ln \left (b x \right )^{m} y+a \ln \left (b x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.332 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}-a b \,x^{n +1} \ln \left (x \right ) y+b \ln \left (x \right )+b \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
3.271 |
|
|
\[ {}y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+a \,x^{n +1} \ln \left (x \right )^{m} y-a \ln \left (x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.411 |
|
|
\[ {}y^{\prime } = a \ln \left (x \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
4.208 |
|
|
\[ {}y^{\prime } = a \ln \left (x \right )^{n} y^{2}+b \ln \left (x \right )^{m} y+b c \ln \left (x \right )^{m}-a \,c^{2} \ln \left (x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.691 |
|
|
\[ {}x y^{\prime } = \left (a y+b \ln \left (x \right )\right )^{2} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
1.66 |
|
|
\[ {}x y^{\prime } = a \ln \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \ln \left (\lambda x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.96 |
|
|
\[ {}x y^{\prime } = a \,x^{n} \left (y+b \ln \left (x \right )\right )^{2}-b \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
2.03 |
|
|
\[ {}x y^{\prime } = a \,x^{2 n} \ln \left (x \right ) y^{2}+\left (b \,x^{n} \ln \left (x \right )-n \right ) y+c \ln \left (x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.723 |
|
|
\[ {}x^{2} y^{\prime } = y^{2} a^{2} x^{2}-x y+b^{2} \ln \left (x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.816 |
|
|
\[ {}\left (a \ln \left (x \right )+b \right ) y^{\prime } = y^{2}+c \ln \left (x \right )^{n} y-\lambda ^{2}+\lambda c \ln \left (x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.789 |
|
|
\[ {}\left (a \ln \left (x \right )+b \right ) y^{\prime } = \ln \left (x \right )^{n} y^{2}+c y-\lambda ^{2} \ln \left (x \right )^{n}+c \lambda \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
10.08 |
|
|
\[ {}y^{\prime } = \alpha y^{2}+\beta +\gamma \sin \left (\lambda x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
6.474 |
|
|
\[ {}y^{\prime } = y^{2}-a^{2}+a \lambda \sin \left (\lambda x \right )+a^{2} \sin \left (\lambda x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
8.052 |
|
|
\[ {}y^{\prime } = y^{2}+\lambda ^{2}+c \sin \left (\lambda x +a \right )^{n} \sin \left (\lambda x +b \right )^{-n -4} \] |
1 |
0 |
0 |
[_Riccati] |
✗ |
N/A |
101.086 |
|
|
\[ {}y^{\prime } = y^{2}+a \sin \left (\beta x \right ) y+a b \sin \left (\beta x \right )-b^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.875 |
|
|
\[ {}y^{\prime } = y^{2}+a \sin \left (b x \right )^{m} y+a \sin \left (b x \right )^{m} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
21.685 |
|
|
\[ {}y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+\lambda \sin \left (\lambda x \right )^{3} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.08 |
|
|
\[ {}2 y^{\prime } = \left (\lambda +a -a \sin \left (\lambda x \right )\right ) y^{2}+\lambda -a -a \sin \left (\lambda x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✗ |
165.824 |
|
|
\[ {}y^{\prime } = \left (\lambda +a \sin \left (\lambda x \right )^{2}\right ) y^{2}+\lambda -a +a \sin \left (\lambda x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
7.181 |
|
|
\[ {}y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} \sin \left (x \right )^{m} y-a \sin \left (x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
20.835 |
|
|
\[ {}y^{\prime } = a \sin \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
4.291 |
|
|
\[ {}x y^{\prime } = a \sin \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \sin \left (\lambda x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
12.188 |
|
|
\[ {}\left (a \sin \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \sin \left (\mu x \right ) y-d^{2}+c d \sin \left (\mu x \right ) \] |
1 |
0 |
1 |
[_Riccati] |
✗ |
N/A |
75.029 |
|
|
\[ {}\left (a \sin \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )-a \,\lambda ^{2} \sin \left (\lambda x \right ) = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.806 |
|
|
\[ {}y^{\prime } = \alpha y^{2}+\beta +\gamma \cos \left (\lambda x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.688 |
|
|
\[ {}y^{\prime } = y^{2}-a^{2}+a \lambda \cos \left (\lambda x \right )+\cos \left (\lambda x \right )^{2} a^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
5.29 |
|
|
\[ {}y^{\prime } = y^{2}+\lambda ^{2}+c \cos \left (\lambda x +a \right )^{n} \cos \left (\lambda x +b \right )^{-n -4} \] |
1 |
0 |
0 |
[_Riccati] |
✗ |
N/A |
90.988 |
|
|
\[ {}y^{\prime } = y^{2}+a \cos \left (\beta x \right ) y+a b \cos \left (\beta x \right )-b^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.187 |
|
|
\[ {}y^{\prime } = y^{2}+a \cos \left (b x \right )^{m} y+a \cos \left (b x \right )^{m} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
13.831 |
|
|
\[ {}y^{\prime } = \lambda \cos \left (\lambda x \right ) y^{2}+\lambda \cos \left (\lambda x \right )^{3} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
15.277 |
|
|
