These are ode’s called First order homogeneous type D2 where change of variables \(y(x)=u(x)x\) is used and if this results in ode in \(u(x)\) which is either quadrature or separable, then it is used. Number of problems in this table is 938
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) |
|
\[ {}y^{\prime } = -x +y+1 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.482 |
|
|
\[ {}y^{\prime } = x -y+1 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.478 |
|
|
\[ {}y^{\prime }+2 x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.871 |
|
|
\[ {}y^{\prime } = \sin \left (x \right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.98 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = 4 y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.167 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = 2 y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.298 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.815 |
|
|
\[ {}y^{\prime } = -y+4 x^{3} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.009 |
|
|
\[ {}\tan \left (x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.139 |
|
|
\[ {}-y+x y^{\prime } = 2 x^{2} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.973 |
|
|
\[ {}x y^{\prime }+2 y = 3 x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.953 |
|
|
\[ {}y+3 x y^{\prime } = 12 x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.562 |
|
|
\[ {}-y+x y^{\prime } = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.707 |
|
|
\[ {}x y^{\prime }+y = 3 x y \] |
1 |
0 |
1 |
[_separable] |
✓ |
✓ |
1.724 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = x -y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.521 |
|
|
\[ {}2 x y y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.878 |
|
|
\[ {}\left (x -y\right ) y^{\prime } = x +y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.955 |
|
|
\[ {}x \left (x +y\right ) y^{\prime } = y \left (x -y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.985 |
|
|
\[ {}\left (2 y+x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.862 |
|
|
\[ {}x y^{2} y^{\prime } = y^{3}+x^{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.965 |
|
|
\[ {}x^{2} y^{\prime } = {\mathrm e}^{\frac {y}{x}} x^{2}+x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.047 |
|
|
\[ {}x^{2} y^{\prime } = x y+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.517 |
|
|
\[ {}x y y^{\prime } = x^{2}+3 y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.107 |
|
|
\[ {}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.424 |
|
|
\[ {}y \left (3 x +y\right )+x \left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.957 |
|
|
\[ {}2 x +3 y+\left (3 x +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.327 |
|
|
\[ {}4 x -y+\left (-x +6 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.744 |
|
|
\[ {}3 x^{2}+2 y^{2}+\left (4 x y+6 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.955 |
|
|
\[ {}\frac {2 x^{\frac {5}{2}}-3 y^{\frac {5}{3}}}{2 x^{\frac {5}{2}} y^{\frac {2}{3}}}+\frac {\left (-2 x^{\frac {5}{2}}+3 y^{\frac {5}{3}}\right ) y^{\prime }}{3 x^{\frac {3}{2}} y^{\frac {5}{3}}} = 0 \] |
1 |
1 |
6 |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
1.786 |
|
|
\[ {}x y+y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.591 |
|
|
\[ {}3 y+x^{4} y^{\prime } = 2 x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.549 |
|
|
\[ {}2 x y+x^{2} y^{\prime } = y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.942 |
|
|
\[ {}x^{2} y^{\prime } = x y+3 y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.075 |
|
|
\[ {}6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.483 |
|
|
\[ {}x^{3} y^{\prime } = x^{2} y-y^{3} \] |
1 |
2 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.033 |
|
|
\[ {}2 x^{2} y-x^{3} y^{\prime } = y^{3} \] |
1 |
2 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.299 |
|
|
\[ {}y^{\prime } = \frac {-3 x^{2}-2 y^{2}}{4 x y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.454 |
|
|
\[ {}y^{\prime } = \frac {x +3 y}{-3 x +y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.993 |
|
|
\[ {}-y+t y^{\prime } = t^{2} {\mathrm e}^{-t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.972 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+x y+y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.453 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+3 y^{2}}{2 x y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.633 |
|
|
\[ {}y^{\prime } = \frac {4 y-3 x}{2 x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.151 |
|
|
\[ {}y^{\prime } = -\frac {4 x +3 y}{y+2 x} \] |
1 |
1 |
9 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.331 |
|
|
\[ {}y^{\prime } = \frac {x +3 y}{x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.486 |
|
|
\[ {}x^{2}+3 x y+y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.265 |
|
|
\[ {}y^{\prime } = \frac {x^{2}-3 y^{2}}{2 x y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.742 |
|
|
\[ {}y^{\prime } = \frac {3 y^{2}-x^{2}}{2 x y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.518 |
|
|
\[ {}y+\left (t -4\right ) t y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.551 |
|
|
\[ {}y^{\prime } = -\frac {4 t}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.775 |
|
|
\[ {}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.393 |
|
|
\[ {}2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.071 |
|
|
\[ {}y^{\prime } = \frac {-x a -b y}{b x +c y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.531 |
|
|
\[ {}y^{\prime } = \frac {-x a +b y}{b x -c y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.492 |
|
|
\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.527 |
|
|
\[ {}2 x -y+\left (2 y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.914 |
|
|
\[ {}2 x y+3 x^{2} y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
✓ |
3.155 |
|
|
\[ {}3 x y+y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.201 |
|
|
\[ {}x +y+\left (2 y+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.832 |
|
|
\[ {}\left (1+{\mathrm e}^{x}\right ) y^{\prime } = y-{\mathrm e}^{x} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.78 |
|
|
\[ {}x y^{\prime } = x \,{\mathrm e}^{\frac {y}{x}}+y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.954 |
|
|
\[ {}3 t +2 y = -t y^{\prime } \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.25 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.519 |
|
|
\[ {}2 x y+3 y^{2}-\left (x^{2}+2 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.812 |
|
|
\[ {}y^{\prime }+3 x^{2} y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.029 |
|
|
\[ {}x y^{\prime }+y \ln \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.622 |
|
|
\[ {}x y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.262 |
|
|
\[ {}x^{2} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.134 |
|
|
\[ {}y^{\prime }+\frac {\left (1+x \right ) y}{x} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.648 |
|
|
\[ {}x y^{\prime }+\left (1+\frac {1}{\ln \left (x \right )}\right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.164 |
|
|
\[ {}x y^{\prime }+\left (1+x \cot \left (x \right )\right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.635 |
|
|
\[ {}y^{\prime }-\frac {2 x y}{x^{2}+1} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.544 |
|
|
\[ {}y^{\prime }+\frac {k y}{x} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.545 |
|
|
\[ {}y^{\prime }+\tan \left (k x \right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.376 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.148 |
|
|
\[ {}x +y y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.77 |
|
|
\[ {}\left (1+x \right ) \left (-2+x \right ) y^{\prime }+y = 0 \] |
1 |
0 |
1 |
[_separable] |
✓ |
✓ |
2.488 |
|
|
\[ {}y^{\prime } = 2 x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.059 |
|
|
\[ {}y^{\prime } = \frac {2 x +3 y}{x -4 y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.502 |
|
|
\[ {}y^{\prime } = \frac {y+x \,{\mathrm e}^{-\frac {y}{x}}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.342 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}+x y-x^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
3.518 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.011 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.347 |
|
|
\[ {}x y^{3} y^{\prime } = y^{4}+x^{4} \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.851 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\sec \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.759 |
|
|
\[ {}x^{2} y^{\prime } = x^{2}+x y+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.52 |
|
|
\[ {}x y y^{\prime } = x^{2}+2 y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.96 |
|
|
\[ {}y^{\prime } = \frac {2 y^{2}+x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}}{2 x y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
1.977 |
|
|
\[ {}y^{\prime } = \frac {x y+y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.893 |
|
|
\[ {}y^{\prime } = \frac {y^{3}+x^{3}}{x y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.781 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.448 |
|
|
\[ {}y^{\prime } = \frac {y^{2}-3 x y-5 x^{2}}{x^{2}} \] |
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 |
|
|
\[ {}x y y^{\prime } = 3 x^{2}+4 y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.984 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.582 |
|
|
\[ {}y^{\prime } = \frac {y^{3}+2 x y^{2}+x^{2} y+x^{3}}{x \left (x +y\right )^{2}} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.686 |
|
|
\[ {}y^{\prime } = \frac {2 y+x}{y+2 x} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.706 |
|
|
\[ {}y^{\prime } = \frac {y}{-2 x +y} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.826 |
|
|
\[ {}y^{\prime } = \frac {x y^{2}+2 y^{3}}{x^{3}+x^{2} y+x y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
87.84 |
|
|
\[ {}y^{\prime } = \frac {x^{3}+x^{2} y+3 y^{3}}{x^{3}+3 x y^{2}} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.707 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}+x y-4 x^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
3.735 |
|
|
\[ {}x y y^{\prime } = x^{2}-x y+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.616 |
|
|
\[ {}y^{\prime } = \frac {2 y^{2}-x y+2 x^{2}}{x y+2 x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.976 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+x y+y^{2}}{x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.73 |
|
|
\[ {}6 x^{2} y^{2}+4 x^{3} y y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.474 |
|
|
\[ {}4 x +7 y+\left (4 y+3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.97 |
|
|
\[ {}2 x +y+\left (2 y+2 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.662 |
|
|
\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.012 |
|
|
\[ {}7 x +4 y+\left (4 x +3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.935 |
|
|
\[ {}x^{2}+y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
2.431 |
|
|
\[ {}-y^{2}+x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.15 |
|
|
\[ {}y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.003 |
|
|
\[ {}3 x^{2} y+2 x^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.039 |
|
|
\[ {}27 x y^{2}+8 y^{3}+\left (18 x^{2} y+12 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
16 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.234 |
|
|
\[ {}x^{2} y+4 x y+2 y+\left (x^{2}+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.771 |
|
|
\[ {}-y+\left (x^{4}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.483 |
|
|
\[ {}x^{4} y^{4}+x^{5} y^{3} y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.446 |
|
|
\[ {}3 x y+2 y^{2}+y+\left (x^{2}+2 x y+x +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.622 |
