This is list of all ode’s \(y'=f(x,y)\) solved by the program using Lie symmetry methods where \(\xi ,\eta \) are calculated from the linearized similarity condition PDE.
This is only for first order odes. I have not yet implemented Lie symmetry for second order ode’s. Number of problems in this table is 1312
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) |
|
\[ {}y^{\prime } = 3 \sqrt {x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
11.688 |
|
|
\[ {}y^{\prime } = 4 \left (x y\right )^{\frac {1}{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
91.221 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = x -y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.521 |
|
|
\[ {}x y^{\prime } = y+2 \sqrt {x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.587 |
|
|
\[ {}\left (x -y\right ) y^{\prime } = x +y \] |
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 |
|
|
\[ {}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.424 |
|
|
\[ {}x y y^{\prime } = y^{2}+x \sqrt {4 x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.627 |
|
|
\[ {}x y^{\prime } = y+\sqrt {x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.341 |
|
|
\[ {}x +y y^{\prime } = \sqrt {x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.68 |
|
|
\[ {}y \left (3 x +y\right )+x \left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.957 |
|
|
\[ {}\left ({\mathrm e}^{y}+x \right ) y^{\prime } = -1+x \,{\mathrm e}^{-y} \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
2.134 |
|
|
\[ {}2 x +3 y+\left (3 x +2 y\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}6 y^{3} x +2 y^{4}+\left (9 x^{2} y^{2}+8 y^{3} x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.483 |
|
|
\[ {}y^{\prime } = x^{2}-2 x y+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.438 |
|
|
\[ {}y^{\prime } = \frac {x +3 y}{-3 x +y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.993 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+x y+y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.453 |
|
|
\[ {}y^{\prime } = \frac {4 y-3 x}{2 x -y} \] |
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 |
|
|
\[ {}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.393 |
|
|
\[ {}y^{\prime } = \frac {-x a -b y}{b x +c y} \] |
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 |
|
|
\[ {}2 x -y+\left (-x +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.914 |
|
|
\[ {}y+\left (-{\mathrm e}^{-2 y}+2 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
2.399 |
|
|
\[ {}3 x y+y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
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 |
|
|
\[ {}y^{\prime } = \frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.122 |
|
|
\[ {}y^{\prime } = -1-\frac {x}{2}+\frac {\sqrt {x^{2}+4 x +4 y}}{2} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
2.417 |
|
|
\[ {}\frac {x y^{\prime }}{y}+2 \ln \left (y\right ) = 4 x^{2} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
4.343 |
|
|
\[ {}\frac {y^{\prime }}{\left (y+1\right )^{2}}-\frac {1}{x \left (y+1\right )} = -\frac {3}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
2.29 |
|
|
\[ {}x y^{\prime }-2 y = \frac {x^{6}}{y+x^{2}} \] |
1 |
1 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
8.738 |
|
|
\[ {}y^{\prime } = \frac {2 x +3 y}{x -4 y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.502 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}+x y-x^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
3.518 |
|
|
\[ {}x^{2} y^{\prime } = x^{2}+x y+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.52 |
|
|
\[ {}y^{\prime } = \frac {2 y^{2}+x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}}{2 x y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
1.977 |
|
|
\[ {}y^{\prime } = \frac {y^{2}-3 x y-5 x^{2}}{x^{2}} \] |
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 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.582 |
|
|
\[ {}\left (-y+x y^{\prime }\right ) \left (\ln \left (y\right )-\ln \left (x \right )\right ) = x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
4.368 |
|
|
\[ {}y^{\prime } = \frac {y^{3}+2 x y^{2}+x^{2} y+x^{3}}{x \left (x +y\right )^{2}} \] |
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 |
|
|
\[ {}x^{3} y^{\prime } = 2 y^{2}+2 x^{2} y-2 x^{4} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
3.026 |
|
|
\[ {}y^{\prime } = y^{2} {\mathrm e}^{-x}+4 y+2 \,{\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
1.691 |
|
|
\[ {}2 x \left (y+2 \sqrt {x}\right ) y^{\prime } = \left (y+\sqrt {x}\right )^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.043 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x} = \frac {3 x^{2} y^{2}+6 x y+2}{x^{2} \left (2 x y+3\right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
16.555 |
|
|
\[ {}y^{\prime }+\frac {3 y}{x} = \frac {3 x^{4} y^{2}+10 x^{2} y+6}{x^{3} \left (2 x^{2} y+5\right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
12.26 |
|
|
\[ {}y^{\prime } = 1+x -\left (2 x +1\right ) y+x y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.421 |
|
|
\[ {}4 x +7 y+\left (3 x +4 y\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}{\mathrm e}^{x y} \left (x^{4} y+4 x^{3}\right )+3 y+\left (x^{5} {\mathrm e}^{x y}+3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
16.681 |
|
|
\[ {}7 x +4 y+\left (4 x +3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.935 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x} = -\frac {2 x y}{x^{2}+2 x^{2} y+1} \] |
1 |
1 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.012 |
|
|
\[ {}y^{\prime }+2 x y = -\frac {{\mathrm e}^{-x^{2}} \left (3 x +2 y \,{\mathrm e}^{x^{2}}\right )}{2 x +3 y \,{\mathrm e}^{x^{2}}} \] |
1 |
1 |
1 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
44.569 |
|
|
\[ {}y+\left (2 x +\frac {1}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.641 |
|
|
\[ {}27 x y^{2}+8 y^{3}+\left (18 x^{2} y+12 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
16 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.234 |
|
|
\[ {}x^{4} y^{3}+y+\left (x^{5} y^{2}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.156 |
|
|
\[ {}12 x y+6 y^{3}+\left (9 x^{2}+10 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.186 |
|
|
\[ {}y^{\prime }+y^{2}+4 x y+4 x^{2}+2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.258 |
|
|
\[ {}\left (2 x +1\right ) \left (y^{\prime }+y^{2}\right )-2 y-2 x -3 = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
4.83 |
|
|
\[ {}\left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-\left (3 x +2\right ) y-6 x +8 = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
5.227 |
|
|
\[ {}x^{2} \left (y^{\prime }+y^{2}\right )-7 x y+7 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
3.356 |
|
|
\[ {}t y^{\prime } = y+\sqrt {t^{2}+y^{2}} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.692 |
|
|
\[ {}\left (t -\sqrt {t y}\right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.657 |
|
|
\[ {}y^{\prime } = \frac {t +y}{t -y} \] |
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 |
|
|
\[ {}y^{\prime } = \frac {t +y+1}{t -y+3} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.988 |
|
|
\[ {}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.902 |
|
|
\[ {}t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.261 |
|
|
\[ {}\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.016 |
|
|
\[ {}3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
7.145 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{\left (-t +y\right )^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.563 |
|
|
\[ {}\left (x +y\right ) y^{\prime }+x = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.139 |
|
|
\[ {}-y+x y^{\prime } = \sqrt {x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.856 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{x +4 y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.781 |
|
|
\[ {}-y+x y^{\prime } = \sqrt {x^{2}-y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.621 |
|
|
\[ {}x +y y^{\prime } = 2 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.059 |
|
|
\[ {}x y^{\prime }-y+\sqrt {-x^{2}+y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.514 |
|
|
\[ {}\left (x y-x^{2}\right ) y^{\prime }-y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.395 |
|
|
\[ {}x y^{\prime }+y = 2 \sqrt {x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
18.583 |
|
|
\[ {}x +y+\left (x -y\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}\left (\frac {x}{y}+\frac {y}{x}\right ) y^{\prime }+1 = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.8 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
1 |
0 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.561 |
|
|
\[ {}\left (3 x y-2 x^{2}\right ) y^{\prime } = 2 y^{2}-x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
6.517 |
|
|
\[ {}y^{\prime } = \frac {y}{x -k \sqrt {x^{2}+y^{2}}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
6.158 |
|
|
\[ {}y^{2} \left (y y^{\prime }-x \right )+x^{3} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.408 |
|
|
\[ {}x +y-\left (x -y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.943 |
|
|
\[ {}x +\left (x -2 y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
5.287 |
|
|
\[ {}2 x -y+1+\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.047 |
|
|
\[ {}x -y+2+\left (x +y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.987 |
|
|
\[ {}x -y+\left (-x +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.164 |
|
|
\[ {}y^{\prime } = \frac {x +y-1}{x -y-1} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.024 |
|
|
\[ {}x +y+\left (2 x +2 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.849 |
|
|
\[ {}x -y+1+\left (x -y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.875 |
|
|
\[ {}x +2 y+\left (3 x +6 y+3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.882 |
|
|
\[ {}x +2 y+2 = \left (2 x +y-1\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.508 |
|
|
\[ {}3 x -y+1+\left (x -3 y-5\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.16 |
|
|
\[ {}6 x -3 y+6+\left (2 x -y+5\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.849 |
|
|
\[ {}2 x +3 y+2+\left (y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
0 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
10.464 |
|
|
\[ {}x +y+4 = \left (2 x +2 y-1\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.935 |
|
|
\[ {}2 x +3 y-1+\left (2 x +3 y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.653 |
|
|
\[ {}3 x -y+2+\left (x +2 y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
0 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
9.152 |
|
|
\[ {}3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
13.745 |
|
|
\[ {}x -2 y+3+\left (1-x +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.68 |
|
|
\[ {}2 x +y+\left (4 x +2 y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.239 |
|
|
\[ {}2 x +y+\left (4 x -2 y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