\[ {}2 y^{\prime } = \left (\lambda +a -a \cos \left (\lambda x \right )\right ) y^{2}+\lambda -a -a \cos \left (\lambda x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
26.537 |
|
|
\[ {}y^{\prime } = \left (\lambda +a \cos \left (\lambda x \right )^{2}\right ) y^{2}+\lambda -a +a \cos \left (\lambda x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
8.991 |
|
|
\[ {}y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} \cos \left (x \right )^{m} y-a \cos \left (x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
21.884 |
|
|
\[ {}y^{\prime } = a \cos \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
5.94 |
|
|
\[ {}x y^{\prime } = a \cos \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \cos \left (\lambda x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
13.526 |
|
|
\[ {}\left (a \cos \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \cos \left (\mu x \right ) y-d^{2}+c d \cos \left (\mu x \right ) \] |
1 |
0 |
1 |
[_Riccati] |
✗ |
N/A |
75.735 |
|
|
\[ {}\left (a \cos \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )-a \,\lambda ^{2} \cos \left (\lambda x \right ) = 0 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.257 |
|
|
\[ {}y^{\prime } = y^{2}+a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
5.743 |
|
|
\[ {}y^{\prime } = y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
6.959 |
|
|
\[ {}y^{\prime } = a y^{2}+b \tan \left (x \right ) y+c \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.842 |
|
|
\[ {}y^{\prime } = a y^{2}+2 a b \tan \left (x \right ) y+b \left (a b -1\right ) \tan \left (x \right )^{2} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
2.634 |
|
|
\[ {}y^{\prime } = y^{2}+a \tan \left (\beta x \right ) y+a b \tan \left (\beta x \right )-b^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
62.734 |
|
|
\[ {}y^{\prime } = y^{2}+a x \tan \left (b x \right )^{m} y+a \tan \left (b x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
11.513 |
|
|
\[ {}y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} \tan \left (x \right )^{m} y-a \tan \left (x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
19.612 |
|
|
\[ {}y^{\prime } = a \tan \left (\lambda x \right )^{n} y^{2}-a \,b^{2} \tan \left (\lambda x \right )^{n +2}+b \lambda \tan \left (\lambda x \right )^{2}+b \lambda \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
67.178 |
|
|
\[ {}y^{\prime } = a \tan \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✗ |
N/A |
65.097 |
|
|
\[ {}x y^{\prime } = a \tan \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \tan \left (\lambda x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
20.34 |
|
|
\[ {}\left (a \tan \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+k \tan \left (\mu x \right ) y-d^{2}+k d \tan \left (\mu x \right ) \] |
1 |
0 |
1 |
[_Riccati] |
✗ |
N/A |
74.821 |
|
|
\[ {}y^{\prime } = y^{2}+a \lambda +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
6.776 |
|
|
\[ {}y^{\prime } = y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
8.389 |
|
|
\[ {}y^{\prime } = y^{2}-2 a b \cot \left (x a \right ) y+b^{2}-a^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
19.195 |
|
|
\[ {}y^{\prime } = y^{2}+a \cot \left (\beta x \right ) y+a b \cot \left (\beta x \right )-b^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
5.083 |
|
|
\[ {}y^{\prime } = y^{2}+a x \cot \left (b x \right )^{m} y+a \cot \left (b x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
8.09 |
|
|
\[ {}y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} \cot \left (x \right )^{m} y-a \cot \left (x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
19.724 |
|
|
\[ {}y^{\prime } = a \cot \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \] |
1 |
0 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✗ |
N/A |
64.715 |
|
|
\[ {}x y^{\prime } = a \cot \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \cot \left (\lambda x \right )^{m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
13.916 |
|
|
\[ {}\left (a \cot \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \cot \left (\mu x \right ) y-d^{2}+c d \cot \left (\mu x \right ) \] |
1 |
0 |
1 |
[_Riccati] |
✗ |
N/A |
76.847 |
|
|
\[ {}y^{\prime } = y^{2}+\lambda ^{2}+c \sin \left (\lambda x \right )^{n} \cos \left (\lambda x \right )^{-n -4} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
16.077 |
|
|
\[ {}y^{\prime } = a \sin \left (\lambda x \right ) y^{2}+b \sin \left (\lambda x \right ) \cos \left (\lambda x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
5.107 |
|
|
\[ {}y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+a \cos \left (\lambda x \right )^{n} y-a \cos \left (\lambda x \right )^{n -1} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
43.741 |
|
|
\[ {}y^{\prime } = a \cos \left (\lambda x \right ) y^{2}+b \cos \left (\lambda x \right ) \sin \left (\lambda x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
7.491 |
|
|
\[ {}y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+a \,x^{n} \cos \left (\lambda x \right ) y-a \,x^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
8.113 |
|
|