|
|
\[ {}\cos \left (t \right ) y+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.659 |
|
|
\[ {}\sqrt {t}\, \sin \left (t \right ) y+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.694 |
|
|
\[ {}\sqrt {t^{2}+1}\, y+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.88 |
|
|
\[ {}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.794 |
|
|
\[ {}3 t y^{\prime } = \cos \left (t \right ) y \] |
1 |
0 |
1 |
[_separable] |
✓ |
✓ |
3.656 |
|
|
\[ {}2 t y y^{\prime } = 3 y^{2}-t^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.518 |
|
|
\[ {}y^{\prime } = \frac {t +y}{t -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.089 |
|
|
\[ {}{\mathrm e}^{\frac {t}{y}} \left (-t +y\right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.985 |
|
|
\[ {}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.492 |
|
|
\[ {}3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
7.145 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.477 |
|
|
\[ {}x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
6.561 |
|
|
\[ {}x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.438 |
|
|
\[ {}y^{\prime } = 2 x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.27 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.742 |
|
|
\[ {}x y+\sqrt {x^{2}+1}\, y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.79 |
|
|
\[ {}y = x y+x^{2} y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.965 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.68 |
|
|
\[ {}x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.239 |
|
|
\[ {}x^{2} y^{\prime }+y^{2} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.876 |
|
|
\[ {}x +y = x y^{\prime } \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.223 |
|
|
\[ {}\left (x +y\right ) y^{\prime }+x = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.139 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{x +4 y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.781 |
|
|
\[ {}x +y y^{\prime } = 2 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.059 |
|
|
\[ {}x^{2}+y^{2} = x y y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.809 |
|
|
\[ {}\left (x y-x^{2}\right ) y^{\prime }-y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.395 |
|
|
\[ {}x +y+\left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.725 |
|
|
\[ {}y \left (x^{2}-x y+y^{2}\right )+x y^{\prime } \left (x^{2}+x y+y^{2}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.396 |
|
|
\[ {}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.111 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\cosh \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.426 |
|
|
\[ {}x^{2}+y^{2} = 2 x y y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.511 |
|
|
\[ {}\left (\frac {x}{y}+\frac {y}{x}\right ) y^{\prime }+1 = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.8 |
|
|
\[ {}x \,{\mathrm e}^{\frac {y}{x}}+y = x y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.766 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
1 |
0 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.561 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.964 |
|
|
\[ {}\left (3 x y-2 x^{2}\right ) y^{\prime } = 2 y^{2}-x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
6.517 |
|
|
\[ {}y^{2} \left (y y^{\prime }-x \right )+x^{3} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.408 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\tanh \left (\frac {y}{x}\right ) \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.241 |
|
|
\[ {}x +y+\left (x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.179 |
|
|
\[ {}3 x +y+\left (x +3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.376 |
|
|
\[ {}2 x y-\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.753 |
|
|
\[ {}\frac {2 x y-1}{y}+\frac {\left (x +3 y\right ) y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.958 |
|
|
\[ {}\frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
1.707 |
|
|
\[ {}\frac {x y+1}{y}+\frac {\left (2 y-x \right ) y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.969 |
|
|
\[ {}\frac {x^{2}+3 y^{2}}{x \left (3 x^{2}+4 y^{2}\right )}+\frac {\left (2 x^{2}+y^{2}\right ) y^{\prime }}{y \left (3 x^{2}+4 y^{2}\right )} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
18.233 |
|
|
\[ {}\frac {x^{2}-y^{2}}{x \left (2 x^{2}+y^{2}\right )}+\frac {\left (x^{2}+2 y^{2}\right ) y^{\prime }}{y \left (2 x^{2}+y^{2}\right )} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
23.792 |
|
|
\[ {}x y^{\prime }+\ln \left (x \right )-y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.441 |
|
|
\[ {}y \left (y-x^{2}\right )+x^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.716 |
|
|
\[ {}2 x^{2} y y^{\prime }+x^{4} {\mathrm e}^{x}-2 x y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
2.105 |
|
|
\[ {}y \left (x^{2}-1\right )+x \left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.358 |
|
|
\[ {}y+\left (2 x -3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.38 |
|
|
\[ {}x y y^{\prime } = x^{2}-y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.55 |
|
|
\[ {}x^{2} y^{\prime }+y^{2} = x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.638 |
|
|
\[ {}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.587 |
|
|
\[ {}2 x +y-\left (x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.431 |
|
|
\[ {}x^{2} y-\left (y^{3}+x^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.58 |
|
|
\[ {}y+\left (3 x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.609 |
|
|
\[ {}r^{\prime } = r \cot \left (\theta \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.394 |
|
|
\[ {}\left (4 y+3 x \right ) y^{\prime }+y+2 x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.538 |
|
|
\[ {}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
3.323 |
|
|
\[ {}y \cos \left (\frac {x}{y}\right )-\left (y+x \cos \left (\frac {x}{y}\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.761 |
|
|
\[ {}x y-y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.412 |
|
|
\[ {}\left (-2 x^{2}-3 x y\right ) y^{\prime }+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.416 |
|
|
\[ {}x^{2}+y^{2} = 2 x y y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
3.538 |
|
|
\[ {}3 x y+\left (3 x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
6.322 |
|
|
\[ {}y^{3}+2 x^{2} y+\left (-3 x^{3}-2 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
10.947 |
|
|
\[ {}y^{\prime } = x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.436 |
|
|
\[ {}y^{\prime } = \frac {y}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.388 |
|
|
\[ {}y^{\prime } = -\frac {t}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.953 |
|
|
\[ {}y^{\prime } = \left (t^{2}+1\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.48 |
|
|
\[ {}t y^{\prime } = y+t^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.724 |
|
|
\[ {}y^{\prime } = \frac {2 y}{t +1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.977 |
|
|
\[ {}\frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.223 |
|
|
\[ {}2 x y^{\prime }+3 x +y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.684 |
|
|
\[ {}\left (y-x \right ) y^{\prime }+2 x +3 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.97 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.706 |
|
|
\[ {}y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}} \] |
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 |
|
|
\[ {}y^{\prime } = 2 x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.505 |
|
|
\[ {}y^{\prime } = \frac {y}{x \ln \left (x \right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.674 |
|
|
\[ {}y-\left (-2+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.615 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = 2 \ln \left (x \right ) x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.595 |
|
|
\[ {}\left (3 x -y\right ) y^{\prime } = 3 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.94 |
|
|
\[ {}y^{\prime } = \frac {\left (x +y\right )^{2}}{2 x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.915 |
|
|
\[ {}\sin \left (\frac {y}{x}\right ) \left (-y+x y^{\prime }\right ) = x \cos \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.482 |
|
|
\[ {}x \left (x^{2}-y^{2}\right )-x \left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.763 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y-2 x^{2}}{x^{2}-x y+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.046 |
|
|
\[ {}2 x y y^{\prime }-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}-2 y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
0.896 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}+3 x y+x^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.714 |
|
|
\[ {}2 x \left (y+2 x \right ) y^{\prime } = y \left (4 x -y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.148 |
|
|
\[ {}x y^{\prime } = x \tan \left (\frac {y}{x}\right )+y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.953 |
|
|
\[ {}y^{\prime } = \frac {y}{2 x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.488 |
|
|
\[ {}-y+x y^{\prime } = \ln \left (x \right ) x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.58 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = \frac {4 x^{2} \cos \left (x \right )}{y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
2.286 |
|
|
\[ {}y^{\prime } = \frac {-2 x +y}{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.744 |
|
|
\[ {}x^{3}+y^{3}-x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.392 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+y^{2}}{2 x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.107 |
|
|
\[ {}x y^{\prime } = x +y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.824 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{y+2 x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
7.978 |
|
|
\[ {}y y^{\prime } = x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.506 |
|
|
\[ {}x y^{\prime }+y = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.986 |
|
|
\[ {}-y+x y^{\prime } = x^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.661 |
|
|
\[ {}x y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.723 |
|
|
\[ {}\left (1-x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.188 |
|
|
\[ {}y^{\prime } = \frac {4 x y}{x^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.889 |
|
|
\[ {}y^{\prime } = \frac {2 y}{x^{2}-1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.866 |
|
|
\[ {}-y^{2}+x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.083 |
|
|
\[ {}y^{\prime }+2 x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.104 |
|
|
\[ {}\cot \left (x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.666 |
|
|
\[ {}x y^{\prime } = x y+y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.151 |
|
|
\[ {}\left (1-x \right ) y^{\prime } = x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.834 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime } = \left (x^{2}+1\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.848 |
|
|
\[ {}x y y^{\prime } = 2 x^{2}-y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.446 |
|
|
\[ {}x^{2}-y^{2}+x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.035 |
|
|
\[ {}x^{2} y^{\prime }-2 x y-2 y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.959 |
|
|
\[ {}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
5.107 |
|
|
\[ {}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.435 |
|
|
\[ {}x y^{\prime } = y+2 \,{\mathrm e}^{-\frac {y}{x}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
0.848 |
|
|
\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.069 |
|
|
\[ {}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.973 |
|
|
\[ {}1+y+\left (1-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.994 |
|
|