42.992 |
|
|
\[ {}x +y+\left (x -2 y\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}a_{1} x +b_{1} y+c_{1} +\left (b_{1} x +b_{2} y+c_{2} \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.795 |
|
|
\[ {}2 x y-\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.753 |
|
|
\[ {}\frac {y \left (2+x^{3} y\right )}{x^{3}} = \frac {\left (1-2 x^{3} y\right ) y^{\prime }}{x^{2}} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.761 |
|
|
\[ {}\frac {2 y}{x^{3}}+\frac {2 x}{y^{2}} = \left (\frac {1}{x^{2}}+\frac {2 x^{2}}{y^{3}}\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
5.387 |
|
|
\[ {}\frac {x^{2}+3 y^{2}}{x \left (3 x^{2}+4 y^{2}\right )}+\frac {\left (2 x^{2}+y^{2}\right ) y^{\prime }}{y \left (3 x^{2}+4 y^{2}\right )} = 0 \] |
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 |
|
|
\[ {}x y+\left (y+x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
9 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.876 |
|
|
\[ {}\left (x^{3} y^{3}-1\right ) y^{\prime }+x^{2} y^{4} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.335 |
|
|
\[ {}y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.576 |
|
|
\[ {}2 x y+\left (y-x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.267 |
|
|
\[ {}y = x \left (x^{2} y-1\right ) y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.134 |
|
|
\[ {}\left (2 x +3 x^{2} y\right ) y^{\prime }+y+2 x y^{2} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.182 |
|
|
\[ {}x^{2} y^{2}-y+\left (2 x^{3} y+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.316 |
|
|
\[ {}y \left (x +y^{2}\right )+x \left (x -y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
18.458 |
|
|
\[ {}y+\left (2 x -3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.38 |
|
|
\[ {}1 = \left ({\mathrm e}^{y}+x \right ) y^{\prime } \] |
1 |
1 |
1 |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
1.615 |
|
|
\[ {}2 y = \left (y^{4}+x \right ) y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.933 |
|
|
\[ {}y+2 \left (x -2 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
5.5 |
|
|
\[ {}y^{\prime } = x \left (1-{\mathrm e}^{2 y-x^{2}}\right ) \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
3.736 |
|
|
\[ {}2 y = \left (x^{2} y^{4}+x \right ) y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.773 |
|
|
\[ {}y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}x -2 y+1+\left (y-2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.158 |
|
|
\[ {}2 \,{\mathrm e}^{x}-t^{2}+t \,{\mathrm e}^{x} x^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.315 |
|
|
\[ {}x -3 y = \left (3 y-x +2\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.128 |
|
|
\[ {}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.58 |
|
|
\[ {}2 x y+y^{4}+\left (y^{3} x -2 x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.268 |
|
|
\[ {}y+\left (3 x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.609 |
|
|
\[ {}\left (3 x +4 y\right ) y^{\prime }+y+2 x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.538 |
|
|
\[ {}x y^{\prime }-y-\sqrt {x^{2}+y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
6.164 |
|
|
\[ {}x +y+\left (2 x +3 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.397 |
|
|
\[ {}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
3.323 |
|
|
\[ {}y \sqrt {x^{2}+y^{2}}+x y = x^{2} y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
6.528 |
|
|
\[ {}y \cos \left (\frac {x}{y}\right )-\left (y+x \cos \left (\frac {x}{y}\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.761 |
|
|
\[ {}y \left (3 x^{2}+y\right )-x \left (x^{2}-y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
6.574 |
|
|
\[ {}x +\left (2 x +3 y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
5.302 |
|
|
\[ {}\left (-2 x^{2}-3 x y\right ) y^{\prime }+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.416 |
|
|
\[ {}3 x y+\left (3 x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
6.322 |
|
|
\[ {}x -2 y+3 = \left (x -2 y+1\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.958 |
|
|
\[ {}y^{2}+\left (x^{3}-2 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
15.165 |
|
|
\[ {}y^{3}+2 x^{2} y+\left (-3 x^{3}-2 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
10.947 |
|
|
\[ {}2 x^{2} y+{y^{\prime }}^{2} = x^{3} y^{\prime } \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
12.752 |
|
|
\[ {}x^{2}-3 y y^{\prime }+{y^{\prime }}^{2} x = 0 \] |
2 |
2 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
15.878 |
|
|
\[ {}{y^{\prime }}^{3}+x y y^{\prime } = 2 y^{2} \] |
3 |
1 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
173.565 |
|
|
\[ {}\left (x +y^{3}\right ) y^{\prime } = y \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
0.571 |
|
|
\[ {}\left (y-x \right ) y^{\prime }+2 x +3 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.97 |
|
|
\[ {}y^{\prime } = -\frac {x +y}{3 x +3 y-4} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.69 |
|
|
\[ {}x \left (1-2 x^{2} y\right ) y^{\prime }+y = 3 x^{2} y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.697 |
|
|
\[ {}y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}} \] |
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 |
|
|
\[ {}\left (5 x +y-7\right ) y^{\prime } = 3+3 x +3 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.904 |
|
|
\[ {}\left (3 x -y\right ) y^{\prime } = 3 y \] |
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 |
|
|
\[ {}x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.104 |
|
|
\[ {}-y+x y^{\prime } = \sqrt {9 x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.286 |
|
|
\[ {}x \left (x^{2}-y^{2}\right )-x \left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.763 |
|
|
\[ {}x y^{\prime }+y \ln \left (x \right ) = y \ln \left (y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.011 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y-2 x^{2}}{x^{2}-x y+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.046 |
|
|
\[ {}2 x y y^{\prime }-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}} = 0 \] |
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 |
|
|
\[ {}y y^{\prime } = \sqrt {x^{2}+y^{2}}-x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.407 |
|
|
\[ {}2 x \left (y+2 x \right ) y^{\prime } = y \left (4 x -y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.148 |
|
|
\[ {}y^{\prime } = \frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.997 |
|
|
\[ {}-y+x y^{\prime } = \sqrt {4 x^{2}-y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.148 |
|
|
\[ {}y^{\prime } = \sin \left (3 x -3 y+1\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
6.854 |
|
|
\[ {}y^{\prime } = \frac {y \left (\ln \left (x y\right )-1\right )}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
1.297 |
|
|
\[ {}y^{\prime } = 2 x \left (x +y\right )^{2}-1 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
1.493 |
|
|
\[ {}y^{\prime } = \frac {x +2 y-1}{2 x -y+3} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.549 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x}-y^{2} = -\frac {2}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.568 |
|
|
\[ {}y^{\prime }+\frac {7 y}{x}-3 y^{2} = \frac {3}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
0.924 |
|
|
\[ {}\frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x} = \frac {1-2 \ln \left (x \right )}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.614 |
|
|
\[ {}4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.534 |
|
|
\[ {}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.762 |
|
|
\[ {}3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.983 |
|
|
\[ {}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.013 |
|
|
\[ {}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.622 |
|
|
\[ {}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.014 |
|
|
\[ {}2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.457 |
|
|
\[ {}x^{2} y^{\prime } = \left (y-1\right ) x +\left (y-1\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
1.263 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+y^{2}}{2 x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.107 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{y+2 x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
7.978 |
|
|
\[ {}y^{\prime } = \frac {3 x -y+1}{3 y-x +5} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.987 |
|
|
\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.057 |
|
|
\[ {}\left (x +y-1\right ) y^{\prime } = x -y+1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.594 |
|
|
\[ {}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
5.107 |
|
|
\[ {}y^{\prime } = \sin \left (x -y+1\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
2.507 |
|
|
\[ {}y^{\prime } = \frac {x +y+4}{x -y-6} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.974 |
|
|
\[ {}y^{\prime } = \frac {x +y+4}{x +y-6} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.003 |
|
|
\[ {}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.217 |
|
|
\[ {}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.34 |
|
|
\[ {}\left (x +3 x^{3} y^{4}\right ) y^{\prime }+y = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.339 |
|
|
\[ {}\left (x -1-y^{2}\right ) y^{\prime }-y = 0 \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
0.852 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = y-x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.237 |
|
|
\[ {}\left (1-x y\right ) y^{\prime } = y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.646 |
|
|
\[ {}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.294 |
|
|
\[ {}x y^{\prime } = \sqrt {x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
11.182 |
|
|
\[ {}y^{2} = \left (x^{3}-x y\right ) y^{\prime } \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.336 |
|
|
\[ {}\left (x y-x^{2}\right ) y^{\prime } = y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.762 |
|
|
\[ {}6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.287 |
|
|
\[ {}\cos \left (x +y\right )-x \sin \left (x +y\right ) = x \sin \left (x +y\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
3.343 |
|
|
\[ {}y^{\prime } \ln \left (x -y\right ) = 1+\ln \left (x -y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
1.388 |
|
|
\[ {}y^{2}-3 x y-2 x^{2} = \left (x^{2}-x y\right ) y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.286 |
|
|
\[ {}\frac {x}{x^{2}+y^{2}}+\frac {y}{x^{2}}+\left (\frac {y}{x^{2}+y^{2}}-\frac {1}{x}\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}x y^{\prime } = y \left (1+\ln \left (y\right )-\ln \left (x \right )\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.218 |
|
|
\[ {}x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}\left (3+2 x +4 y\right ) y^{\prime } = x +2 y+1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.247 |
|
|
\[ {}y^{\prime } = \frac {2 x +y-1}{x -y-2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.213 |
|
|