\[ {}\sin \left (2 x \right )^{n +1} y^{\prime } = a y^{2} \sin \left (x \right )^{2 n}+b \cos \left (x \right )^{2 n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
14.986 |
|
|
\[ {}y^{\prime } = y^{2}-y \tan \left (x \right )+a \left (1-a \right ) \cot \left (x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
6.871 |
|
|
\[ {}y^{\prime } = y^{2}-m y \tan \left (x \right )+b^{2} \cos \left (x \right )^{2 m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
117.879 |
|
|
\[ {}y^{\prime } = y^{2}+m y \cot \left (x \right )+b^{2} \sin \left (x \right )^{2 m} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
56.028 |
|
|
\[ {}y^{\prime } = y^{2}-2 \lambda ^{2} \tan \left (x \right )^{2}-2 \lambda ^{2} \cot \left (\lambda x \right )^{2} \] |
1 |
0 |
0 |
[_Riccati] |
✗ |
N/A |
108.796 |
|
|
\[ {}y^{\prime } = y^{2}+a \lambda +b \lambda +2 a b +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2}+b \left (\lambda -b \right ) \cot \left (\lambda x \right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
8.46 |
|
|
\[ {}y^{\prime } = y^{2}-\frac {\lambda ^{2}}{2}-\frac {3 \lambda ^{2} \tan \left (\lambda x \right )^{2}}{4}+a \cos \left (\lambda x \right )^{2} \sin \left (\lambda x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
15.905 |
|
|
\[ {}y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+a \sin \left (\lambda x \right ) y-a \tan \left (\lambda x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
5.273 |
|
|
\[ {}y^{\prime } = y^{2}+\lambda \arcsin \left (x \right )^{n} y-a^{2}+a \lambda \arcsin \left (x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.146 |
|
|
\[ {}y^{\prime } = y^{2}+\lambda x \arcsin \left (x \right )^{n} y+\arcsin \left (x \right )^{n} \lambda \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.367 |
|
|
\[ {}y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+\lambda \arcsin \left (x \right )^{n} \left (x^{1+k} y-1\right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
50.332 |
|
|
\[ {}y^{\prime } = \lambda \arcsin \left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \arcsin \left (x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
5.394 |
|
|
\[ {}y^{\prime } = \lambda \arcsin \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arcsin \left (x \right )^{n} y+b m \,x^{m -1} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
18.415 |
|
|
\[ {}y^{\prime } = \lambda \arcsin \left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arcsin \left (x \right )^{n} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
35.628 |
|
|
\[ {}y^{\prime } = \lambda \arcsin \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
18.722 |
|
|
\[ {}x y^{\prime } = \lambda \arcsin \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arcsin \left (x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
22.781 |
|
|
\[ {}x y^{\prime } = \left (a \,x^{2 m} y^{2}+b \,x^{n} y+c \right ) \arcsin \left (x \right )^{m}-n y \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
37.218 |
|
|
\[ {}y^{\prime } = y^{2}+\lambda \arccos \left (x \right )^{n} y-a^{2}+a \lambda \arccos \left (x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✗ |
15.007 |
|
|
\[ {}y^{\prime } = y^{2}+\lambda x \arccos \left (x \right )^{n} y+\lambda \arccos \left (x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
5.089 |
|
|
\[ {}y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+\lambda \arccos \left (x \right )^{n} \left (x^{1+k} y-1\right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
45.421 |
|
|
\[ {}y^{\prime } = \lambda \arccos \left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \arccos \left (x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
9.422 |
|
|
\[ {}y^{\prime } = \lambda \arccos \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arccos \left (x \right )^{n} y+b m \,x^{m -1} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
22.444 |
|
|
\[ {}y^{\prime } = \lambda \arccos \left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arccos \left (x \right )^{n} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
42.609 |
|
|
\[ {}y^{\prime } = \lambda \arccos \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
24.128 |
|
|
\[ {}x y^{\prime } = \lambda \arccos \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arccos \left (x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
23.808 |
|
|
\[ {}x y^{\prime } = \left (a \,x^{2 m} y^{2}+b \,x^{n} y+c \right ) \arccos \left (x \right )^{m}-n y \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
50.481 |
|
|
\[ {}y^{\prime } = y^{2}+\lambda \arctan \left (x \right )^{n} y-a^{2}+a \lambda \arctan \left (x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.76 |
|
|
\[ {}y^{\prime } = y^{2}+\lambda x \arctan \left (x \right )^{n} y+\arctan \left (x \right )^{n} \lambda \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
8.543 |
|
|
\[ {}y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+\lambda \arctan \left (x \right )^{n} \left (x^{1+k} y-1\right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
38.991 |
|
|