\[ {}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.34 |
|
|
\[ {}x y^{\prime } = x^{5}+x^{3} y^{2}+y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.711 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = y-x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.237 |
|
|
\[ {}x y^{\prime } = y+x^{2}+9 y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.45 |
|
|
\[ {}\left (x y-x^{2}\right ) y^{\prime } = y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.762 |
|
|
\[ {}y+x^{2} = x y^{\prime } \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.75 |
|
|
\[ {}y^{2}-3 x y-2 x^{2} = \left (x^{2}-x y\right ) y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.286 |
|
|
\[ {}2 x y+x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.918 |
|
|
\[ {}\frac {x}{x^{2}+y^{2}}+\frac {y}{x^{2}}+\left (\frac {y}{x^{2}+y^{2}}-\frac {1}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.257 |
|
|
\[ {}y^{\prime }+\frac {x}{y}+2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.401 |
|
|
\[ {}-y+x y^{\prime } = x \cot \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.013 |
|
|
\[ {}x \cos \left (\frac {y}{x}\right )^{2}-y+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.566 |
|
|
\[ {}x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.681 |
|
|
\[ {}\left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.858 |
|
|
\[ {}x^{2}-x y+y^{2}-x y y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.362 |
|
|
\[ {}2 x y+\left (x^{2}+2 x y+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.705 |
|
|
\[ {}y \left (2 x -y+2\right )+2 \left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.152 |
|
|
\[ {}x^{2}+y+y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.753 |
|
|
\[ {}y-2 x^{3} \tan \left (\frac {y}{x}\right )-x y^{\prime } = 0 \] |
1 |
2 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
3.208 |
|
|
\[ {}y^{\prime } = \frac {y+2}{1+x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.021 |
|
|
\[ {}x y^{\prime } = y-x \,{\mathrm e}^{\frac {y}{x}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.384 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{\frac {x y^{\prime }}{y}} \] |
0 |
2 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.599 |
|
|
\[ {}y^{\prime } = a \,x^{n} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.195 |
|
|
\[ {}y^{\prime } = y \cot \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.142 |
|
|
\[ {}y^{\prime } = \left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.082 |
|
|
\[ {}y^{\prime } = y \sec \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.773 |
|
|
\[ {}y^{\prime } = y \tan \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.871 |
|
|
\[ {}y^{\prime } = \left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.095 |
|
|
\[ {}x y^{\prime }+x +y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.751 |
|
|
\[ {}x y^{\prime }+x^{2}-y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.603 |
|
|
\[ {}x y^{\prime } = 1+x^{3}+y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.631 |
|
|
\[ {}x y^{\prime } = x^{m}+y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.914 |
|
|
\[ {}x y^{\prime } = x^{2} \sin \left (x \right )+y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.682 |
|
|
\[ {}x y^{\prime } = a y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.015 |
|
|
\[ {}x y^{\prime } = x a +b y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.046 |
|
|
\[ {}x y^{\prime }+\left (b x +a \right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.05 |
|
|
\[ {}x y^{\prime } = x^{3}+\left (-2 x^{2}+1\right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.874 |
|
|
\[ {}x y^{\prime } = x^{2}+y \left (y+1\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.05 |
|
|
\[ {}x y^{\prime } = x^{2} a +y+b y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.128 |
|
|
\[ {}x y^{\prime } = \left (1-x y\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.707 |
|
|
\[ {}x y^{\prime } = \left (x y+1\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.716 |
|
|
\[ {}x y^{\prime } = x^{3}+\left (2 x^{2}+1\right ) y+x y^{2} \] |
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 |
|
|
\[ {}x y^{\prime } = y+\left (x^{2}-y^{2}\right ) f \left (x \right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
1.607 |
|
|
\[ {}x y^{\prime } = y \left (1+y^{2}\right ) \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.431 |
|
|
\[ {}x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.011 |
|
|
\[ {}x y^{\prime } = y-x \cos \left (\frac {y}{x}\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.992 |
|
|
\[ {}x y^{\prime }-y+x \sec \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.012 |
|
|
\[ {}x y^{\prime } = y+x \sec \left (\frac {y}{x}\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.026 |
|
|
\[ {}x y^{\prime } = y+x \sin \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.843 |
|
|
\[ {}x y^{\prime } = y-x \tan \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.0 |
|
|
\[ {}x y^{\prime } = x \,{\mathrm e}^{\frac {y}{x}}+y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.691 |
|
|
\[ {}x y^{\prime } = x +y+x \,{\mathrm e}^{\frac {y}{x}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.001 |
|
|
\[ {}x y^{\prime } = y-2 x \tanh \left (\frac {y}{x}\right ) \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.108 |
|
|
\[ {}x^{2} y^{\prime } = a +b x +c \,x^{2}+x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.619 |
|
|
\[ {}x^{2} y^{\prime } = \left (b x +a \right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.684 |
|
|
\[ {}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.688 |
|
|
\[ {}x^{2} y^{\prime } = \left (a y+x \right ) y \] |
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 |
|
|
\[ {}x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y = 0 \] |
1 |
2 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.843 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = 5-x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.663 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+a -x y = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.687 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.552 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = \left (2 b x +a \right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.69 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime } = b +x y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.928 |
|
|
\[ {}x \left (1+x \right ) y^{\prime } = \left (1-2 x \right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.655 |
|
|
\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.49 |
|
|
\[ {}2 x^{2} y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.647 |
|
|
\[ {}2 x^{2} y^{\prime } = 2 x y+\left (1-x \cot \left (x \right )\right ) \left (x^{2}-y^{2}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
1.714 |
|
|
\[ {}a \,x^{2} y^{\prime } = x^{2}+a x y+b^{2} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.956 |
|
|
\[ {}x^{3} y^{\prime } = 3-x^{2}+x^{2} y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.605 |
|
|
\[ {}x^{3} y^{\prime } = y \left (y+x^{2}\right ) \] |
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 |
|
|
\[ {}x^{3} y^{\prime } = \left (2 x^{2}+y^{2}\right ) y \] |
1 |
2 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.748 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime } = a \,x^{3}+y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.788 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime } = \left (-x^{2}+1\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.647 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime } = \left (x^{2}-x +1\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.71 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime } = a \,x^{3}+\left (-2 x^{2}+1\right ) y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.964 |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime } = \left (2-x \right ) x y-y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.813 |
|
|
\[ {}2 x^{3} y^{\prime } = \left (x^{2}-y^{2}\right ) y \] |
1 |
2 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.756 |
|
|
\[ {}2 x^{3} y^{\prime } = \left (3 x^{2}+a y^{2}\right ) y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.921 |
|
|
\[ {}x \left (c \,x^{2}+b x +a \right ) y^{\prime }+x^{2}-\left (c \,x^{2}+b x +a \right ) y = y^{2} \] |
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 |
|
|
\[ {}x \left (-2 x^{3}+1\right ) y^{\prime } = 2 \left (-x^{3}+1\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.826 |
|
|
\[ {}x \left (-x^{4}+1\right ) y^{\prime } = 2 x \left (x^{2}-y^{2}\right )+\left (-x^{4}+1\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.354 |
|
|
\[ {}\left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime } = \tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.974 |
|
|
\[ {}\left (1-\sin \left (x \right )\right ) y^{\prime }+y \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.358 |
|
|
\[ {}\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.652 |
|
|
\[ {}y^{\prime } x \ln \left (x \right ) = a x \left (1+\ln \left (x \right )\right )-y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.815 |
|
|
\[ {}x +y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
0.987 |
|
|
\[ {}y y^{\prime }+x a +b y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
11.408 |
|
|
\[ {}y y^{\prime }+4 \left (1+x \right ) x +y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.223 |
|
|
\[ {}\left (x +y\right ) y^{\prime }+y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.407 |
|
|
\[ {}\left (x -y\right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.863 |
|
|
\[ {}\left (x +y\right ) y^{\prime }+x -y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.908 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = x -y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.351 |
|
|
\[ {}\left (x -y\right ) y^{\prime } = y \left (1+2 x y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.059 |
|
|
\[ {}\left (x -y\right ) y^{\prime } = \left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.217 |
|
|
\[ {}\left (y+2 x \right ) y^{\prime }+x -2 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.872 |
|
|
\[ {}\left (4 x -y\right ) y^{\prime }+2 x -5 y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.383 |
|
|
\[ {}2 y y^{\prime }+2 x +x^{2}+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.248 |
|
|
\[ {}\left (x -2 y\right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.911 |
|
|
\[ {}\left (2 y+x \right ) y^{\prime }+2 x -y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.891 |
|
|
\[ {}\left (x -2 y\right ) y^{\prime }+2 x +y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.19 |
|
|
\[ {}\left (x +4 y\right ) y^{\prime }+4 x -y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.891 |
|
|
\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.203 |
|
|
\[ {}\left (x a +b y\right ) y^{\prime }+x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
17.747 |
|
|
\[ {}\left (x a +b y\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.525 |
|
|
\[ {}\left (x a +b y\right ) y^{\prime }+b x +a y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.478 |
|
|
\[ {}\left (x a +b y\right ) y^{\prime } = b x +a y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.796 |
|
|
\[ {}x y y^{\prime } = x +y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.72 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.955 |
|
|
\[ {}x y y^{\prime }+x^{4}-y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.75 |
|
|
\[ {}x y y^{\prime } = a \,x^{3} \cos \left (x \right )+y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
0.971 |
|
|
\[ {}x y y^{\prime } = x^{2}-x y+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.839 |