\[ {}y+2 = \left (-4+2 x +y\right ) y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.103 |
|
|
\[ {}y^{\prime } = \sin \left (x -y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.862 |
|
|
\[ {}y^{\prime } = \left (1+x \right )^{2}+\left (4 y+1\right )^{2}+8 x y+1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.57 |
|
|
\[ {}x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y} = 0 \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
3.205 |
|
|
\[ {}2 x y+\left (x^{2}+2 x y+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.705 |
|
|
\[ {}y+x \left (y^{2}+\ln \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
3.78 |
|
|
\[ {}y^{2}+\left (x y+y^{2}-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
1.128 |
|
|
\[ {}2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
2.742 |
|
|
\[ {}x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
4.504 |
|
|
\[ {}y^{2}-\left (x y+x^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.819 |
|
|
\[ {}2 x^{2} y^{2}+y+\left (x^{3} y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.677 |
|
|
\[ {}y^{2}+\left (x y+\tan \left (x y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
32.595 |
|
|
\[ {}y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
3.072 |
|
|
\[ {}y^{2}+\left ({\mathrm e}^{x}-y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.551 |
|
|
\[ {}x^{2} y^{2}-2 y+\left (x^{3} y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.405 |
|
|
\[ {}2 x^{3} y+y^{3}-\left (x^{4}+2 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.938 |
|
|
\[ {}\left (y^{3}+\frac {x}{y}\right ) y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.215 |
|
|
\[ {}1+\left (x -y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
0.944 |
|
|
\[ {}y^{2}+\left (x y+y^{2}-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
1.112 |
|
|
\[ {}y+\left (y^{2} {\mathrm e}^{y}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.271 |
|
|
\[ {}1+y+\left (x -y \left (y+1\right )^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
4.974 |
|
|
\[ {}y^{\prime } = \frac {4 x^{3} y^{2}}{x^{4} y+2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.477 |
|
|
\[ {}6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime } = 0 \] |
1 |
1 |
6 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.864 |
|
|
\[ {}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \] |
3 |
1 |
7 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
84.592 |
|
|
\[ {}{y^{\prime }}^{3}+y^{2} = x y y^{\prime } \] |
3 |
1 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
111.411 |
|
|
\[ {}2 x y^{\prime }-y = y^{\prime } \ln \left (y y^{\prime }\right ) \] |
0 |
1 |
4 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
2.922 |
|
|
\[ {}y = x y^{\prime }-x^{2} {y^{\prime }}^{3} \] |
3 |
1 |
2 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
92.662 |
|
|
\[ {}y \left (y-2 x y^{\prime }\right )^{3} = {y^{\prime }}^{2} \] |
3 |
1 |
6 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
103.855 |
|
|
\[ {}5 y+{y^{\prime }}^{2} = x \left (x +y^{\prime }\right ) \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
4.176 |
|
|
\[ {}2 \sqrt {x y}-y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
13.593 |
|
|
\[ {}y^{\prime } = \left (x -y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.586 |
|
|
\[ {}y^{\prime } = 3-3 x +3 y+\left (x -y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.682 |
|
|
\[ {}y^{\prime } = x \left (x^{3}+2\right )-\left (2 x^{2}-y\right ) y \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
0.895 |
|
|
\[ {}y^{\prime } = 1+x \left (-x^{3}+2\right )+\left (2 x^{2}-y\right ) y \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
1.597 |
|
|
\[ {}y^{\prime } = 1-x -x^{3}+\left (2 x^{2}+1\right ) y-x y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.721 |
|
|
\[ {}y^{\prime } = x +\left (1-2 x \right ) y-\left (1-x \right ) y^{2} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.438 |
|
|
\[ {}y^{\prime } = \left (a +b x y\right ) y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
8.756 |
|
|
\[ {}y^{\prime } = a \,x^{\frac {n}{-n +1}}+b y^{n} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
1.043 |
|
|
\[ {}y^{\prime } = x a +b \sqrt {y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
3.365 |
|
|
\[ {}y^{\prime }+x^{3} = x \sqrt {x^{4}+4 y} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.598 |
|
|
\[ {}y^{\prime } = a +b \cos \left (A x +B y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
90.74 |
|
|
\[ {}y^{\prime } = f \left (a +b x +c y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.694 |
|
|
\[ {}2 y^{\prime }+x a = \sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
2.02 |
|
|
\[ {}3 y^{\prime } = x +\sqrt {x^{2}-3 y} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
2.079 |
|
|
\[ {}x y^{\prime } = x^{3}+\left (2 x^{2}+1\right ) y+x y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.095 |
|
|
\[ {}x y^{\prime } = 2 x -y+a \,x^{n} \left (x -y\right )^{2} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
1.286 |
|
|
\[ {}x y^{\prime } = y+\sqrt {x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.869 |
|
|
\[ {}x y^{\prime } = y+\sqrt {x^{2}-y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.917 |
|
|
\[ {}x y^{\prime } = y+a \sqrt {y^{2}+b^{2} x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.506 |
|
|
\[ {}x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.011 |
|
|
\[ {}x y^{\prime }+x +\tan \left (x +y\right ) = 0 \] |
1 |
1 |
4 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.714 |
|
|
\[ {}x y^{\prime } = \left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right ) \] |
1 |
1 |
1 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
1.962 |
|
|
\[ {}x y^{\prime } = x +y+x \,{\mathrm e}^{\frac {y}{x}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.001 |
|
|
\[ {}x y^{\prime } = \left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.326 |
|
|
\[ {}x y^{\prime }+\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
1.304 |
|
|
\[ {}x y^{\prime } = y f \left (x^{m} y^{n}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
0.991 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = 1+y+\left (1+x \right ) \sqrt {y+1} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.514 |
|
|
\[ {}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.688 |
|
|
\[ {}x^{2} y^{\prime } = \left (1+2 x -y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
1.639 |
|
|
\[ {}x^{2} y^{\prime }+x^{2} a +b x y+c y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.764 |
|
|
\[ {}x^{2} y^{\prime }+2+x y \left (4+x y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.003 |
|
|
\[ {}x^{2} y^{\prime } = a +b \,x^{2} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
1.735 |
|
|
\[ {}x^{2} y^{\prime } = a +b x y+c \,x^{2} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
2.024 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = 1-\left (2 x -y\right ) y \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.006 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime } = a^{2}+3 x y-2 y^{2} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
3.102 |
|
|
\[ {}\left (x -a \right )^{2} y^{\prime }+k \left (x +y-a \right )^{2}+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
1.631 |
|
|
\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
2.243 |
|
|
\[ {}2 x^{2} y^{\prime }+1+2 x y-x^{2} y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
0.979 |
|
|
\[ {}x \left (1-2 x \right ) y^{\prime } = 4 x -\left (1+4 x \right ) y+y^{2} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.909 |
|
|
\[ {}a \,x^{2} y^{\prime } = x^{2}+a x y+b^{2} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.956 |
|
|
\[ {}x^{3} y^{\prime } = x^{4}+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
0.602 |
|
|
\[ {}x^{3} y^{\prime } = x^{2} \left (y-1\right )+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.47 |
|
|
\[ {}x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.165 |
|
|
\[ {}x^{4} y^{\prime }+a^{2}+x^{4} y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
1.111 |
|
|
\[ {}x^{4} y^{\prime }+x^{3} y+\csc \left (x y\right ) = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
5.848 |
|
|
\[ {}\left (c \,x^{2}+b x +a \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
3.77 |
|
|
\[ {}x^{n} y^{\prime } = a^{2} x^{2 n -2}+b^{2} y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
3.025 |
|
|
\[ {}y y^{\prime }+x a +b y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
11.408 |
|
|
\[ {}\left (y+1\right ) y^{\prime } = x +y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.916 |
|
|
\[ {}\left (x +y\right ) y^{\prime }+y = 0 \] |
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 |
|
|
\[ {}\left (x -y\right ) y^{\prime } = \left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.217 |
|
|
\[ {}\left (1+x +y\right ) y^{\prime }+1+4 x +3 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.18 |
|
|
\[ {}\left (x +y+2\right ) y^{\prime } = 1-x -y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.888 |
|
|
\[ {}\left (3-x -y\right ) y^{\prime } = 1+x -3 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.21 |
|
|
\[ {}\left (3-x +y\right ) y^{\prime } = 11-4 x +3 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.207 |
|
|
\[ {}\left (y+2 x \right ) y^{\prime }+x -2 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.872 |
|
|
\[ {}\left (2+2 x -y\right ) y^{\prime }+3+6 x -3 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.756 |
|
|
\[ {}\left (2 x -y+3\right ) y^{\prime }+2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.776 |
|
|
\[ {}\left (4+2 x -y\right ) y^{\prime }+5+x -2 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.676 |
|
|
\[ {}\left (5-2 x -y\right ) y^{\prime }+4-x -2 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.998 |
|
|
\[ {}\left (1-3 x +y\right ) y^{\prime } = 2 x -2 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.745 |
|
|
\[ {}\left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.981 |
|
|
\[ {}\left (4 x -y\right ) y^{\prime }+2 x -5 y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.383 |
|
|
\[ {}\left (6-4 x -y\right ) y^{\prime } = 2 x -y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.574 |
|
|
\[ {}\left (1+5 x -y\right ) y^{\prime }+5+x -5 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.514 |
|
|
\[ {}\left (a +b x +y\right ) y^{\prime }+a -b x -y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.61 |
|
|
\[ {}\left (x^{2}-y\right ) y^{\prime } = 4 x y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.272 |
|
|
\[ {}\left (x -2 y\right ) y^{\prime } = y \] |
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 |
|
|
\[ {}\left (x -2 y+1\right ) y^{\prime } = 1+2 x -y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.033 |
|
|
\[ {}\left (x +2 y+1\right ) y^{\prime }+1-x -2 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.711 |
|
|