\[ {}y^{\prime } = \lambda \arctan \left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \arctan \left (x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
5.361 |
|
|
\[ {}y^{\prime } = \lambda \arctan \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arctan \left (x \right )^{n} y+b m \,x^{m -1} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
37.891 |
|
|
\[ {}y^{\prime } = \lambda \arctan \left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arctan \left (x \right )^{n} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
38.494 |
|
|
\[ {}y^{\prime } = \lambda \arctan \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
17.001 |
|
|
\[ {}x y^{\prime } = \lambda \arctan \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arctan \left (x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
34.692 |
|
|
\[ {}x y^{\prime } = \left (a \,x^{2 m} y^{2}+b \,x^{n} y+c \right ) \arctan \left (x \right )^{m}-n y \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
38.444 |
|
|
\[ {}y^{\prime } = y^{2}+\lambda \operatorname {arccot}\left (x \right )^{n} y-a^{2}+a \lambda \operatorname {arccot}\left (x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
4.935 |
|
|
\[ {}y^{\prime } = y^{2}+\lambda x \operatorname {arccot}\left (x \right )^{n} y+\operatorname {arccot}\left (x \right )^{n} \lambda \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
14.819 |
|
|
\[ {}y^{\prime } = -\left (1+k \right ) x^{k} y^{2}+\lambda \operatorname {arccot}\left (x \right )^{n} \left (x^{1+k} y-1\right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
40.262 |
|
|
\[ {}y^{\prime } = \lambda \operatorname {arccot}\left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \operatorname {arccot}\left (x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
8.333 |
|
|
\[ {}y^{\prime } = \lambda \operatorname {arccot}\left (x \right )^{n} y^{2}-b \lambda \,x^{m} \operatorname {arccot}\left (x \right )^{n} y+b m \,x^{m -1} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
40.612 |
|
|
\[ {}y^{\prime } = \lambda \operatorname {arccot}\left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \operatorname {arccot}\left (x \right )^{n} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
40.046 |
|
|
\[ {}y^{\prime } = \lambda \operatorname {arccot}\left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
22.6 |
|
|
\[ {}x y^{\prime } = \lambda \operatorname {arccot}\left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \operatorname {arccot}\left (x \right )^{n} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
35.312 |
|
|
\[ {}x y^{\prime } = \left (a \,x^{2 m} y^{2}+b \,x^{n} y+c \right ) \operatorname {arccot}\left (x \right )^{m}-n y \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
56.868 |
|
|
\[ {}y^{\prime } = y^{2}+f \left (x \right ) y-a^{2}-a f \left (x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.848 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}-a y-a b -b^{2} f \left (x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.316 |
|
|
\[ {}y^{\prime } = y^{2}+x f \left (x \right ) y+f \left (x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.094 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}-a \,x^{n} f \left (x \right ) y+a n \,x^{n -1} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
1.922 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}+a n \,x^{n -1}-a^{2} x^{2 n} f \left (x \right ) \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
2.168 |
|
|
\[ {}y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+x^{n +1} f \left (x \right ) y-f \left (x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.671 |
|
|
\[ {}x y^{\prime } = f \left (x \right ) y^{2}+n y+a \,x^{2 n} f \left (x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.434 |
|
|
\[ {}x y^{\prime } = x^{2 n} f \left (x \right ) y^{2}+\left (a \,x^{n} f \left (x \right )-n \right ) y+f \left (x \right ) b \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.541 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}+g \left (x \right ) y-a^{2} f \left (x \right )-a g \left (x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.256 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}+g \left (x \right ) y+a n \,x^{n -1}-a \,x^{n} g \left (x \right )-a^{2} x^{2 n} f \left (x \right ) \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
2.632 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}-a \,x^{n} g \left (x \right ) y+a n \,x^{n -1}+a^{2} x^{2 n} \left (g \left (x \right )-f \left (x \right )\right ) \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
2.948 |
|
|
\[ {}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+\lambda f \left (x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.315 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}-a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
4.577 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right ) \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