|
|
\[ {}x y y^{\prime }+2 x^{2}-2 x y-y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.984 |
|
|
\[ {}x y y^{\prime }+x^{2} \operatorname {arccot}\left (\frac {y}{x}\right )-y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.49 |
|
|
\[ {}x y y^{\prime }+x^{2} {\mathrm e}^{-\frac {2 y}{x}}-y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.916 |
|
|
\[ {}x \left (x +y\right ) y^{\prime }+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.396 |
|
|
\[ {}x \left (x -y\right ) y^{\prime }+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.925 |
|
|
\[ {}x \left (x +y\right ) y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.95 |
|
|
\[ {}x \left (x -y\right ) y^{\prime }+2 x^{2}+3 x y-y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.451 |
|
|
\[ {}x \left (y+2 x \right ) y^{\prime } = x^{2}+x y-y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.181 |
|
|
\[ {}x \left (4 x -y\right ) y^{\prime }+4 x^{2}-6 x y-y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.661 |
|
|
\[ {}\left (x +a \right ) \left (x +b \right ) y^{\prime } = x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.069 |
|
|
\[ {}x^{2}+y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.293 |
|
|
\[ {}2 x y y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.924 |
|
|
\[ {}x \left (x -2 y\right ) y^{\prime }+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.421 |
|
|
\[ {}x \left (2 y+x \right ) y^{\prime }+\left (2 x -y\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.434 |
|
|
\[ {}x \left (x -2 y\right ) y^{\prime }+\left (2 x -y\right ) y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.526 |
|
|
\[ {}x \left (2 x +3 y\right ) y^{\prime } = y^{2} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.437 |
|
|
\[ {}x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.763 |
|
|
\[ {}a x y y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.403 |
|
|
\[ {}a x y y^{\prime }+x^{2}-y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.078 |
|
|
\[ {}x \left (x -a y\right ) y^{\prime } = y \left (-x a +y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.023 |
|
|
\[ {}\left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right ) = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
3.071 |
|
|
\[ {}2 x^{2} y y^{\prime } = x^{2} \left (2 x +1\right )-y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.65 |
|
|
\[ {}x^{2} \left (x -2 y\right ) y^{\prime } = 2 x^{3}-4 x y^{2}+y^{3} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
2.968 |
|
|
\[ {}x^{2} \left (4 x -3 y\right ) y^{\prime } = \left (6 x^{2}-3 x y+2 y^{2}\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.125 |
|
|
\[ {}8 x^{3} y y^{\prime }+3 x^{4}-6 x^{2} y^{2}-y^{4} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.09 |
|
|
\[ {}x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.749 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime } = x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.924 |
|
|
\[ {}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.559 |
|
|
\[ {}\left (x^{2}-y^{2}\right ) y^{\prime }+x \left (2 y+x \right ) = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
7.746 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
9.385 |
|
|
\[ {}\left (3 x^{2}-y^{2}\right ) y^{\prime } = 2 x y \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.833 |
|
|
\[ {}\left (x^{2}+2 x y-y^{2}\right ) y^{\prime }+x^{2}-2 x y+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.846 |
|
|
\[ {}\left (x +y\right )^{2} y^{\prime } = x^{2}-2 x y+5 y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.983 |
|
|
\[ {}\left (2 x^{2}+4 x y-y^{2}\right ) y^{\prime } = x^{2}-4 x y-2 y^{2} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
3.232 |
|
|
\[ {}\left (3 x +y\right )^{2} y^{\prime } = 4 \left (3 x +2 y\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.04 |
|
|
\[ {}\left (2 x^{2}+3 y^{2}\right ) y^{\prime }+x \left (3 x +y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.871 |
|
|
\[ {}\left (3 x^{2}+2 x y+4 y^{2}\right ) y^{\prime }+2 x^{2}+6 x y+y^{2} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
1.765 |
|
|
\[ {}\left (x^{2}+a y^{2}\right ) y^{\prime } = x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.386 |
|
|
\[ {}\left (x^{2}+x y+a y^{2}\right ) y^{\prime } = x^{2} a +x y+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.31 |
|
|
\[ {}\left (x^{2} a +2 x y-a y^{2}\right ) y^{\prime }+x^{2}-2 a x y-y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
10.048 |
|
|
\[ {}\left (x^{2} a +2 b x y+c y^{2}\right ) y^{\prime }+k \,x^{2}+2 a x y+b y^{2} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
3.106 |
|
|
\[ {}x \left (x^{2}+y^{2}\right ) y^{\prime } = \left (x^{2}+x^{4}+y^{2}\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
✓ |
1.078 |
|
|
\[ {}x \left (2 x^{2}+y^{2}\right ) y^{\prime } = \left (2 x^{2}+3 y^{2}\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.135 |
|
|
\[ {}x \left (x^{2}-x y+y^{2}\right ) y^{\prime }+\left (x^{2}+x y+y^{2}\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.157 |
|
|
\[ {}x \left (x^{2}-x y-y^{2}\right ) y^{\prime } = \left (x^{2}+x y-y^{2}\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.309 |
|
|
|
||||||||
|
\[ {}x \left (x^{2}+a x y+y^{2}\right ) y^{\prime } = \left (x^{2}+b x y+y^{2}\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.513 |
|
|
\[ {}x \left (x^{2}-2 y^{2}\right ) y^{\prime } = \left (2 x^{2}-y^{2}\right ) y \] |
1 |
1 |
6 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.329 |
|
|
\[ {}x \left (x^{2}+2 y^{2}\right ) y^{\prime } = \left (2 x^{2}+3 y^{2}\right ) y \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.257 |
|
|
\[ {}2 x \left (5 x^{2}+y^{2}\right ) y^{\prime } = x^{2} y-y^{3} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.391 |
|
|
\[ {}x \left (x^{2}+a x y+2 y^{2}\right ) y^{\prime } = \left (x a +2 y\right ) y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.135 |
|
|
\[ {}x \left (x^{2}-6 y^{2}\right ) y^{\prime } = 4 \left (x^{2}+3 y^{2}\right ) y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.709 |
|
|
\[ {}\left (x^{3}-y^{3}\right ) y^{\prime }+x^{2} y = 0 \] |
1 |
1 |
10 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.447 |
|
|
\[ {}\left (y^{3}+x^{3}\right ) y^{\prime }+x^{2} \left (x a +3 y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
4.654 |
|
|
\[ {}\left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right ) = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
1.694 |
|
|
\[ {}2 y^{3} y^{\prime } = x^{3}-x y^{2} \] |
1 |
1 |
6 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
6.335 |
|
|
\[ {}\left (3 x^{2}+2 y^{2}\right ) y y^{\prime }+x^{3} = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.286 |
|
|
\[ {}\left (5 x^{2}+2 y^{2}\right ) y y^{\prime }+x \left (x^{2}+5 y^{2}\right ) = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
1.744 |
|
|
\[ {}\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
3.194 |
|
|
\[ {}\left (x^{3}+a y^{3}\right ) y^{\prime } = x^{2} y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.381 |
|
|
\[ {}x \left (2 x^{3}+y^{3}\right ) y^{\prime } = \left (2 x^{3}-x^{2} y+y^{3}\right ) y \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.92 |
|
|
\[ {}x \left (2 x^{3}-y^{3}\right ) y^{\prime } = \left (x^{3}-2 y^{3}\right ) y \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.336 |
|
|
\[ {}x \left (x^{3}+3 x^{2} y+y^{3}\right ) y^{\prime } = \left (3 x^{2}+y^{2}\right ) y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.106 |
|
|
\[ {}x \left (x^{3}-2 y^{3}\right ) y^{\prime } = \left (2 x^{3}-y^{3}\right ) y \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.612 |
|
|
\[ {}\left (a \,x^{3}+\left (x a +b y\right )^{3}\right ) y y^{\prime }+x \left (\left (x a +b y\right )^{3}+b y^{3}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.631 |
|
|
\[ {}x \left (x -y \tan \left (\frac {y}{x}\right )\right ) y^{\prime }+\left (x +y \tan \left (\frac {y}{x}\right )\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.917 |
|
|
\[ {}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2} \] |
2 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.948 |
|
|
\[ {}\left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-x y-2 y^{2}\right ) y^{\prime }-y \left (x -y\right ) = 0 \] |
2 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.136 |
|
|
\[ {}\left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-4 x^{2}+y^{2} = 0 \] |
2 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.957 |
|
|
\[ {}4 x^{2} y^{2} {y^{\prime }}^{2} = \left (x^{2}+y^{2}\right )^{2} \] |
2 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.309 |
|
|
\[ {}\left (2 y+x \right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (y+2 x \right ) y^{\prime } = 0 \] |
3 |
1 |
4 |
[_quadrature] |
✓ |
✓ |
1.062 |
|
|
\[ {}y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0 \] |
0 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.098 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}-y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.12 |
|
|
\[ {}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
5.584 |
|
|
\[ {}y+x y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.744 |
|
|
\[ {}\left (y-x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.105 |
|
|
\[ {}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.442 |
|
|
\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.527 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.347 |
|
|
\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.67 |
|
|
\[ {}x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.637 |
|
|
\[ {}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.676 |
|
|
\[ {}y = x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}} \] |
1 |
2 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
5.283 |
|
|
\[ {}2 x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
9.542 |
|
|
\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.359 |
|
|
\[ {}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.28 |
|
|
\[ {}2 x^{2} y+y^{3}+\left (x y^{2}-2 x^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.447 |
|
|
\[ {}\frac {y \cos \left (\frac {y}{x}\right )}{x}-\left (\frac {x \sin \left (\frac {y}{x}\right )}{y}+\cos \left (\frac {y}{x}\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.806 |
|
|
\[ {}y+x \ln \left (\frac {y}{x}\right ) y^{\prime }-2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.474 |
|
|
\[ {}2 y \,{\mathrm e}^{\frac {x}{y}}+\left (y-2 x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.985 |
|
|
\[ {}x \,{\mathrm e}^{\frac {y}{x}}-y \sin \left (\frac {y}{x}\right )+x \sin \left (\frac {y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.615 |
|
|
\[ {}x^{2}+y^{2} = 2 x y y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.574 |
|
|
\[ {}x \,{\mathrm e}^{\frac {y}{x}}+y = x y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.81 |
|
|
\[ {}y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.86 |
|
|
\[ {}x y-y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.472 |
|
|
\[ {}-y+x y^{\prime } = x^{2} \sin \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.083 |
|
|
\[ {}x y^{\prime }+x y^{2}-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.94 |
|
|
\[ {}x^{2} \left (-1+x \right ) y^{\prime }-y^{2}-x \left (-2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.212 |
|
|
\[ {}y^{\prime } = 1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
3.303 |
|
|
\[ {}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.274 |
|
|
\[ {}2 y-x y \ln \left (x \right )-2 y^{\prime } x \ln \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.997 |
|
|
\[ {}x y^{\prime } = x +y+x \,{\mathrm e}^{\frac {y}{x}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.658 |