\[ {}\left (x +2 y+1\right ) y^{\prime }+7+x -4 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.697 |
|
|
\[ {}\left (3+2 x -2 y\right ) y^{\prime } = 1+6 x -2 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.346 |
|
|
\[ {}\left (1-4 x -2 y\right ) y^{\prime }+2 x +y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.0 |
|
|
\[ {}\left (6 x -2 y\right ) y^{\prime } = 2+3 x -y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.848 |
|
|
\[ {}\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.625 |
|
|
\[ {}\left (x \,{\mathrm e}^{-x}-2 y\right ) y^{\prime } = 2 x \,{\mathrm e}^{-2 x}-\left ({\mathrm e}^{-x}+x \,{\mathrm e}^{-x}-2 y\right ) y \] |
1 |
1 |
2 |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.798 |
|
|
\[ {}\left (x -3 y\right ) y^{\prime }+4+3 x -y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.618 |
|
|
\[ {}\left (4-x -3 y\right ) y^{\prime }+3-x -3 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.747 |
|
|
\[ {}\left (2 x +3 y+2\right ) y^{\prime } = 1-2 x -3 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.739 |
|
|
\[ {}\left (5-2 x -3 y\right ) y^{\prime }+1-2 x -3 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.742 |
|
|
\[ {}\left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.846 |
|
|
\[ {}\left (x +4 y\right ) y^{\prime }+4 x -y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.891 |
|
|
\[ {}\left (3+2 x +4 y\right ) y^{\prime } = x +2 y+1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.718 |
|
|
\[ {}\left (5+2 x -4 y\right ) y^{\prime } = x -2 y+3 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.953 |
|
|
\[ {}\left (5+3 x -4 y\right ) y^{\prime } = 2+7 x -3 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.467 |
|
|
\[ {}4 \left (1-x -y\right ) y^{\prime }+2-x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.184 |
|
|
\[ {}\left (11-11 x -4 y\right ) y^{\prime } = 62-8 x -25 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.689 |
|
|
\[ {}\left (6+3 x +5 y\right ) y^{\prime } = 2+x +7 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.254 |
|
|
\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.203 |
|
|
\[ {}\left (5-x +6 y\right ) y^{\prime } = 3-x +4 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.732 |
|
|
\[ {}3 \left (2 y+x \right ) y^{\prime } = 1-x -2 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.709 |
|
|
\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.565 |
|
|
\[ {}\left (1+x +9 y\right ) y^{\prime }+1+x +5 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.249 |
|
|
\[ {}\left (8+5 x -12 y\right ) y^{\prime } = 3+2 x -5 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.115 |
|
|
\[ {}\left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.699 |
|
|
\[ {}\left (3+9 x +21 y\right ) y^{\prime } = 45+7 x -5 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.666 |
|
|
\[ {}\left (x a +b y\right ) y^{\prime }+x = 0 \] |
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 |
|
|
\[ {}x y y^{\prime } = x^{2}-x y+y^{2} \] |
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 |
|
|
\[ {}\left (1+x y\right ) y^{\prime }+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.757 |
|
|
\[ {}x \left (4+y\right ) y^{\prime } = 2 x +2 y+y^{2} \] |
1 |
1 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.195 |
|
|
\[ {}x \left (x +y\right ) y^{\prime }+y^{2} = 0 \] |
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 |
|
|
\[ {}x \left (x +y\right ) y^{\prime }-y \left (x +y\right )+x \sqrt {x^{2}-y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.695 |
|
|
\[ {}x \left (y+2 x \right ) y^{\prime } = x^{2}+x y-y^{2} \] |
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 |
|
|
\[ {}x \left (x^{3}+y\right ) y^{\prime } = \left (x^{3}-y\right ) y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.257 |
|
|
\[ {}x \left (2 x^{3}+y\right ) y^{\prime } = \left (2 x^{3}-y\right ) y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.253 |
|
|
\[ {}x \left (2 x^{3}+y\right ) y^{\prime } = 6 y^{2} \] |
1 |
1 |
6 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.349 |
|
|
\[ {}x \left (x -2 y\right ) y^{\prime }+y^{2} = 0 \] |
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 |
|
|
\[ {}2 x \left (2 x^{2}+y\right ) y^{\prime }+\left (12 x^{2}+y\right ) y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.415 |
|
|
\[ {}x \left (2 x +3 y\right ) y^{\prime } = y^{2} \] |
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 |
|
|
\[ {}x \left (x -a y\right ) y^{\prime } = y \left (-x a +y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.023 |
|
|
\[ {}x \left (x^{n}+a y\right ) y^{\prime }+\left (b +c y\right ) y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
6.516 |
|
|
\[ {}x \left (1-x y\right ) y^{\prime }+\left (1+x y\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.041 |
|
|
\[ {}x \left (2-x y\right ) y^{\prime }+2 y-x y^{2} \left (1+x y\right ) = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
0.848 |
|
|
\[ {}x \left (3-x y\right ) y^{\prime } = y \left (x y-1\right ) \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.184 |
|
|
\[ {}x \left (1-2 x y\right ) y^{\prime }+\left (1+2 x y\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.144 |
|
|
\[ {}x \left (1+2 x y\right ) y^{\prime }+\left (2+3 x y\right ) y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.707 |
|
|
\[ {}x \left (1+2 x y\right ) y^{\prime }+\left (1+2 x y-x^{2} y^{2}\right ) y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
0.883 |
|
|
\[ {}x^{2} \left (x -2 y\right ) y^{\prime } = 2 x^{3}-4 x y^{2}+y^{3} \] |
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 |
|
|
\[ {}\left (1-x^{3} y\right ) y^{\prime } = x^{2} y^{2} \] |
1 |
1 |
9 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.39 |
|
|
\[ {}x \left (3+2 x^{2} y\right ) y^{\prime }+\left (4+3 x^{2} y\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
6.575 |
|
|
\[ {}8 x^{3} y y^{\prime }+3 x^{4}-6 x^{2} y^{2}-y^{4} = 0 \] |
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 |
|
|
\[ {}\left (1-x^{2}+y^{2}\right ) y^{\prime } = 1+x^{2}-y^{2} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
0.654 |
|
|
\[ {}\left (3 x^{2}-y^{2}\right ) y^{\prime } = 2 x y \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.833 |
|
|
\[ {}\left (x^{4}+y^{2}\right ) y^{\prime } = 4 x^{3} y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.571 |
|
|
\[ {}\left (1+y+x y+y^{2}\right ) y^{\prime }+1+y = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
2.296 |
|
|
\[ {}\left (x +y\right )^{2} y^{\prime } = a^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.724 |
|
|
\[ {}\left (x -y\right )^{2} y^{\prime } = a^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
2.306 |
|
|
\[ {}\left (x^{2}+2 x y-y^{2}\right ) y^{\prime }+x^{2}-2 x y+y^{2} = 0 \] |
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 |
|
|
\[ {}\left (a +b +x +y\right )^{2} y^{\prime } = 2 \left (a +y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
1.479 |
|
|
\[ {}\left (2 x^{2}+4 x y-y^{2}\right ) y^{\prime } = x^{2}-4 x y-2 y^{2} \] |
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 |
|
|
\[ {}\left (1-3 x -y\right )^{2} y^{\prime } = \left (1-2 y\right ) \left (3-6 x -4 y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
3.851 |
|
|
\[ {}\left (2 x^{2}+3 y^{2}\right ) y^{\prime }+x \left (3 x +y\right ) = 0 \] |
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 |
|
|
\[ {}\left (1-3 x +2 y\right )^{2} y^{\prime } = \left (4+2 x -3 y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
5.158 |
|
|
\[ {}\left (x^{2}+a y^{2}\right ) y^{\prime } = x y \] |
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 |
|
|
\[ {}x \left (3 x -y^{2}\right ) y^{\prime }+\left (5 x -2 y^{2}\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.765 |
|
|
\[ {}x \left (1-x^{2}+y^{2}\right ) y^{\prime }+\left (1+x^{2}-y^{2}\right ) y = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
5.356 |
|
|
\[ {}x \left (a -x^{2}-y^{2}\right ) y^{\prime }+\left (a +x^{2}+y^{2}\right ) y = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
5.602 |
|
|
\[ {}x \left (2 x^{2}+y^{2}\right ) y^{\prime } = \left (2 x^{2}+3 y^{2}\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.135 |
|
|
\[ {}\left (x \left (a -x^{2}-y^{2}\right )+y\right ) y^{\prime }+x -\left (a -x^{2}-y^{2}\right ) y = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
2.066 |
|
|
\[ {}x \left (x^{2}-x y+y^{2}\right ) y^{\prime }+\left (x^{2}+x y+y^{2}\right ) y = 0 \] |
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 |
|
|
\[ {}x \left (x -3 y^{2}\right ) y^{\prime }+\left (2 x -y^{2}\right ) y = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
3.18 |
|
|
\[ {}x \left (x +6 y^{2}\right ) y^{\prime }+x y-3 y^{3} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.339 |
|
|
\[ {}x \left (x^{2}-6 y^{2}\right ) y^{\prime } = 4 \left (x^{2}+3 y^{2}\right ) y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.709 |
|
|
\[ {}x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.315 |
|
|
\[ {}\left (1-x^{2} y^{2}\right ) y^{\prime } = y^{3} x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
0.975 |
|
|
\[ {}\left (1-x^{2} y^{2}\right ) y^{\prime } = \left (1+x y\right ) y^{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.971 |
|
|
\[ {}x \left (1+x y^{2}\right ) y^{\prime }+y = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.185 |
|
|
\[ {}x \left (1+x y^{2}\right ) y^{\prime } = \left (2-3 x y^{2}\right ) y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.484 |
|
|
\[ {}x \left (1-x y\right )^{2} y^{\prime }+\left (1+x^{2} y^{2}\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.223 |
|
|
\[ {}\left (1-x^{4} y^{2}\right ) y^{\prime } = x^{3} y^{3} \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.205 |
|
|
\[ {}\left (x^{3}-y^{3}\right ) y^{\prime }+x^{2} y = 0 \] |
1 |
1 |
10 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.447 |
|
|
\[ {}\left (x^{3}+y^{3}\right ) y^{\prime }+x^{2} \left (x a +3 y\right ) = 0 \] |
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 |
|
|
\[ {}x \left (x -y^{3}\right ) y^{\prime } = \left (3 x +y^{3}\right ) y \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.442 |
|
|
\[ {}x \left (2 x^{3}+y^{3}\right ) y^{\prime } = \left (2 x^{3}-x^{2} y+y^{3}\right ) y \] |
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 |
|
|
\[ {}x \left (x^{4}-2 y^{3}\right ) y^{\prime }+\left (2 x^{4}+y^{3}\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
5.208 |
|
|
\[ {}x \left (2-x y^{2}-2 y^{3} x \right ) y^{\prime }+1+2 y = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.363 |
|
|
\[ {}x \left (1-x y\right ) \left (1-x^{2} y^{2}\right ) y^{\prime }+\left (1+x y\right ) \left (1+x^{2} y^{2}\right ) y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.201 |
|
|
\[ {}\left (x^{2}-y^{4}\right ) y^{\prime } = x y \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.335 |
|
|
\[ {}\left (x^{3}-y^{4}\right ) y^{\prime } = 3 x^{2} y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.968 |