3.252 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}+\lambda y+a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.203 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}-f \left (x \right ) \left ({\mathrm e}^{\lambda x} a +b \right ) y+a \lambda \,{\mathrm e}^{\lambda x} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
5.406 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{\lambda x} f \left (x \right ) y^{2}+\left (a f \left (x \right )-\lambda \right ) y+b \,{\mathrm e}^{-\lambda x} f \left (x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.375 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}+g \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{\lambda x} g \left (x \right )-a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right ) \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
3.322 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}-a \,{\mathrm e}^{\lambda x} g \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x}+a^{2} {\mathrm e}^{2 \lambda x} \left (g \left (x \right )-f \left (x \right )\right ) \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
3.463 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} f \left (x \right ) {\mathrm e}^{2 \lambda \,x^{2}} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
2.914 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}+\lambda x y+a f \left (x \right ) {\mathrm e}^{\lambda x} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
2.235 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}-a \tanh \left (\lambda x \right )^{2} \left (a f \left (x \right )+\lambda \right )+a \lambda \] |
1 |
0 |
0 |
[_Riccati] |
✗ |
N/A |
266.436 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}-a \coth \left (\lambda x \right )^{2} \left (a f \left (x \right )+\lambda \right )+a \lambda \] |
1 |
0 |
0 |
[_Riccati] |
✗ |
N/A |
166.462 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \sinh \left (\lambda x \right )-a^{2} f \left (x \right ) \sinh \left (\lambda x \right )^{2} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
49.226 |
|
|
\[ {}x y^{\prime } = f \left (x \right ) y^{2}+a -a^{2} f \left (x \right ) \ln \left (x \right )^{2} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
4.026 |
|
|
\[ {}x y^{\prime } = f \left (x \right ) \left (y+a \ln \left (x \right )\right )^{2}-a \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
5.224 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}-a x \ln \left (x \right ) f \left (x \right ) y+a \ln \left (x \right )+a \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
1.733 |
|
|
\[ {}y^{\prime } = -a \ln \left (x \right ) y^{2}+a f \left (x \right ) \left (x \ln \left (x \right )-x \right ) y-f \left (x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
5.499 |
|
|
\[ {}y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+f \left (x \right ) \cos \left (\lambda x \right ) y-f \left (x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
10.557 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \sin \left (\lambda x \right )+a^{2} f \left (x \right ) \sin \left (\lambda x \right )^{2} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
53.092 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \cos \left (\lambda x \right )+a^{2} f \left (x \right ) \cos \left (\lambda x \right )^{2} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
53.049 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}-a \tan \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+a \lambda \] |
1 |
0 |
0 |
[_Riccati] |
✗ |
N/A |
176.561 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}-a \cot \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+a \lambda \] |
1 |
0 |
0 |
[_Riccati] |
✗ |
N/A |
151.456 |
|
|
\[ {}y^{\prime } = y^{2}-f \left (x \right )^{2}+f^{\prime }\left (x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
0.621 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}-f \left (x \right ) g \left (x \right ) y+g^{\prime }\left (x \right ) \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
0.8 |
|
|
\[ {}y^{\prime } = -f^{\prime }\left (x \right ) y^{2}+f \left (x \right ) g \left (x \right ) y-g \left (x \right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
0.904 |
|
|
\[ {}y^{\prime } = g \left (x \right ) \left (y-f \left (x \right )\right )^{2}+f^{\prime }\left (x \right ) \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
0.834 |
|
|
\[ {}y^{\prime } = \frac {y^{2} f^{\prime }\left (x \right )}{g \left (x \right )}-\frac {g^{\prime }\left (x \right )}{f \left (x \right )} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.332 |
|
|
\[ {}f \left (x \right )^{2} y^{\prime }-f^{\prime }\left (x \right ) y^{2}+g \left (x \right ) \left (y-f \left (x \right )\right ) = 0 \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
1.255 |
|
|
\[ {}y^{\prime } = f^{\prime }\left (x \right ) y^{2}+a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+{\mathrm e}^{\lambda x} a \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.279 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}+g^{\prime }\left (x \right ) y+a f \left (x \right ) {\mathrm e}^{2 g \left (x \right )} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
0.686 |
|
|