|
|
\[ {}x^{3} y^{\prime }-y^{2}-x^{2} y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.043 |
|
|
\[ {}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.015 |
|
|
\[ {}\left (x y-x^{2}\right ) y^{\prime }+y^{2}-3 x y-2 x^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.047 |
|
|
\[ {}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.434 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.011 |
|
|
\[ {}2 x y y^{\prime }+3 x^{2}-y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.442 |
|
|
\[ {}\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
10.768 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
12.457 |
|
|
\[ {}2 y^{3} y^{\prime }+x y^{2}-x^{3} = 0 \] |
1 |
1 |
6 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
6.738 |
|
|
\[ {}y^{\prime }+y \tan \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.778 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.135 |
|
|
\[ {}x y+\left (-x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.023 |
|
|
\[ {}y^{2}-x y+\left (x y+x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.007 |
|
|
\[ {}y^{\prime } = \frac {y}{x}-\tan \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.213 |
|
|
\[ {}y^{\prime } = \frac {2 y^{2}}{x}+\frac {y}{x}-2 x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.372 |
|
|
\[ {}x^{2} y^{\prime }-x y = \frac {1}{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.643 |
|
|
\[ {}y+2 x -x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.604 |
|
|
\[ {}\left (y+2 x \right ) y^{\prime }-x +2 y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.436 |
|
|
\[ {}\sin \left (x \right )^{2} y^{\prime }+\sin \left (x \right )^{2}+\left (x +y\right ) \sin \left (2 x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.256 |
|
|
\[ {}3 x^{2} y+x^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.992 |
|
|
\[ {}-y+x y^{\prime } = x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.856 |
|
|
\[ {}x y^{\prime } = x y+y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.536 |
|
|
\[ {}y^{\prime } = 3 x^{2} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.51 |
|
|
\[ {}x y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.454 |
|
|
\[ {}x^{\prime } = 3 x t^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.547 |
|
|
\[ {}y^{\prime } = 2 y-2 t y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.283 |
|
|
\[ {}\left (t^{2}+1\right ) y^{\prime } = t y-y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.053 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+2 x +1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.583 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = x \,{\mathrm e}^{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.122 |
|
|
\[ {}x^{2} y+x^{4} \cos \left (x \right )-x^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.118 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = x y+1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.216 |
|
|
\[ {}-y+x y^{\prime } = x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.578 |
|
|
\[ {}\left (x^{3}+x y^{2}\right ) y^{\prime } = 2 y^{3} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.816 |
|
|
\[ {}x^{2}-2 x y+5 y^{2} = \left (x^{2}+2 x y+y^{2}\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.461 |
|
|
\[ {}y+\left (x^{2}-4 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.238 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}+2 x y} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.571 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}-x y y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.341 |
|
|
\[ {}x^{2} y^{\prime }+y^{2} = x y y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.405 |
|
|
\[ {}2 x y y^{\prime } = x^{2}-y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.6 |
|
|
\[ {}x \left (1+y^{2}\right )-\left (x^{2}+1\right ) y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.521 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.075 |
|
|
\[ {}x y^{\prime } = 2 y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.257 |
|
|
\[ {}y y^{\prime }+x = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.714 |
|
|
\[ {}2 x^{3} y^{\prime } = y \left (3 x^{2}+y^{2}\right ) \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.546 |
|
|
\[ {}4 y+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.306 |
|
|
\[ {}y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.185 |
|
|
\[ {}1+y-\left (1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.408 |
|
|
\[ {}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.992 |
|
|
\[ {}y^{2} \left (x^{2}+2\right )+\left (y^{3}+x^{3}\right ) \left (y-x y^{\prime }\right ) = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
✓ |
1.699 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.198 |
|
|
\[ {}y^{2}-x^{2}+x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.685 |
|
|
\[ {}x^{3}+y^{3}+3 x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
2.03 |
|
|
\[ {}x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.536 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.356 |
|
|
\[ {}y \left (x -2 y\right )-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.345 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.536 |
|
|
\[ {}x^{2}+y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.734 |
|
|
\[ {}y^{\prime }+y = 2 x +2 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.349 |
|
|
\[ {}y^{\prime }-y = x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.299 |
|
|
\[ {}y-2 x y+x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.016 |
|
|
\[ {}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.745 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.875 |
|
|
\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.274 |
|
|
\[ {}\frac {1}{y}+\sec \left (\frac {y}{x}\right )-\frac {x y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
23.208 |
|
|
\[ {}y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.178 |
|
|
\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.446 |
|
|
\[ {}x^{2}-y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.927 |
|
|
\[ {}-y+x y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.256 |
|
|
\[ {}x +y y^{\prime }+y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.022 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.06 |
|
|
\[ {}y^{\prime } = x^{2} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.765 |
|
|
\[ {}y y^{\prime } = x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.651 |
|
|
\[ {}x y^{\prime } = 2 y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.975 |
|
|
\[ {}x y^{\prime } = y+x^{2}+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.287 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.279 |
|
|
\[ {}2 x y y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.457 |
|
|
\[ {}y^{\prime } = \frac {y^{2}}{x y-x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.466 |
|
|
\[ {}x y^{\prime } = 2 x^{2} y+y \ln \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.501 |
|
|
\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.158 |
|
|
\[ {}1+y+\left (1-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.761 |
|
|
\[ {}x y^{\prime }+y = x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.171 |
|
|
\[ {}x^{2} y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.053 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+y^{2}}{x^{2}-y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.42 |
|
|
\[ {}y^{\prime } = \frac {2 y+x}{2 x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.238 |
|
|
\[ {}2 x y+x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.572 |
|
|
\[ {}-y+x y^{\prime } = 2 x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.21 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.302 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+2 y^{2}}{x^{2}-2 y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.646 |
|
|
\[ {}\frac {1}{y}-\frac {x y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.627 |
|
|
\[ {}y^{\prime } = 2 x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.815 |
|
|
\[ {}x y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.5 |
|
|
\[ {}x^{2} y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.664 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = x^{2} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.743 |
|
|
\[ {}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2} \] |
2 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.195 |
|
|
\[ {}\left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y = 0 \] |
2 |
1 |
3 |
[_quadrature] |
✓ |
✓ |
0.836 |
|
|
\[ {}\left (x -y\right )^{2} {y^{\prime }}^{2} = y^{2} \] |
2 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.11 |
|
|
\[ {}\left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2} = 4 x^{2} y^{2} \] |
2 |
1 |
5 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.7 |
|
|
\[ {}\left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+x y-x^{2}\right ) y^{\prime }+y \left (y-x \right ) = 0 \] |
2 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.439 |
|
|
\[ {}x y \left (x^{2}+y^{2}\right ) \left ({y^{\prime }}^{2}-1\right ) = y^{\prime } \left (x^{4}+x^{2} y^{2}+y^{4}\right ) \] |
2 |
1 |
6 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.103 |
|
|
\[ {}y^{\prime } = \frac {y}{x \ln \left (x \right )} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.048 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{x +4 y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.537 |
|
|
\[ {}y^{\prime } = \frac {2 y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.167 |
|
|
\[ {}y^{\prime } = \frac {2 y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.577 |
|
|
\[ {}x^{2} y^{\prime }+y^{2} = x y y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.532 |
|
|
\[ {}y^{\prime } = \frac {5 x^{2}-x y+y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
2.058 |
|
|
\[ {}y y^{\prime }-y = x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.423 |
|
|
\[ {}y^{\prime } = \frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
4.036 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{-\frac {y}{x}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.303 |
|
|
\[ {}y^{\prime } = 2 x^{2} \sin \left (\frac {y}{x}\right )^{2}+\frac {y}{x} \] |
1 |
2 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
4.247 |
|
|
\[ {}y^{\prime } = a x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.506 |
|
|
\[ {}y^{\prime } = \cos \left (x \right )+\frac {y}{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.673 |
|
|
\[ {}y^{\prime }-\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.509 |
|
|
\[ {}x y^{\prime }-y-\frac {x}{\ln \left (x \right )} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.069 |
|
|
\[ {}x y^{\prime }-y-x^{2} \sin \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.191 |
|
|
\[ {}x y^{\prime }-y-\frac {x \cos \left (\ln \left (\ln \left (x \right )\right )\right )}{\ln \left (x \right )} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
3.878 |
|
|
\[ {}x y^{\prime }+a y^{2}-y+b \,x^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.899 |
|
|
\[ {}x y^{\prime }+x y^{2}-y = 0 \] |
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 |
|
|
\[ {}x y^{\prime }-x \,{\mathrm e}^{\frac {y}{x}}-y-x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.657 |
|
|
\[ {}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.385 |
|
|
\[ {}x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.705 |
|
|
\[ {}x y^{\prime }+x \tan \left (\frac {y}{x}\right )-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.679 |
|
|
\[ {}x^{2} y^{\prime }-\left (-1+x \right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.096 |
|
|