|
|
\[ {}\left (a^{2} x^{2}+\left (x^{2}+y^{2}\right )^{2}\right ) y^{\prime } = a^{2} x y \] |
1 |
1 |
4 |
[_rational] |
✓ |
✓ |
6.356 |
|
|
\[ {}2 \left (x -y^{4}\right ) y^{\prime } = y \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.197 |
|
|
\[ {}\left (a \,x^{3}+\left (x a +b y\right )^{3}\right ) y y^{\prime }+x \left (\left (x a +b y\right )^{3}+b y^{3}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.631 |
|
|
\[ {}2 x \left (x^{3}+y^{4}\right ) y^{\prime } = \left (x^{3}+2 y^{4}\right ) y \] |
1 |
1 |
8 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.709 |
|
|
\[ {}x \left (1-x^{2} y^{4}\right ) y^{\prime }+y = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.585 |
|
|
\[ {}\left (x^{2}-y^{5}\right ) y^{\prime } = 2 x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.212 |
|
|
\[ {}x \left (x^{3}+y^{5}\right ) y^{\prime } = \left (x^{3}-y^{5}\right ) y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.368 |
|
|
\[ {}\left (1+a \left (x +y\right )\right )^{n} y^{\prime }+a \left (x +y\right )^{n} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.24 |
|
|
\[ {}x \left (a +x y^{n}\right ) y^{\prime }+b y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.418 |
|
|
\[ {}\left (1+\sqrt {x +y}\right ) y^{\prime }+1 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.79 |
|
|
\[ {}y^{\prime } \sqrt {x y}+x -y = \sqrt {x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
9.322 |
|
|
\[ {}\left (x -2 \sqrt {x y}\right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
5.217 |
|
|
\[ {}\left (x -\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.154 |
|
|
\[ {}x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }+y \sqrt {x^{2}+y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
78.474 |
|
|
\[ {}x y \left (x +\sqrt {x^{2}-y^{2}}\right ) y^{\prime } = x y^{2}-\left (x^{2}-y^{2}\right )^{\frac {3}{2}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
1.333 |
|
|
\[ {}\left (x \sqrt {1+x^{2}+y^{2}}-y \left (x^{2}+y^{2}\right )\right ) y^{\prime } = x \left (x^{2}+y^{2}\right )+y \sqrt {1+x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.963 |
|
|
\[ {}\left (1+\left (x +y\right ) \tan \left (y\right )\right ) y^{\prime }+1 = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.122 |
|
|
\[ {}x \left (x -y \tan \left (\frac {y}{x}\right )\right ) y^{\prime }+\left (x +y \tan \left (\frac {y}{x}\right )\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.917 |
|
|
\[ {}\left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.09 |
|
|
\[ {}{y^{\prime }}^{2} = y+x^{2} \] |
2 |
2 |
2 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
2.932 |
|
|
\[ {}{y^{\prime }}^{2}+x^{2} = 4 y \] |
2 |
2 |
3 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
2.751 |
|
|
\[ {}{y^{\prime }}^{2}+3 x^{2} = 8 y \] |
2 |
2 |
2 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
3.812 |
|
|
\[ {}{y^{\prime }}^{2}+x^{2} a +b y = 0 \] |
2 |
1 |
0 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
2.79 |
|
|
\[ {}{y^{\prime }}^{2}+a x y^{\prime }+b \,x^{2}+c y = 0 \] |
2 |
1 |
0 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
4.085 |
|
|
\[ {}{y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
9.748 |
|
|
\[ {}{y^{\prime }}^{2}-2 a \,x^{3} y^{\prime }+4 a \,x^{2} y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
5.714 |
|
|
\[ {}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.308 |
|
|
\[ {}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0 \] |
2 |
2 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.498 |
|
|
\[ {}{y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right ) = 0 \] |
2 |
2 |
3 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
4.219 |
|
|
\[ {}{y^{\prime }}^{2}+x y^{2} y^{\prime }+y^{3} = 0 \] |
2 |
1 |
6 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
75.362 |
|
|
\[ {}{y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3} = 0 \] |
2 |
1 |
6 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
18.745 |
|
|
\[ {}{y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4} = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
4.079 |
|
|
\[ {}{y^{\prime }}^{2}-3 x y^{\frac {2}{3}} y^{\prime }+9 y^{\frac {5}{3}} = 0 \] |
2 |
1 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
6.318 |
|
|
\[ {}2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 x y = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
7.216 |
|
|
\[ {}3 {y^{\prime }}^{2}+4 x y^{\prime }+x^{2}-y = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
1.894 |
|
|
\[ {}4 {y^{\prime }}^{2}+2 x \,{\mathrm e}^{-2 y} y^{\prime }-{\mathrm e}^{-2 y} = 0 \] |
2 |
2 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
11.534 |
|
|
\[ {}9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5} = 0 \] |
2 |
2 |
5 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
82.548 |
|
|
\[ {}{y^{\prime }}^{2} x +y y^{\prime }+x^{3} = 0 \] |
2 |
1 |
2 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
8.079 |
|
|
\[ {}{y^{\prime }}^{2} x +y y^{\prime }-y^{4} = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
2.631 |
|
|
\[ {}{y^{\prime }}^{2} x -3 y y^{\prime }+9 x^{2} = 0 \] |
2 |
2 |
4 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
5.328 |
|
|
\[ {}4 {y^{\prime }}^{2} x +4 y y^{\prime }-y^{4} = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
2.632 |
|
|
\[ {}16 {y^{\prime }}^{2} x +8 y y^{\prime }+y^{6} = 0 \] |
2 |
2 |
7 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
3.387 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x +y \left (y+1\right ) = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
3.608 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+2 x \left (y+2 x \right ) y^{\prime }-4 a +y^{2} = 0 \] |
2 |
2 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
4.254 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+x \left (x^{3}-2 y\right ) y^{\prime }-\left (2 x^{3}-y\right ) y = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
9.777 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+x^{3}+2 y^{2} = 0 \] |
2 |
2 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
16.458 |
|
|
\[ {}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+x^{2} = 0 \] |
2 |
1 |
3 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
90.2 |
|
|
\[ {}x^{3} {y^{\prime }}^{2}+x y^{\prime }-y = 0 \] |
2 |
2 |
0 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
16.725 |
|
|
\[ {}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a = 0 \] |
2 |
2 |
4 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
5.416 |
|
|
\[ {}x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.308 |
|
|
\[ {}x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4 = 0 \] |
2 |
2 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.475 |
|
|
\[ {}x^{4} {y^{\prime }}^{2}+x y^{2} y^{\prime }-y^{3} = 0 \] |
2 |
2 |
6 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
38.073 |
|
|
\[ {}4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9 = 0 \] |
2 |
2 |
4 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
5.716 |
|
|
\[ {}x^{6} {y^{\prime }}^{2}-2 x y^{\prime }-4 y = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.532 |
|
|
\[ {}x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y = 0 \] |
2 |
2 |
3 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
4.646 |
|
|
\[ {}y {y^{\prime }}^{2} = {\mathrm e}^{2 x} \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
4.884 |
|
|
\[ {}y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y = 0 \] |
2 |
2 |
7 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
6.483 |
|
|
\[ {}9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y = 0 \] |
2 |
2 |
7 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
6.322 |
|
|
\[ {}\left (x^{2}-a y\right ) {y^{\prime }}^{2}-2 x y y^{\prime } = 0 \] |
2 |
1 |
2 |
[_quadrature] |
✓ |
✓ |
0.816 |
|
|
\[ {}x y {y^{\prime }}^{2}-\left (a -b \,x^{2}+y^{2}\right ) y^{\prime }-b x y = 0 \] |
2 |
1 |
0 |
[_rational] |
✓ |
✓ |
66.336 |
|
|
\[ {}y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y = 0 \] |
2 |
2 |
5 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
4.924 |
|
|
\[ {}y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y = 0 \] |
2 |
2 |
5 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
5.02 |
|
|
\[ {}9 y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y = 0 \] |
2 |
2 |
5 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
3.781 |
|
|
\[ {}x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+x \,a^{2} = 0 \] |
2 |
2 |
6 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
5.448 |
|
|
\[ {}2 x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }-a = 0 \] |
2 |
2 |
8 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.208 |
|
|
\[ {}4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \] |
2 |
2 |
6 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
5.898 |
|
|
\[ {}3 x y^{4} {y^{\prime }}^{2}-y^{5} y^{\prime }+1 = 0 \] |
2 |
1 |
12 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.103 |
|
|
\[ {}9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-a = 0 \] |
2 |
1 |
12 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.038 |
|
|
\[ {}{y^{\prime }}^{3}-a x y y^{\prime }+2 a y^{2} = 0 \] |
3 |
1 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
16.117 |
|
|
\[ {}{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5} = 0 \] |
3 |
1 |
4 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
17.514 |
|
|
\[ {}3 {y^{\prime }}^{3}-x^{4} y^{\prime }+2 x^{3} y = 0 \] |
3 |
1 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
86.383 |
|
|
\[ {}x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0 \] |
3 |
1 |
11 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
93.679 |
|
|
\[ {}2 x^{3} {y^{\prime }}^{3}+6 x^{2} y {y^{\prime }}^{2}-\left (1-6 x y\right ) y y^{\prime }+2 y^{3} = 0 \] |
3 |
1 |
4 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
21.441 |
|
|
\[ {}x^{4} {y^{\prime }}^{3}-x^{3} y {y^{\prime }}^{2}-x^{2} y^{2} y^{\prime }+y^{3} x = 1 \] |
3 |
1 |
6 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
18.007 |
|
|
\[ {}x^{6} {y^{\prime }}^{3}-x y^{\prime }-y = 0 \] |
3 |
1 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
100.911 |
|
|
\[ {}y^{2} {y^{\prime }}^{3}-x y^{\prime }+y = 0 \] |
3 |
1 |
5 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
81.401 |
|
|
\[ {}y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \] |
3 |
1 |
7 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
87.318 |
|
|
\[ {}4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y = 0 \] |
3 |
1 |
7 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
47.616 |
|
|
\[ {}16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \] |
3 |
1 |
7 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
86.735 |
|
|
\[ {}y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0 \] |
3 |
1 |
10 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