\[ {}y^{\prime } = y^{2}+a^{2} f \left (x a +b \right ) \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
0.684 |
|
|
\[ {}y^{\prime } = y^{2}+\frac {f \left (\frac {1}{x}\right )}{x^{4}} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
0.774 |
|
|
\[ {}y^{\prime } = y^{2}+\frac {f \left (\frac {x a +b}{c x +d}\right )}{\left (c x +d \right )^{4}} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
1.447 |
|
|
\[ {}x^{2} y^{\prime } = x^{4} f \left (x \right ) y^{2}+1 \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
1.27 |
|
|
\[ {}x^{2} y^{\prime } = x^{4} y^{2}+x^{2 n} f \left (a \,x^{n}+b \right )-\frac {n^{2}}{4}+\frac {1}{4} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
1.606 |
|
|
\[ {}y^{\prime } = f \left (x \right ) y^{2}+g \left (x \right ) y+h \left (x \right ) \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
0.952 |
|
|
\[ {}y^{\prime } = y^{2}+{\mathrm e}^{2 \lambda x} f \left ({\mathrm e}^{\lambda x}\right )-\frac {\lambda ^{2}}{4} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
1.012 |
|
|
\[ {}y^{\prime } = y^{2}-\frac {\lambda ^{2}}{4}+\frac {{\mathrm e}^{2 \lambda x} f \left (\frac {{\mathrm e}^{\lambda x} a +b}{c \,{\mathrm e}^{\lambda x}+d}\right )}{\left (c \,{\mathrm e}^{\lambda x}+d \right )^{4}} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
14.124 |
|
|
\[ {}y^{\prime } = y^{2}-\lambda ^{2}+\frac {f \left (\coth \left (\lambda x \right )\right )}{\sinh \left (\lambda x \right )^{4}} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
28.228 |
|
|
\[ {}y^{\prime } = y^{2}-\lambda ^{2}+\frac {f \left (\tanh \left (\lambda x \right )\right )}{\cosh \left (\lambda x \right )^{4}} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
10.156 |
|
|
\[ {}x^{2} y^{\prime } = x^{2} y^{2}+f \left (a \ln \left (x \right )+b \right )+\frac {1}{4} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
1.028 |
|
|
\[ {}y^{\prime } = y^{2}+\lambda ^{2}+\frac {f \left (\cot \left (\lambda x \right )\right )}{\sin \left (\lambda x \right )^{4}} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
29.443 |
|
|
\[ {}y^{\prime } = y^{2}+\lambda ^{2}+\frac {f \left (\tan \left (\lambda x \right )\right )}{\cos \left (\lambda x \right )^{4}} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
9.927 |
|
|
\[ {}y^{\prime } = y^{2}+\lambda ^{2}+\frac {f \left (\frac {\sin \left (\lambda x +a \right )}{\sin \left (\lambda x +b \right )}\right )}{\sin \left (\lambda x +b \right )^{4}} \] |
1 |
1 |
0 |
[_Riccati] |
✓ |
✓ |
61.176 |
|
|
\[ {}\left (1+x \right ) y^{2}-x^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.849 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.946 |
|
|
\[ {}y+2 x y^{2}-x^{2} y^{3}+2 x^{2} y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.801 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.939 |
|
|
\[ {}-y+x y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.434 |
|
|
\[ {}x y^{\prime }-a y+b y^{2} = c \,x^{2 a} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.706 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.538 |
|
|
\[ {}y+x y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.929 |
|
|
\[ {}x y^{\prime }+y-y^{2} \ln \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.163 |
|
|
\[ {}y^{\prime }+2 x y = x^{2}+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
2.116 |
|
|
\[ {}x^{\prime } = x^{2}+t^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
1.108 |
|
|
\[ {}R^{\prime } = \left (t +1\right ) \left (1+R^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.952 |
|
|
\[ {}\left (t +1\right ) x^{\prime }+x^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.79 |
|
|
|
||||||||
|
\[ {}x^{\prime } = \left (4 t -x\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
2.657 |
|
|
\[ {}x^{\prime } = 2 t x^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.859 |
|
|
\[ {}T^{\prime } = 2 a t \left (T^{2}-a^{2}\right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.982 |
|
|
\[ {}y^{\prime } = \frac {2 t y^{2}}{t^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.32 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 t y}{t^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.068 |
|
|
\[ {}y^{\prime } = -y^{2} {\mathrm e}^{-t^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.162 |
|
|
\[ {}x^{\prime } = t -x^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
0.973 |
|
|
\[ {}x^{\prime } = \left (t +x\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.888 |
|
|
\[ {}x^{\prime } = x \left (1+x \,{\mathrm e}^{t}\right ) \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
0.825 |
|
|
\[ {}t^{2} y^{\prime }+2 t y-y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.054 |
|
|
\[ {}x^{2}-t^{2} x^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.919 |
|
|
\[ {}y^{\prime } = \frac {y^{2}}{-2+x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.306 |
|
|
\[ {}y^{2}+2 x y-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.13 |
|
|
\[ {}2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.425 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = -\frac {y^{2}}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.38 |