\[ {}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0 \] |
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 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }-x y+a = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.601 |
|
|
\[ {}3 x^{2} y^{\prime }-7 y^{2}-3 x y-x^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.614 |
|
|
\[ {}x^{3} y^{\prime }-y^{2}-x^{2} y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.181 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime }+x^{2} y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.967 |
|
|
\[ {}x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.795 |
|
|
\[ {}x^{2} \left (-1+x \right ) y^{\prime }-y^{2}-x \left (-2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.302 |
|
|
\[ {}\left (x^{2} a +b x +c \right ) \left (-y+x y^{\prime }\right )-y^{2}+x^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
2.892 |
|
|
\[ {}\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.318 |
|
|
\[ {}y^{\prime } x \ln \left (x \right )+y-a x \left (1+\ln \left (x \right )\right ) = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.624 |
|
|
\[ {}y y^{\prime }+a y+x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
22.648 |
|
|
\[ {}y y^{\prime }+4 \left (1+x \right ) x +y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
2.217 |
|
|
\[ {}y y^{\prime }-x \,{\mathrm e}^{\frac {x}{y}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.521 |
|
|
\[ {}\left (2 y-x \right ) y^{\prime }-y-2 x = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.146 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.885 |
|
|
\[ {}x y y^{\prime }-y^{2}+a \,x^{3} \cos \left (x \right ) = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
1.794 |
|
|
\[ {}\left (x y-x^{2}\right ) y^{\prime }+y^{2}-3 x y-2 x^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.605 |
|
|
\[ {}2 x y y^{\prime }-y^{2}+x^{2} a = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.811 |
|
|
|
||||||||
|
\[ {}x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.754 |
|
|
\[ {}2 x^{2} y y^{\prime }+y^{2}-2 x^{3}-x^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
2.801 |
|
|
\[ {}\left (2 x^{2} y-x^{3}\right ) y^{\prime }+y^{3}-4 x y^{2}+2 x^{3} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.803 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
10.35 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }-y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.717 |
|
|
\[ {}\left (-x^{2}+y^{2}\right ) y^{\prime }+2 x y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.542 |
|
|
\[ {}x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.559 |
|
|
\[ {}\left (4 y^{2}+x^{2}\right ) y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.81 |
|
|
\[ {}\left (3 x^{2}+2 x y+4 y^{2}\right ) y^{\prime }+2 x^{2}+6 x y+y^{2} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.693 |
|
|
\[ {}\left (a y^{2}+2 b x y+c \,x^{2}\right ) y^{\prime }+b y^{2}+2 c x y+d \,x^{2} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
4.631 |
|
|
\[ {}x \left (y^{2}+x y-x^{2}\right ) y^{\prime }-y^{3}+x y^{2}+x^{2} y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.986 |
|
|
\[ {}2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }+y^{3}-x^{2} y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.911 |
|
|
\[ {}\left (y^{3}-x^{3}\right ) y^{\prime }-x^{2} y = 0 \] |
1 |
1 |
10 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.938 |
|
|
\[ {}2 y^{3} y^{\prime }+x y^{2} = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
2.089 |
|
|
\[ {}\left (2 y^{3}+5 x^{2} y\right ) y^{\prime }+5 x y^{2}+x^{3} = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.622 |
|
|
\[ {}\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
4.909 |
|
|
\[ {}\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.033 |
|
|
\[ {}y \left (y^{3}-2 x^{3}\right ) y^{\prime }+\left (2 y^{3}-x^{3}\right ) x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
13.04 |
|
|
\[ {}y \left (\left (b x +a y\right )^{3}+b \,x^{3}\right ) y^{\prime }+x \left (\left (b x +a y\right )^{3}+a y^{3}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
6.096 |
|
|
\[ {}x y^{\prime } \cot \left (\frac {y}{x}\right )+2 x \sin \left (\frac {y}{x}\right )-y \cot \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
2.95 |
|
|
\[ {}\left (-y+x y^{\prime }\right ) \cos \left (\frac {y}{x}\right )^{2}+x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.676 |
|
|
\[ {}\left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }-\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.265 |
|
|
\[ {}x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3} = 0 \] |
2 |
1 |
4 |
[_separable] |
✓ |
✓ |
1.033 |
|
|
\[ {}x \left (\sqrt {1+{y^{\prime }}^{2}}+y^{\prime }\right )-y = 0 \] |
1 |
2 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
3.247 |
|
|
\[ {}y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0 \] |
0 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.886 |
|
|
\[ {}y^{\prime } = \frac {y+F \left (\frac {y}{x}\right )}{-1+x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
1.589 |
|
|
\[ {}y^{\prime } = \frac {y+F \left (\frac {y}{x}\right ) x^{2}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
0.601 |
|
|
\[ {}y^{\prime } = \frac {y+x^{3} a \,{\mathrm e}^{x}+a \,x^{4}+a \,x^{3}-x y^{2} {\mathrm e}^{x}-x^{2} y^{2}-x y^{2}}{x} \] |
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 |
|
|
\[ {}y^{\prime } = \frac {y+x^{3} b \ln \left (\frac {1}{x}\right )+x^{4} b +b \,x^{3}+x a y^{2} \ln \left (\frac {1}{x}\right )+x^{2} a y^{2}+a x y^{2}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
1.874 |
|
|
\[ {}y^{\prime } = \frac {y+\ln \left (\left (-1+x \right ) \left (1+x \right )\right ) x^{3}+7 \ln \left (\left (-1+x \right ) \left (1+x \right )\right ) x y^{2}}{x} \] |
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 |
|
|
\[ {}y^{\prime } = \frac {-{\mathrm e}^{x} y+x y-x^{3} \ln \left (x \right )-x^{3}-x y^{2} \ln \left (x \right )-x y^{2}}{\left (-{\mathrm e}^{x}+x \right ) x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
2.129 |
|
|
\[ {}y^{\prime } = \frac {x y \ln \left (x \right )-y+2 x^{5} b +2 x^{3} a y^{2}}{\left (x \ln \left (x \right )-1\right ) x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
2.013 |
|
|
\[ {}y^{\prime } = \frac {x y+x^{3}+x y^{2}+y^{3}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
✓ |
4.526 |
|
|
\[ {}y^{\prime } = \frac {x y+x +y^{2}}{\left (-1+x \right ) \left (x +y\right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.531 |
|
|
\[ {}y^{\prime } = \frac {x^{3} y+x^{3}+x y^{2}+y^{3}}{\left (-1+x \right ) x^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
✓ |
5.474 |
|
|
\[ {}y^{\prime } = \frac {y \ln \left (x \right )+\cosh \left (x \right ) x a y^{2}+\cosh \left (x \right ) x^{3} b}{x \ln \left (x \right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
4.746 |
|
|
\[ {}y^{\prime } = \frac {y \left (x^{3}+x^{2} y+y^{2}\right )}{x^{2} \left (-1+x \right ) \left (x +y\right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
7.444 |
|
|
\[ {}y^{\prime } = \frac {\sin \left (\frac {y}{x}\right ) \left (y+2 x^{2} \sin \left (\frac {y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )\right )}{2 \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
15.951 |
|
|
\[ {}y^{\prime } = \frac {\sin \left (\frac {y}{x}\right ) \left (y+2 x^{3} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )\right )}{2 \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
22.625 |
|
|
\[ {}y^{\prime } = \frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{3} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
38.3 |
|
|
\[ {}y^{\prime } = \frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{2} \sin \left (\frac {y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
32.956 |
|
|
\[ {}y^{\prime } = \frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +2 \sin \left (\frac {y}{x}\right ) x^{3} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{4} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
54.065 |
|
|
\[ {}y^{\prime } = \frac {-\sin \left (\frac {y}{x}\right ) y x -y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{4} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x \left (1+x \right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
71.731 |
|
|
\[ {}y^{\prime } = \frac {y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )-\sin \left (\frac {y}{x}\right ) y x -y \sin \left (\frac {y}{x}\right )+2 \sin \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x}{2 \cos \left (\frac {y}{x}\right ) \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right ) \left (1+x \right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
47.311 |
|
|
\[ {}y^{\prime } = \frac {y \left (y^{2}+x y+x^{2}+x \right )}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
✓ |
5.063 |
|
|
\[ {}y^{\prime } = -F \left (x \right ) \left (-x^{2} a +y^{2}\right )+\frac {y}{x} \] |
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 |
|
|
\[ {}y^{\prime } = -F \left (x \right ) \left (x^{2}+2 x y-y^{2}\right )+\frac {y}{x} \] |
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 |
|
|
\[ {}y^{\prime } = f \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.033 |
|
|
\[ {}\left (x^{2} a +b x +e \right ) \left (-y+x y^{\prime }\right )-y^{2}+x^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
2.059 |
|
|
\[ {}\left (a \,x^{n}+b \,x^{m}+c \right ) \left (-y+x y^{\prime }\right )+s \,x^{k} \left (y^{2}-\lambda \,x^{2}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
3.273 |
|
|
\[ {}\frac {1+2 x y}{y}+\frac {\left (y-x \right ) y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.813 |
|
|
\[ {}\frac {y^{2}-2 x^{2}}{x y^{2}-x^{3}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
6.898 |
|
|
\[ {}y+x +x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.278 |
|
|
\[ {}x \,{\mathrm e}^{\frac {y}{x}}+y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.009 |
|
|
\[ {}2 x^{2} y+3 y^{3}-\left (x^{3}+2 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.087 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.946 |
|
|
\[ {}2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0 \] |
1 |
2 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.338 |
|
|
\[ {}y^{3}+x^{3} y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.187 |
|
|
\[ {}x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.654 |
|
|
\[ {}y^{2} \left (3 y-6 x y^{\prime }\right )-x \left (y-2 x y^{\prime }\right ) = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.021 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.939 |
|
|
\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.5 |
|
|
\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.666 |
|
|
\[ {}-y+x y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.434 |
|
|
\[ {}3 x^{2}+6 x y+3 y^{2}+\left (2 x^{2}+3 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.418 |
|
|
\[ {}x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
0.923 |
|
|
\[ {}y^{2}-x^{2}+2 m x y+\left (m y^{2}-m \,x^{2}-2 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
11.212 |
|
|
\[ {}x y^{\prime }-y+2 x^{2} y-x^{3} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.48 |
|
|
\[ {}x +y y^{\prime }+y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.106 |
|
|
\[ {}\left (y-x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.315 |
|
|
\[ {}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.359 |
|
|
\[ {}y+x y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.929 |
|
|
\[ {}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.365 |
|
|
\[ {}1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.179 |
|
|
\[ {}x^{\prime } = \frac {2 x}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.427 |
|
|
\[ {}x^{\prime } = -\frac {t}{x} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.038 |