143.295 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}-y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.12 |
|
|
\[ {}y^{\prime } = \frac {x +y-3}{x -y-1} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.603 |
|
|
\[ {}y^{\prime } = \frac {2 x +y-1}{4 x +2 y+5} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.064 |
|
|
\[ {}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
5.584 |
|
|
\[ {}\left (y-x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.105 |
|
|
\[ {}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.198 |
|
|
\[ {}x y^{\prime }-y-\sqrt {x^{2}+y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.44 |
|
|
\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.527 |
|
|
\[ {}2 x -y+1+\left (2 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.587 |
|
|
\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.013 |
|
|
\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.613 |
|
|
\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \] |
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 |
|
|
\[ {}\left (x^{2} y^{2}+x y\right ) y+\left (x^{2} y^{2}-1\right ) x y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.265 |
|
|
\[ {}\left (x^{3} y^{3}+x^{2} y^{2}+x y+1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-x y+1\right ) x y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.514 |
|
|
\[ {}2 x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
9.542 |
|
|
\[ {}\left (x +\sqrt {y^{2}-x y}\right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.41 |
|
|
\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.359 |
|
|
\[ {}2 x^{2} y+y^{3}+\left (x y^{2}-2 x^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.447 |
|
|
\[ {}y^{2}+\left (x \sqrt {-x^{2}+y^{2}}-x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
5.064 |
|
|
\[ {}\frac {y \cos \left (\frac {y}{x}\right )}{x}-\left (\frac {x \sin \left (\frac {y}{x}\right )}{y}+\cos \left (\frac {y}{x}\right )\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}x +2 y-4-\left (2 x -4 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.886 |
|
|
\[ {}3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.258 |
|
|
\[ {}x +y-1+\left (2 x +2 y-3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.178 |
|
|
\[ {}x +y-1-\left (x -y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.878 |
|
|
\[ {}x +y+\left (2 x +2 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.141 |
|
|
\[ {}x +2 y+\left (3 x +6 y+3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.178 |
|
|
\[ {}x +2 y+\left (y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.835 |
|
|
\[ {}3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.572 |
|
|
\[ {}x +y+\left (3 x +3 y-4\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.444 |
|
|
\[ {}3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.75 |
|
|
\[ {}y+7+\left (2 x +y+3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.445 |
|
|
\[ {}x +y+2-\left (x -y-4\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.932 |
|
|
\[ {}y \left (2 x^{2} y^{3}+3\right )+x \left (x^{2} y^{3}-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.148 |
|
|
\[ {}x^{2}-y^{2}-y-\left (x^{2}-y^{2}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
2.471 |
|
|
\[ {}y^{\prime } = \frac {1}{x^{2}}-\frac {y}{x}-y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
2.769 |
|
|
\[ {}y^{\prime } = 1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
3.303 |
|
|
\[ {}\left (1+x \right ) y^{\prime }-y-1 = \left (1+x \right ) \sqrt {y+1} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.615 |
|
|
\[ {}{\mathrm e}^{y} \left (y^{\prime }+1\right ) = {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.761 |
|
|
\[ {}\left (x -y\right )^{2} y^{\prime } = 4 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
2.873 |
|
|
\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.292 |
|
|
\[ {}\left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.098 |
|
|
\[ {}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.274 |
|
|
\[ {}y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.566 |
|
|
\[ {}y^{\prime } = \left (x^{2}+2 y-1\right )^{\frac {2}{3}}-x \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
2.453 |
|
|
\[ {}x y^{\prime } = x \,{\mathrm e}^{\frac {y}{x}}+x +y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.658 |
|
|
\[ {}x y^{\prime }-y \left (\ln \left (x y\right )-1\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
3.353 |
|
|
\[ {}y^{2}-3 x y-2 x^{2}+\left (x y-x^{2}\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}y^{2}+12 x^{2} y+\left (2 x y+4 x^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.901 |
|
|
\[ {}\left (x^{2}-y\right ) y^{\prime }-4 x y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.718 |
|
|
\[ {}\left (2 y^{3} x -x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
10.768 |
|
|
\[ {}\left (x y-1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.541 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0 \] |
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 |
|
|
\[ {}-a y^{3}-\frac {b}{x^{\frac {3}{2}}}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
✓ |
0.852 |
|
|
\[ {}a x y^{3}+b y^{2}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
4.519 |
|
|
\[ {}y^{\prime }+y^{2} = \frac {a^{2}}{x^{4}} \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
1.376 |
|
|
\[ {}\left (x -y\right ) y^{\prime }+1+x +y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.817 |
|
|
\[ {}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.135 |
|
|
\[ {}x y+\left (-x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}y^{\prime } = \cos \left (x +y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.887 |
|
|
\[ {}y^{\prime } = x y^{2}-\frac {2 y}{x}-\frac {1}{x^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.128 |
|
|
\[ {}y^{\prime } = y^{2} {\mathrm e}^{-x}+y-{\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
0.921 |
|
|
\[ {}\left (y+2 x \right ) y^{\prime }-x +2 y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.436 |
|
|
\[ {}y^{\prime }-\sin \left (x +y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.845 |
|
|
\[ {}\left ({\mathrm e}^{4 y}+2 x \right ) y^{\prime }-1 = 0 \] |
1 |
1 |
2 |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
4.855 |
|
|
\[ {}\left (x^{3}+x y^{2}\right ) y^{\prime } = 2 y^{3} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.816 |
|
|
\[ {}\left (3 x +3 y-4\right ) y^{\prime } = -x -y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.756 |
|
|
\[ {}x -y-1+\left (4 y+x -1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.734 |
|
|
\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.688 |
|
|
\[ {}\left (1+x y\right ) y+x \left (1+x y+x^{2} y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.46 |
|
|
\[ {}x^{2}-2 x y+5 y^{2} = \left (x^{2}+2 x y+y^{2}\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.461 |
|
|
\[ {}y^{\prime } = \frac {2 x y+y^{2}}{x^{2}+2 x y} \] |
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 |
|
|
\[ {}y^{2}+x^{2} y^{\prime } = x y y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.405 |
|
|
\[ {}y^{\prime } = \frac {x -2 y+1}{2 x -4 y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.503 |
|
|
\[ {}x y^{2}+y+\left (x^{2} y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.543 |
|
|
\[ {}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.992 |
|
|
\[ {}y \sqrt {x^{2}+y^{2}}-x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
4.592 |
|
|
\[ {}x +y+1+\left (2 x +2 y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.803 |
|
|
\[ {}2 x y^{\prime }-2 y = \sqrt {x^{2}+4 y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.997 |
|
|
\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.744 |
|
|
\[ {}\left (1+2 x y\right ) y+x \left (1-x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.641 |
|
|
\[ {}3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.863 |
|
|
\[ {}y^{\prime } = -2 \left (2 x +3 y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.867 |
|
|
\[ {}x +y+1-\left (x -y-3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.921 |
|
|
\[ {}2+y^{2}-\left (x y+2 y+y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
6.585 |
|
|
\[ {}1+y^{2} = \left (\arctan \left (y\right )-x \right ) y^{\prime } \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
10.002 |
|
|
\[ {}3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.763 |
|
|
\[ {}y^{2} {y^{\prime }}^{2}+3 x y^{\prime }-y = 0 \] |
2 |
2 |
5 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
5.545 |
|
|
\[ {}16 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \] |
2 |
2 |
6 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
7.541 |
|
|
\[ {}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \] |
3 |
1 |
7 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
94.018 |
|
|
\[ {}y^{2} {y^{\prime }}^{2}+3 x y^{\prime }-y = 0 \] |
2 |
2 |
5 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
4.674 |
|
|
\[ {}y = -x y^{\prime }+x^{4} {y^{\prime }}^{2} \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.43 |
|
|
\[ {}{y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y = 0 \] |
3 |
1 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
117.097 |
|
|
\[ {}y^{\prime } = \cos \left (x -y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.181 |
|
|
\[ {}y^{\prime } = \cos \left (x -y-1\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.274 |
|
|
\[ {}y^{\prime }+\sin \left (x +y\right )^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.364 |
|
|
\[ {}y^{\prime } = 2 \sqrt {2 x +y+1} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
4.118 |
|
|
\[ {}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (1+x +y\right )^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
1.73 |
|
|
\[ {}y+2 = \left (-4+2 x +y\right ) y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.622 |
|
|
\[ {}\left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right ) = \frac {x +y}{x +3} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
6.257 |
|
|
\[ {}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.745 |
|
|
\[ {}x y^{\prime }-2 \sqrt {x y} = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.694 |
|
|
\[ {}y^{\prime } = \frac {x +y-1}{3+x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.736 |
|
|
\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.274 |
|
|
\[ {}y+\sqrt {x^{2}+y^{2}}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.021 |
|
|
\[ {}\left (1+x^{2} y^{2}\right ) y+\left (x^{2} y^{2}-1\right ) x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.478 |
|
|
\[ {}x +y y^{\prime }+y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.022 |
|
|
\[ {}y^{\prime } = \frac {\left (x +y-1\right )^{2}}{2 \left (2+x \right )^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
2.06 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.279 |
|
|
\[ {}x y^{\prime }+y = x^{4} {y^{\prime }}^{2} \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
7.297 |
|
|