|
|
\[ {}y^{\prime } = \left (1-x \right ) y^{2}+\left (2 x -1\right ) y-x \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.596 |
|
|
\[ {}y^{\prime } = -y^{2}+x y+1 \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.264 |
|
|
\[ {}y^{\prime } = -8 x y^{2}+4 x \left (1+4 x \right ) y-8 x^{3}-4 x^{2}+1 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
3.138 |
|
|
\[ {}2 x^{2}+x y+y^{2}+2 x^{2} y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
4.295 |
|
|
\[ {}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.773 |
|
|
\[ {}y^{\prime } = y^{2} {\mathrm e}^{-t^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.004 |
|
|
\[ {}x y+y^{2}+x^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.543 |
|
|
\[ {}y^{\prime }-\frac {y}{1+x}+y^{2} = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
1.172 |
|
|
\[ {}y^{\prime } = x +y^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
3.212 |
|
|
\[ {}y^{\prime } = x^{2}-y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.406 |
|
|
\[ {}y^{\prime } = x -y^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
1.542 |
|
|
\[ {}\left (x -y\right ) y-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.256 |
|
|
\[ {}x^{\prime } = \frac {x}{t}+\frac {x^{2}}{t^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.663 |
|
|
\[ {}y^{\prime }-\frac {3 y}{x}+x^{3} y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.12 |
|
|
\[ {}\left (x -y\right ) y-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.2 |
|
|
\[ {}x y^{\prime }+y-y^{2} \ln \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.475 |
|
|
\[ {}x^{2} y^{\prime } = 1+y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.689 |
|
|
\[ {}x y^{\prime }+y = x y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.898 |
|
|
\[ {}y^{\prime } = \frac {1+y^{2}}{x^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.121 |
|
|
\[ {}1+s^{2}-\sqrt {t}\, s^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.293 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }-x y+a x y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.735 |
|
|
\[ {}x y^{\prime } = \left (y \ln \left (x \right )-2\right ) y \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.277 |
|
|
\[ {}y-y^{\prime } \cos \left (x \right ) = y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
4.242 |
|
|
\[ {}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.786 |
|
|
\[ {}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.8 |
|
|
\[ {}x y^{\prime }+y-y^{2} \ln \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.868 |
|
|
\[ {}y^{\prime } = x +y^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
4.751 |
|
|
\[ {}y^{\prime } = x^{2}-y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
0.895 |
|
|
\[ {}y^{\prime } = -x^{2}+y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
0.799 |
|
|
\[ {}x y \left (1-y\right )-2 y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.379 |
|
|
\[ {}y^{\prime } = t^{2} y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.587 |
|
|
\[ {}y^{\prime } = 2 t y^{2}+3 y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.711 |
|
|
\[ {}y^{\prime } = t y^{2}+2 y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.93 |
|
|
\[ {}y^{\prime } = \left (1+y^{2}\right ) t \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.343 |
|
|
\[ {}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.02 |
|
|
\[ {}y^{\prime } = \left (y+\frac {1}{2}\right ) \left (t +y\right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.829 |
|
|
\[ {}y^{\prime } = t y+t y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.455 |
|
|
\[ {}y^{\prime } = t -y^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
4.531 |
|
|
\[ {}y^{\prime } = y^{2}-4 t \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
6.278 |
|
|
\[ {}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.585 |
|
|
\[ {}y^{\prime } = \left (y-2\right ) \left (y+1-\cos \left (t \right )\right ) \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
5.055 |
|
|
\[ {}x^{2} y^{\prime }+x y^{2} = x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.619 |
|
|
\[ {}y^{\prime }-y^{2} = x \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
0.812 |
|
|
\[ {}y^{\prime }+\left (8-x \right ) y-y^{2} = -8 x \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.43 |
|
|
\[ {}y^{\prime } = 3 y^{2}-\sin \left (x \right ) y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.945 |
|
|
\[ {}x y^{\prime } = \left (x -y\right )^{2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.31 |
|
|
\[ {}y^{\prime } = \frac {1+y^{2}}{x^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.79 |
|
|
\[ {}y^{\prime } = 3 y^{2}-\sin \left (x \right ) y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.82 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.79 |
|
|
\[ {}y^{\prime }-3 x^{2} y^{2} = -3 x^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.275 |
|
|
\[ {}y^{\prime }-3 x^{2} y^{2} = 3 x^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.945 |
|
|