|
|
\[ {}2 t x^{\prime } = x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.954 |
|
|
\[ {}x^{\prime } = \frac {2 x}{t +1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.369 |
|
|
\[ {}x^{\prime } = \frac {4 t^{2}+3 x^{2}}{2 x t} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.906 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 t y}{t^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.068 |
|
|
\[ {}x^{\prime } = \left (a +\frac {b}{t}\right ) x \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.794 |
|
|
\[ {}R^{\prime } = \frac {R}{t}+t \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.165 |
|
|
\[ {}x^{\prime } = 2 x t \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.963 |
|
|
\[ {}x^{\prime }+p \left (t \right ) x = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.148 |
|
|
\[ {}x^{\prime } = \frac {2 x}{3 t}+\frac {2 t}{x} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.877 |
|
|
\[ {}t^{2} y^{\prime }+2 t y-y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.054 |
|
|
\[ {}x^{3}+3 t x^{2} x^{\prime } = 0 \] |
1 |
1 |
4 |
[_separable] |
✓ |
✓ |
1.018 |
|
|
\[ {}x^{2}-t^{2} x^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.919 |
|
|
\[ {}y^{\prime }+y = 1+x \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.169 |
|
|
\[ {}x^{2}+y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
2.398 |
|
|
\[ {}3 x +2 y+\left (y+2 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.587 |
|
|
\[ {}y^{2}+2 x y-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.13 |
|
|
\[ {}4 x y+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.021 |
|
|
\[ {}x +y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.896 |
|
|
\[ {}2 x y+3 y^{2}-\left (x^{2}+2 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.822 |
|
|
\[ {}v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.765 |
|
|
\[ {}x \tan \left (\frac {y}{x}\right )+y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.308 |
|
|
\[ {}\left (2 s^{2}+2 s t +t^{2}\right ) s^{\prime }+s^{2}+2 s t -t^{2} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.428 |
|
|
\[ {}x^{2}+3 y^{2}-2 x y y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.539 |
|
|
\[ {}\left (4 x -y\right ) y^{\prime }+2 x -5 y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.181 |
|
|
\[ {}3 x^{2}+9 x y+5 y^{2}-\left (6 x^{2}+4 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.463 |
|
|
\[ {}x +2 y+\left (2 x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.956 |
|
|
\[ {}3 x -y-\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.328 |
|
|
\[ {}x^{2}+2 y^{2}+\left (4 x y-y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.16 |
|
|
\[ {}2 x^{2}+2 x y+y^{2}+\left (x^{2}+2 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.18 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = -\frac {y^{2}}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.38 |
|
|
\[ {}6 x^{2} y-\left (x^{3}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.217 |
|
|
\[ {}3 x -5 y+\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.6 |
|
|
\[ {}{\mathrm e}^{2 x} y^{2}+\left ({\mathrm e}^{2 x} y-2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
2.839 |
|
|
\[ {}2 x^{2}+x y+y^{2}+2 x^{2} y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
4.295 |
|
|
\[ {}y^{\prime } = \frac {2 x -7 y}{3 y-8 x} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.665 |
|
|
\[ {}y^{\prime } = \frac {2 x^{2}+y^{2}}{2 x y-x^{2}} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.46 |
|
|
\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.645 |
|
|
\[ {}y^{\prime } = \frac {2 x +7 y}{2 x -2 y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.665 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.28 |
|
|
\[ {}x^{2} y^{\prime }+x y = \frac {y^{3}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.162 |
|
|
\[ {}x^{\prime } = x t^{2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.078 |
|
|
\[ {}x y^{\prime } = k y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.334 |
|
|
\[ {}i^{\prime } = p \left (t \right ) i \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.553 |
|
|
\[ {}x y+y^{2}+x^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.543 |
|
|
\[ {}x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.42 |
|
|
\[ {}y = x y^{\prime }+\frac {1}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
6.814 |
|
|
\[ {}y \left (x -y\right )-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.256 |
|
|
\[ {}x^{\prime }+5 x = 10 t +2 \] |
1 |
1 |
1 |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.14 |
|
|
\[ {}x^{\prime } = \frac {x}{t}+\frac {x^{2}}{t^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.663 |
|
|
\[ {}y \left (x -y\right )-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.2 |
|
|
\[ {}\left (-x^{2}+y^{2}\right ) y^{\prime }+2 x y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.112 |
|
|
\[ {}5 y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.864 |
|
|
\[ {}y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.044 |
|
|
\[ {}z-\left (-a^{2}+t^{2}\right ) z^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.063 |
|
|
\[ {}r^{\prime }+r \tan \left (t \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.293 |
|
|
\[ {}y-x +\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.889 |
|
|
\[ {}y+x +x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.254 |
|
|
\[ {}x +y+\left (y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.426 |
|
|
\[ {}8 y+10 x +\left (7 x +5 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.751 |
|
|
\[ {}t -s+t s^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.084 |
|
|
\[ {}x y^{2} y^{\prime } = y^{3}+x^{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.569 |
|
|
\[ {}x \cos \left (\frac {y}{x}\right ) \left (x y^{\prime }+y\right ) = y \sin \left (\frac {y}{x}\right ) \left (-y+x y^{\prime }\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.424 |
|
|
\[ {}\frac {x}{\left (x +y\right )^{2}}+\frac {\left (y+2 x \right ) y^{\prime }}{\left (x +y\right )^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.196 |
|
|
\[ {}\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}} = \frac {2 y y^{\prime }}{x^{3}} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.155 |
|
|
\[ {}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.786 |
|
|
\[ {}y = x y^{\prime }+y^{\prime } \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.766 |
|
|
\[ {}y^{\prime } = \frac {2 y}{x}-\sqrt {3} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.802 |
|
|
\[ {}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.8 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }-x y-\alpha = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.156 |
|
|
\[ {}x \cos \left (\frac {y}{x}\right ) y^{\prime } = y \cos \left (\frac {y}{x}\right )-x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.165 |
|
|
\[ {}-y+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.635 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = 1 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.638 |
|
|
\[ {}2 x y+x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.812 |
|
|
\[ {}2 x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.7 |
|
|
\[ {}y^{\prime }-2 x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.699 |
|
|
\[ {}y^{\prime } x \ln \left (x \right )-\left (1+\ln \left (x \right )\right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.98 |
|
|
\[ {}y^{\prime } = x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.642 |
|
|
\[ {}y^{\prime } = -x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.712 |
|
|
\[ {}y^{\prime } = x y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.557 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.197 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.602 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{x +3 y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.579 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.0 |
|
|
\[ {}y^{\prime } = \frac {y}{y-x} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.806 |
|
|
\[ {}y^{\prime } = \cos \left (x \right )+\frac {y}{x} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.202 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\tan \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
5.545 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.887 |
|
|
\[ {}y^{\prime } = \frac {2 x}{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.724 |
|
|
\[ {}y-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.328 |
|
|
\[ {}y^{\prime } = -\frac {y \left (y+2 x \right )}{x \left (2 y+x \right )} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.775 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.926 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\sin \left (x^{2}\right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.747 |
|
|
\[ {}x -y y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.227 |
|
|
\[ {}y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.654 |
|
|
\[ {}x^{2}-y+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.721 |
|
|
\[ {}y \left (2 x -1\right )+x \left (1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.972 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.887 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.849 |
|
|
\[ {}y^{\prime } = \frac {y}{y-x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.643 |
|
|
\[ {}y^{\prime } = \frac {y}{y-x} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.719 |
|
|
\[ {}y^{\prime } = \frac {y}{y-x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.141 |
|
|
\[ {}y^{\prime } = \frac {y}{y-x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.289 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.948 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \] |
1 |
0 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.625 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.802 |
|
|
\[ {}y^{\prime } = \frac {y+1}{t +1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.167 |
|
|
\[ {}y^{\prime } = t^{4} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.699 |
|
|
\[ {}y^{\prime } = \frac {t}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.332 |
|
|
\[ {}w^{\prime } = \frac {w}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.747 |
|
|
\[ {}x^{\prime } = -x t \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.188 |
|
|
\[ {}y^{\prime } = t y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.984 |
|
|
\[ {}y^{\prime } = \left (t +1\right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.127 |
|
|
\[ {}y^{\prime } = -\frac {y}{t}+2 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.137 |
|
|
\[ {}y^{\prime } = -\frac {y}{t}+2 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.484 |
|
|
|
||||||||
|
\[ {}y^{\prime } = t y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.671 |
|
|
\[ {}y^{\prime } = \frac {t y}{t^{2}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.777 |
|
|
\[ {}x^{\prime } = -x t \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.101 |
|
|
\[ {}y y^{\prime } = 2 x \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.46 |
|
|
\[ {}\left (-2+x \right ) y^{\prime } = 3+y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.36 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.408 |
|
|
\[ {}x y y^{\prime } = y^{2}+9 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.068 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.223 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.754 |
|
|
\[ {}y^{\prime } = \frac {y^{2}-1}{x y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
7.687 |
|
|
\[ {}y^{\prime } = y \sin \left (x \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.004 |