\[ {}y^{\prime } = \frac {y^{2}}{x y-x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.466 |
|
|
\[ {}\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.437 |
|
|
\[ {}y^{\prime } = \frac {2 x y^{2}}{1-x^{2} y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.313 |
|
|
\[ {}y-x y^{\prime } = y^{\prime } y^{2} {\mathrm e}^{y} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.62 |
|
|
\[ {}x y^{\prime }+2 = x^{3} \left (y-1\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
5.012 |
|
|
\[ {}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.368 |
|
|
\[ {}2 x \left (1+\sqrt {x^{2}-y}\right ) = \sqrt {x^{2}-y}\, y^{\prime } \] |
1 |
1 |
1 |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
7.158 |
|
|
\[ {}\frac {y-x y^{\prime }}{\left (x +y\right )^{2}}+y^{\prime } = 1 \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
8.179 |
|
|
\[ {}y^{\prime } = \frac {x +y+4}{x -y-6} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.154 |
|
|
\[ {}y^{\prime } = \frac {x +y+4}{x +y-6} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.968 |
|
|
\[ {}2 x -2 y+\left (y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.46 |
|
|
\[ {}y^{\prime } = \frac {x +y-1}{x +4 y+2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
11.516 |
|
|
\[ {}y^{\prime } = \frac {y-x y^{2}}{x +x^{2} y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.674 |
|
|
\[ {}y^{\prime } = \frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right ) \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
24.117 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+y^{2}}{x^{2}-y^{2}} \] |
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 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
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 |
|
|
\[ {}3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.311 |
|
|
\[ {}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
4.935 |
|
|
\[ {}4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \] |
2 |
2 |
6 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
6.27 |
|
|
\[ {}4 y^{3} {y^{\prime }}^{2}+4 x y^{\prime }+y = 0 \] |
2 |
1 |
3 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
22.549 |
|
|
\[ {}y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0 \] |
3 |
1 |
10 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
114.33 |
|
|
\[ {}{y^{\prime }}^{2}+x^{3} y^{\prime }-2 x^{2} y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
5.641 |
|
|
\[ {}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
4.579 |
|
|
\[ {}2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4} = 0 \] |
3 |
1 |
4 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
108.481 |
|
|
\[ {}x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y = 0 \] |
2 |
2 |
3 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
4.955 |
|
|
\[ {}x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4 = 0 \] |
2 |
2 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
5.307 |
|
|
\[ {}3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.55 |
|
|
\[ {}x^{6} {y^{\prime }}^{3}-3 x y^{\prime }-3 y = 0 \] |
3 |
1 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
23.949 |
|
|
\[ {}y = x^{6} {y^{\prime }}^{3}-x y^{\prime } \] |
3 |
1 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
94.164 |
|
|
\[ {}y = x y^{\prime }+x^{3} {y^{\prime }}^{2} \] |
2 |
2 |
0 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
25.161 |
|
|
\[ {}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+4 = 0 \] |
2 |
2 |
4 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
8.249 |
|
|
\[ {}9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5} = 0 \] |
2 |
2 |
5 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
79.343 |
|
|
\[ {}4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \] |
2 |
2 |
6 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
9.931 |
|
|
\[ {}x^{6} {y^{\prime }}^{2}-2 x y^{\prime }-4 y = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
8.614 |
|
|
\[ {}4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9 = 0 \] |
2 |
2 |
4 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
10.965 |
|
|
\[ {}4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y = 0 \] |
3 |
1 |
7 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
83.928 |
|
|
\[ {}16 {y^{\prime }}^{2} x +8 y y^{\prime }+y^{6} = 0 \] |
2 |
2 |
7 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
8.799 |
|
|
\[ {}9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-1 = 0 \] |
2 |
1 |
12 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
7.156 |
|
|
\[ {}x^{6} {y^{\prime }}^{2} = 16 y+8 x y^{\prime } \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
8.246 |
|
|
\[ {}x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0 \] |
3 |
1 |
11 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
117.751 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{x +4 y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.537 |
|
|
\[ {}y^{\prime } = \frac {-x y-1}{4 x^{3} y-2 x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.513 |
|
|
\[ {}y^{\prime } = \sqrt {y}+x \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
✓ |
3.674 |
|
|
\[ {}y^{2}+x^{2} y^{\prime } = x y y^{\prime } \] |
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 |
|
|
\[ {}2 t +3 x+\left (x+2\right ) x^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.444 |
|
|
\[ {}y y^{\prime }-y = x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.423 |
|
|
\[ {}y^{\prime } = -4 \sin \left (x -y\right )-4 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
39.384 |
|
|
\[ {}y^{\prime }+\sin \left (x -y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.358 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{-\frac {y}{x}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.303 |
|
|
\[ {}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
2.548 |
|
|
\[ {}{y^{\prime }}^{2} = \frac {1}{x y} \] |
2 |
2 |
2 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
4.559 |
|
|
\[ {}{y^{\prime }}^{2} = \frac {1}{y^{3} x} \] |
2 |
2 |
2 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
4.829 |
|
|
\[ {}{y^{\prime }}^{4} = \frac {1}{y^{3} x} \] |
4 |
4 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
12.116 |
|
|
\[ {}y^{\prime }+y^{2}-2 x^{2} y+x^{4}-2 x -1 = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
1.682 |
|
|
\[ {}-a y^{3}-\frac {b}{x^{\frac {3}{2}}}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
✓ |
1.441 |
|
|
\[ {}a x y^{3}+b y^{2}+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
9.667 |
|
|
\[ {}y^{\prime }-a y^{n}-b \,x^{\frac {n}{-n +1}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
1.619 |
|
|
\[ {}y^{\prime }-a \sqrt {y}-b x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
4.431 |
|
|
\[ {}y^{\prime }-\sqrt {\frac {a y^{2}+b y+c}{x^{2} a +b x +c}} = 0 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
293.068 |
|
|
\[ {}y^{\prime }-\cos \left (b x +a y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
78.877 |
|
|
\[ {}y^{\prime }+a \sin \left (\alpha y+\beta x \right )+b = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
101.241 |
|
|
\[ {}y^{\prime }-f \left (x a +b y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.006 |
|
|
\[ {}y^{\prime }-\frac {y-x f \left (x^{2}+a y^{2}\right )}{x +a y f \left (x^{2}+a y^{2}\right )} = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
2.263 |
|
|
\[ {}x y^{\prime }+x y^{2}-y-a \,x^{3} = 0 \] |
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 |
|
|
\[ {}x y^{\prime }-y-\sqrt {x^{2}+y^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.572 |
|
|
\[ {}x y^{\prime }+a \sqrt {x^{2}+y^{2}}-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.931 |
|
|
\[ {}x y^{\prime }-x \,{\mathrm e}^{\frac {y}{x}}-y-x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.657 |
|
|
\[ {}x y^{\prime }-y \left (\ln \left (x y\right )-1\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
1.928 |
|
|
\[ {}x y^{\prime }+x \cos \left (\frac {y}{x}\right )-y+x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.705 |
|
|
\[ {}x y^{\prime }-y f \left (x y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
1.169 |
|
|
\[ {}x y^{\prime }-y f \left (x^{a} y^{b}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
1.609 |
|
|
\[ {}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.293 |
|
|
\[ {}x^{2} y^{\prime }-y^{2}-x y-x^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.257 |
|
|
\[ {}x^{2} \left (y^{\prime }+y^{2}\right )+4 x y+2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.753 |
|
|
\[ {}x^{2} \left (y^{\prime }+y^{2}\right )+a x y+b = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
2.507 |
|
|
\[ {}x^{2} \left (y^{\prime }+a y^{2}\right )-b = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
2.336 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+y^{2}-2 x y+1 = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.912 |
|
|
\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
5.833 |
|
|
\[ {}x \left (2 x -1\right ) y^{\prime }+y^{2}-\left (1+4 x \right ) y+4 x = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
3.405 |
|
|
\[ {}3 x^{2} y^{\prime }-7 y^{2}-3 x y-x^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.614 |
|
|
\[ {}x^{3} y^{\prime }-y^{2}-x^{4} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.056 |
|
|
\[ {}x^{3} y^{\prime }-x^{4} y^{2}+x^{2} y+20 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.99 |
|
|
\[ {}x^{4} \left (y^{\prime }+y^{2}\right )+a = 0 \] |
1 |
1 |
1 |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
2.418 |
|
|
\[ {}\left (x^{2} a +b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
5.824 |
|
|
\[ {}x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{2 n -2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
2.357 |
|
|
\[ {}x^{n} y^{\prime }-a y^{2}-b \,x^{2 n -2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
5.237 |
|
|
\[ {}x^{1+2 n} y^{\prime }-a y^{3}-b \,x^{3 n} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
1.615 |
|
|
\[ {}x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (1+m \right )} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
2.809 |
|
|
\[ {}y y^{\prime }+a y+x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
22.648 |
|
|
\[ {}y y^{\prime }-x \,{\mathrm e}^{\frac {x}{y}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.521 |
|
|
\[ {}\left (y+1\right ) y^{\prime }-y-x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
12.486 |
|
|
\[ {}\left (x +y-1\right ) y^{\prime }-y+2 x +3 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.851 |
|
|
\[ {}\left (y+2 x -2\right ) y^{\prime }-y+x +1 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.328 |
|
|
\[ {}\left (y-2 x +1\right ) y^{\prime }+y+x = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.267 |
|
|
\[ {}\left (y-x^{2}\right ) y^{\prime }+4 x y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.253 |
|
|
\[ {}\left (x +2 y+1\right ) y^{\prime }+1-x -2 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.27 |