\[ {}x y^{\prime } = y^{2}-y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.388 |
|
|
\[ {}x y^{\prime } = y^{2}-y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.352 |
|
|
\[ {}y^{\prime }-x y^{2} = \sqrt {x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.527 |
|
|
\[ {}y^{\prime } = 1+\left (x y+3 y\right )^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.67 |
|
|
\[ {}y^{\prime } = 1+\left (y-x \right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.104 |
|
|
\[ {}x^{2} y^{\prime }-x y = y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.936 |
|
|
\[ {}y^{\prime }-\frac {3 y}{x} = \frac {y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.058 |
|
|
\[ {}y^{\prime } = \left (x -y+3\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.824 |
|
|
\[ {}y^{\prime } = x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.08 |
|
|
\[ {}x y^{\prime } = 2 y^{2}-6 y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.752 |
|
|
\[ {}4 y^{2}-x^{2} y^{2}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.845 |
|
|
\[ {}y^{\prime } = x^{2}-2 x y+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.462 |
|
|
\[ {}y^{\prime } = \frac {3 y}{1+x}-y^{2} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
0.89 |
|
|
\[ {}y^{\prime } = x y^{2}+3 y^{2}+x +3 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.981 |
|
|
\[ {}y^{2}-y^{2} \cos \left (x \right )+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.0 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.803 |
|
|
\[ {}y^{\prime }+t^{2} = y^{2} \] |
1 |
0 |
1 |
[_Riccati] |
✗ |
N/A |
3.217 |
|
|
\[ {}y^{\prime } = 4 t^{2}-t y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
9.375 |
|
|
\[ {}y^{\prime } = t y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.537 |
|
|
\[ {}y^{\prime } = t^{2} y^{2}+y^{2}-t^{2}-1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.637 |
|
|
\[ {}4 \left (-1+x \right )^{2} y^{\prime }-3 \left (3+y\right )^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.885 |
|
|
\[ {}y^{\prime } = y^{2} \cos \left (t \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.333 |
|
|
\[ {}y^{\prime } = \left (x +y-4\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.074 |
|
|
\[ {}2 t y+y^{2}-t^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.324 |
|
|
\[ {}5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.608 |
|
|
\[ {}y^{\prime }+y = t y^{2} \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.944 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = t y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.211 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.177 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.685 |
|
|
\[ {}\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.791 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.98 |
|
|
\[ {}y-t y^{\prime } = 2 y^{2} \ln \left (t \right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
1.624 |
|
|
\[ {}y^{\prime } = -x +y^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
3.14 |
|
|
\[ {}y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
1.366 |
|
|
\[ {}y^{\prime } = x^{2}-y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.157 |
|
|
\[ {}y^{\prime } = x^{2}-y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.845 |
|
|
\[ {}y^{\prime } = x +y^{2} \] |
1 |
1 |
1 |
[[_Riccati, _special]] |
✓ |
✓ |
3.363 |
|
|
\[ {}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.477 |
|
|
\[ {}1+y^{2} = x y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.455 |
|
|
\[ {}a^{2}+y^{2}+2 x \sqrt {x a -x^{2}}\, y^{\prime } = 0 \] |
1 |
0 |
1 |
[_separable] |
✓ |
✓ |
5.954 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}-x y+x^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.745 |
|
|
\[ {}2 x^{2} y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.951 |
|
|
\[ {}y^{\prime }+2 x y = 2 x y^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.732 |
|
|
\[ {}y^{\prime }-y \cos \left (x \right ) = y^{2} \cos \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.376 |
|
|
\[ {}y^{\prime } {\mathrm e}^{-x}+y^{2}-2 \,{\mathrm e}^{x} y = 1-{\mathrm e}^{2 x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.674 |
|
|
\[ {}y^{\prime }+y^{2}-2 y \sin \left (x \right )+\sin \left (x \right )^{2}-\cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.881 |
|
|
\[ {}x y^{\prime }-y^{2}+\left (2 x +1\right ) y = x^{2}+2 x \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
0.905 |
|
|
\[ {}x^{2} y^{\prime } = x^{2} y^{2}+x y+1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
0.944 |
|
|
\[ {}y^{\prime } = \left (x -y\right )^{2}+1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.559 |
|
|
\[ {}y-x y^{2} \ln \left (x \right )+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
0.984 |
|
|
\[ {}y+x y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.939 |
|
|
\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \] |
1 |
1 |
1 |
[_Bernoulli] |
✓ |
✓ |
1.35 |
|
|
|
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|
|
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|
|