|
|
\[ {}x y^{\prime } = y+x^{2} \cos \left (x \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.349 |
|
|
\[ {}-y+x y^{\prime } = x^{2} {\mathrm e}^{-x^{2}} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.387 |
|
|
\[ {}x^{2} y^{\prime }-x y = y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.936 |
|
|
\[ {}y^{\prime } = \frac {x}{y}+\frac {y}{x} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.075 |
|
|
\[ {}\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right ) = 1+\sin \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.826 |
|
|
\[ {}y^{\prime } = \frac {x -y}{x +y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.326 |
|
|
\[ {}y^{\prime }-\frac {3 y}{x} = \frac {y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.058 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = \frac {1}{y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.112 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\frac {x^{2}}{y^{2}} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.426 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.184 |
|
|
\[ {}\left (2 x y+2 x^{2}\right ) y^{\prime } = x^{2}+2 x y+2 y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.078 |
|
|
\[ {}2 x y+y^{2}+\left (x^{2}+2 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.411 |
|
|
\[ {}4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.842 |
|
|
\[ {}x^{3}+y^{3}+x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.127 |
|
|
\[ {}3 x y^{3}-y+x y^{\prime } = 0 \] |
1 |
2 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.03 |
|
|
\[ {}x y y^{\prime } = 2 x^{2}+2 y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.588 |
|
|
\[ {}y^{\prime } = \frac {2 y+x}{2 x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.306 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.951 |
|
|
\[ {}x y y^{\prime } = x^{2}+x y+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.259 |
|
|
\[ {}x y^{3} y^{\prime } = y^{4}-x^{2} \] |
1 |
1 |
4 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.307 |
|
|
\[ {}2 x -y-y y^{\prime } = 0 \] |
1 |
1 |
9 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.731 |
|
|
\[ {}y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.553 |
|
|
\[ {}y^{\prime } = -\frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.871 |
|
|
\[ {}y^{\prime } = -\frac {2 y}{x}-3 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.029 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.803 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.975 |
|
|
\[ {}2 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.77 |
|
|
\[ {}y^{\prime } = y \sqrt {t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.45 |
|
|
\[ {}t y^{\prime } = y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.45 |
|
|
\[ {}y^{\prime } = y \tan \left (t \right ) \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.138 |
|
|
\[ {}y^{\prime } = -\frac {t}{y} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
20.007 |
|
|
\[ {}y^{\prime } = \frac {y+1}{t +1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.514 |
|
|
\[ {}y^{\prime } = \sqrt {\frac {y}{t}} \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
123.202 |
|
|
\[ {}y^{\prime } = \cos \left (t \right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.632 |
|
|
\[ {}y^{\prime }+f \left (t \right ) y = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.801 |
|
|
\[ {}y^{\prime } = f \left (t \right ) y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.638 |
|
|
\[ {}t y^{\prime }+y = t \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.537 |
|
|
\[ {}x^{\prime } = \frac {3 x t^{2}}{-t^{3}+1} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.479 |
|
|
\[ {}p^{\prime } = t^{3}+\frac {p}{t} \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.995 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = \ln \left (t \right ) \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.043 |
|
|
\[ {}\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}} = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.712 |
|
|
\[ {}y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
1.697 |
|
|
\[ {}3 t y^{2}+y^{3} y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.883 |
|
|
\[ {}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.963 |
|
|
\[ {}y^{2}+2 t y y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
1.162 |
|
|
\[ {}\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.835 |
|
|
\[ {}2 t y+\left (t^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
10.187 |
|
|
\[ {}3 t^{2}+3 y^{2}+6 t y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
2.386 |
|
|
\[ {}-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
3.513 |
|
|
\[ {}-\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
3.293 |
|
|
\[ {}2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
3.123 |
|
|
\[ {}2 t y^{2}+2 t^{2} y y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.845 |
|
|
\[ {}1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.148 |
|
|
\[ {}t^{2} y+t^{3} y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.45 |
|
|
\[ {}y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.579 |
|
|
\[ {}2 t y+y^{2}-t^{2} y^{\prime } = 0 \] |
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 |
|
|
\[ {}\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.082 |
|
|
\[ {}2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.076 |
|
|
\[ {}t y^{\prime }-y = t y^{3} \sin \left (t \right ) \] |
1 |
2 |
2 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
32.289 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = t y^{2} \] |
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 |
|
|
\[ {}\cos \left (\frac {t}{t +y}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.639 |
|
|
\[ {}y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{t +y} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
15.695 |
|
|
\[ {}\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.791 |
|
|
\[ {}2 t +\left (y-3 t \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.185 |
|
|
\[ {}2 y-3 t +t y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.466 |
|
|
\[ {}t y-y^{2}+t \left (t -3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.457 |
|
|
\[ {}t^{2}+t y+y^{2}-t y y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.678 |
|
|
\[ {}t^{3}+y^{3}-t y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.089 |
|
|
\[ {}y^{\prime } = \frac {4 y+t}{4 t +y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.911 |
|
|
\[ {}t -y+t y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.949 |
|
|
\[ {}y+\left (t +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.825 |
|
|
\[ {}2 t^{2}-7 t y+5 y^{2}+t y y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
15.009 |
|
|
\[ {}y^{2} = \left (t y-4 t^{2}\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.947 |
|
|
\[ {}\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.86 |
|
|
\[ {}t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.488 |
|
|
\[ {}y^{\prime } = \frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.719 |
|
|
\[ {}y^{\prime } = \frac {4 y^{2}-t^{2}}{2 t y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.464 |
|
|
\[ {}t +y-t y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.295 |
|
|
\[ {}y^{3}-t^{3}-t y^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.701 |
|
|
\[ {}t y^{3}-\left (t^{4}+y^{4}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
6.012 |
|
|
\[ {}y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
8.887 |
|
|
\[ {}y^{\prime }-\frac {2 y}{x} = -x^{2} y \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.704 |
|
|
\[ {}y^{\prime } = \frac {y^{2}-t^{2}}{t y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.677 |
|
|
\[ {}y \sin \left (\frac {t}{y}\right )-\left (t +t \sin \left (\frac {t}{y}\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.586 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.98 |
|
|
\[ {}3 t +\left (t -4 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.595 |
|
|
\[ {}y-t +\left (t +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.921 |
|
|
\[ {}y^{2}+\left (t y+t^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.637 |
|
|
\[ {}r^{\prime } = \frac {r^{2}+t^{2}}{r t} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.603 |
|
|
\[ {}x^{\prime } = \frac {5 t x}{x^{2}+t^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.543 |
|
|
\[ {}y-t y^{\prime } = 2 y^{2} \ln \left (t \right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
1.624 |
|
|
\[ {}y^{\prime } = -\frac {y}{t -2} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.637 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
1 |
1 |
2 |
[_separable] |
✓ |
✓ |
2.51 |
|
|
\[ {}y^{\prime } = \frac {y+1}{-1+x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.953 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.728 |
|
|
\[ {}y^{\prime } = -\frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.709 |
|
|
\[ {}x y^{\prime } = 2 x -y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.59 |
|
|
\[ {}y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
3.12 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.441 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = y-1 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
2.071 |
|
|
\[ {}x y^{\prime } = y+x \cos \left (\frac {y}{x}\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.314 |
|
|
\[ {}x -y+x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.218 |
|
|
\[ {}x^{2} y^{\prime } = x^{2}-x y+y^{2} \] |
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 |
|
|
\[ {}4 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.026 |
|
|
\[ {}y-x +\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.454 |
|
|
\[ {}x y^{\prime }+y = 2 x \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
2.009 |
|
|
\[ {}3 x y^{2} y^{\prime }-2 y^{3} = x^{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.863 |
|
|
\[ {}y^{\prime }+3 x y = y \,{\mathrm e}^{x^{2}} \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
1.742 |
|
|
\[ {}x \left (2 x^{2}+y^{2}\right )+y \left (x^{2}+2 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
3.869 |
|
|
\[ {}2 x +\frac {x^{2}+y^{2}}{x^{2} y} = \frac {\left (x^{2}+y^{2}\right ) y^{\prime }}{x y^{2}} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _exact, _rational] |
✓ |
✓ |
2.423 |
|
|
\[ {}\frac {x y}{\sqrt {x^{2}+1}}+2 x y-\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
37.151 |
|
|
\[ {}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
6.991 |
|
|
\[ {}3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
4.919 |
|
|
\[ {}x^{2}+y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.183 |
|
|
\[ {}x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
1.65 |
|
|
\[ {}5 x y-4 y^{2}-6 x^{2}+\left (y^{2}-8 x y+\frac {5 x^{2}}{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
1.411 |
|
|
\[ {}x y y^{\prime }-y^{2} = x^{4} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.998 |
|
|
\[ {}\frac {1}{x^{2}-x y+y^{2}} = \frac {y^{\prime }}{2 y^{2}-x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
16.427 |
|
|
\[ {}y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right ) = 0 \] |
1 |
1 |
1 |
[_separable] |
✓ |
✓ |
0.583 |
|
|
\[ {}x y^{2} y^{\prime }-y^{3} = \frac {x^{4}}{3} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.174 |
|
|
\[ {}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
7.802 |
|
|
\[ {}x^{2}+y^{2}-x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.013 |
|
|
\[ {}y+x y^{2}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.939 |
|
|
\[ {}x^{2}+y^{2}+2 x +2 y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.345 |
|
|
|
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|
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