|
|
\[ {}\left (2 y+x +7\right ) y^{\prime }-y+2 x +4 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.214 |
|
|
\[ {}\left (2 y-x \right ) y^{\prime }-y-2 x = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.146 |
|
|
\[ {}\left (2 y-6 x \right ) y^{\prime }-y+3 x +2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.451 |
|
|
\[ {}\left (3+2 x +4 y\right ) y^{\prime }-2 y-x -1 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.293 |
|
|
\[ {}\left (4 y-2 x -3\right ) y^{\prime }+2 y-x -1 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.315 |
|
|
\[ {}\left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.281 |
|
|
\[ {}\left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.253 |
|
|
\[ {}\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.935 |
|
|
\[ {}\left (a y+b x +c \right ) y^{\prime }+\alpha y+\beta x +\gamma = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
13.463 |
|
|
\[ {}x \left (4+y\right ) y^{\prime }-y^{2}-2 y-2 x = 0 \] |
1 |
1 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
7.61 |
|
|
\[ {}\left (x \left (x +y\right )+a \right ) y^{\prime }-y \left (x +y\right )-b = 0 \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.793 |
|
|
\[ {}y^{2}-3 x y-2 x^{2}+\left (x y-x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.605 |
|
|
\[ {}\left (2 x y+4 x^{3}\right ) y^{\prime }+y^{2}+112 x^{2} y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.468 |
|
|
\[ {}x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.754 |
|
|
\[ {}\left (3 x +2\right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+x y-7 x^{2}-9 x -3 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.573 |
|
|
\[ {}\left (a x y+b \,x^{n}\right ) y^{\prime }+\alpha y^{3}+\beta y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
10.773 |
|
|
\[ {}x \left (x y-2\right ) y^{\prime }+x^{2} y^{3}+x y^{2}-2 y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
1.533 |
|
|
\[ {}x \left (x y-3\right ) y^{\prime }+x y^{2}-y = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.989 |
|
|
\[ {}\left (2 x^{2} y+x \right ) y^{\prime }-x^{2} y^{3}+2 x y^{2}+y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
1.589 |
|
|
\[ {}\left (2 x^{2} y-x \right ) y^{\prime }-2 x y^{2}-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.831 |
|
|
\[ {}\left (2 x^{2} y-x^{3}\right ) y^{\prime }+y^{3}-4 x y^{2}+2 x^{3} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.803 |
|
|
\[ {}2 x \left (x^{3} y+1\right ) y^{\prime }+\left (3 x^{3} y-1\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.406 |
|
|
\[ {}\left (y-x \right ) \sqrt {x^{2}+1}\, y^{\prime }-a \sqrt {\left (1+y^{2}\right )^{3}} = 0 \] |
1 |
1 |
3 |
[‘x=_G(y,y’)‘] |
✓ |
✗ |
100.584 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0 \] |
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 |
|
|
\[ {}\left (x^{4}+y^{2}\right ) y^{\prime }-4 x^{3} y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.52 |
|
|
\[ {}\left (x +y\right )^{2} y^{\prime }-a^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.276 |
|
|
\[ {}x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.559 |
|
|
\[ {}\left (y+3 x -1\right )^{2} y^{\prime }-\left (2 y-1\right ) \left (4 y+6 x -3\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
4.532 |
|
|
\[ {}\left (x^{2}+4 y^{2}\right ) y^{\prime }-x y = 0 \] |
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 |
|
|
\[ {}\left (2 y-3 x +1\right )^{2} y^{\prime }-\left (3 y-2 x -4\right )^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
4.156 |
|
|
\[ {}\left (2 y-4 x +1\right )^{2} y^{\prime }-\left (-2 x +y\right )^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
1.72 |
|
|
|
||||||||
|
\[ {}\left (a y^{2}+2 b x y+c \,x^{2}\right ) y^{\prime }+b y^{2}+2 c x y+d \,x^{2} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
4.631 |
|
|
\[ {}\left (b \left (\beta y+\alpha x \right )^{2}-\beta \left (x a +b y\right )\right ) y^{\prime }+a \left (\beta y+\alpha x \right )^{2}-\alpha \left (x a +b y\right ) = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
2.774 |
|
|
\[ {}\left (a y+b x +c \right )^{2} y^{\prime }+\left (\alpha y+\beta x +\gamma \right )^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
2.499 |
|
|
\[ {}x \left (y^{2}-3 x \right ) y^{\prime }+2 y^{3}-5 x y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
5.332 |
|
|
\[ {}x \left (y^{2}+x^{2}-a \right ) y^{\prime }-\left (a +x^{2}+y^{2}\right ) y = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
5.089 |
|
|
\[ {}x \left (y^{2}+x y-x^{2}\right ) y^{\prime }-y^{3}+x y^{2}+x^{2} y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.986 |
|
|
\[ {}x \left (y^{2}+x^{2} y+x^{2}\right ) y^{\prime }-2 y^{3}-2 x^{2} y^{2}+x^{4} = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
4.655 |
|
|
\[ {}2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }+y^{3}-x^{2} y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.911 |
|
|
\[ {}\left (3 x y^{2}-x^{2}\right ) y^{\prime }+y^{3}-2 x y = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
2.623 |
|
|
\[ {}\left (6 x y^{2}+x^{2}\right ) y^{\prime }-y \left (3 y^{2}-x \right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.961 |
|
|
\[ {}\left (x^{2} y^{2}+x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.464 |
|
|
\[ {}\left (x y-1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.829 |
|
|
\[ {}\left (10 x^{3} y^{2}+x^{2} y+2 x \right ) y^{\prime }+5 x^{2} y^{3}+x y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.185 |
|
|
\[ {}\left (y^{3}-x^{3}\right ) y^{\prime }-x^{2} y = 0 \] |
1 |
1 |
10 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.938 |
|
|
\[ {}\left (2 y^{3}+5 x^{2} y\right ) y^{\prime }+5 x y^{2}+x^{3} = 0 \] |
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 |
|
|
\[ {}\left (2 y^{3} x -x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.033 |
|
|
\[ {}\left (2 x^{2} y^{3}+x^{2} y^{2}-2 x \right ) y^{\prime }-2 y-1 = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
3.747 |
|
|
\[ {}y \left (y^{3}-2 x^{3}\right ) y^{\prime }+\left (2 y^{3}-x^{3}\right ) x = 0 \] |
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 |
|
|
\[ {}a \,x^{2} y^{n} y^{\prime }-2 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.52 |
|
|
\[ {}y^{m} x^{n} \left (a x y^{\prime }+b y\right )+\alpha x y^{\prime }+\beta y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.395 |
|
|
\[ {}\left (f \left (x +y\right )+1\right ) y^{\prime }+f \left (x +y\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
1.382 |
|
|
\[ {}\left (\sqrt {x y}-1\right ) x y^{\prime }-\left (\sqrt {x y}+1\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
5.008 |
|
|
\[ {}\left (2 x^{\frac {5}{2}} y^{\frac {3}{2}}+x^{2} y-x \right ) y^{\prime }-x^{\frac {3}{2}} y^{\frac {5}{2}}+x y^{2}-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
191.197 |
|
|
\[ {}\left (1+\sqrt {x +y}\right ) y^{\prime }+1 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.214 |
|
|
\[ {}\left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.527 |
|
|
\[ {}\left (y \sqrt {x^{2}+y^{2}}+\left (-x^{2}+y^{2}\right ) \sin \left (\alpha \right )-2 x y \cos \left (\alpha \right )\right ) y^{\prime }+x \sqrt {x^{2}+y^{2}}+2 x y \sin \left (\alpha \right )+\left (-x^{2}+y^{2}\right ) \cos \left (\alpha \right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
9.542 |
|
|
\[ {}\left (x \sqrt {1+x^{2}+y^{2}}-y \left (x^{2}+y^{2}\right )\right ) y^{\prime }-y \sqrt {1+x^{2}+y^{2}}-x \left (x^{2}+y^{2}\right ) = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.592 |
|
|
\[ {}x \left (3 \,{\mathrm e}^{x y}+2 \,{\mathrm e}^{-x y}\right ) \left (x y^{\prime }+y\right )+1 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
35.467 |
|
|
\[ {}\left (\ln \left (y\right )+2 x -1\right ) y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
2.277 |
|
|
\[ {}x y^{\prime } \cot \left (\frac {y}{x}\right )+2 x \sin \left (\frac {y}{x}\right )-y \cot \left (\frac {y}{x}\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
2.95 |
|
|
\[ {}\left (x^{2} y \sin \left (x y\right )-4 x \right ) y^{\prime }+x y^{2} \sin \left (x y\right )-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
33.174 |
|
|
\[ {}\left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }-\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.265 |
|
|
\[ {}\left (y f \left (x^{2}+y^{2}\right )-x \right ) y^{\prime }+y+x f \left (x^{2}+y^{2}\right ) = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
9.193 |
|
|
\[ {}{y^{\prime }}^{2}+a y+b \,x^{2} = 0 \] |
2 |
1 |
0 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
6.334 |
|
|
\[ {}{y^{\prime }}^{2}+a x y^{\prime }+b y+c \,x^{2} = 0 \] |
2 |
1 |
0 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
8.793 |
|
|
\[ {}{y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 x y = 0 \] |
2 |
2 |
2 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
52.138 |
|
|
\[ {}{y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
23.797 |
|
|
\[ {}{y^{\prime }}^{2}+\left (y^{\prime }-y\right ) {\mathrm e}^{x} = 0 \] |
2 |
1 |
2 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
13.042 |
|
|
\[ {}{y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right ) = 0 \] |
2 |
2 |
3 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
8.968 |
|
|
\[ {}{y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3} = 0 \] |
2 |
1 |
6 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
35.307 |
|
|
\[ {}{y^{\prime }}^{2}-3 x y^{\frac {2}{3}} y^{\prime }+9 y^{\frac {5}{3}} = 0 \] |
2 |
1 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
14.772 |
|
|
\[ {}2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 x y = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
14.767 |
|
|
\[ {}3 {y^{\prime }}^{2}+4 x y^{\prime }-y+x^{2} = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
3.991 |
|
|
\[ {}a {y^{\prime }}^{2}+b \,x^{2} y^{\prime }+c x y = 0 \] |
2 |
1 |
2 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
44.898 |
|
|
\[ {}{y^{\prime }}^{2} x +y y^{\prime }-x^{2} = 0 \] |
2 |
1 |
2 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
75.885 |
|
|
\[ {}{y^{\prime }}^{2} x +y y^{\prime }+x^{3} = 0 \] |
2 |
1 |
2 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
18.308 |
|
|
\[ {}{y^{\prime }}^{2} x +y y^{\prime }-y^{4} = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
5.524 |
|
|
\[ {}\left (x y^{\prime }+y+2 x \right )^{2}-4 x y-4 x^{2}-4 a = 0 \] |
2 |
2 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
8.199 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y \left (y+1\right )-x = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
8.697 |
|
|
\[ {}\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2} = 0 \] |
2 |
1 |
3 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
132.964 |
|
|
\[ {}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a = 0 \] |
2 |
2 |
4 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
6.274 |
|
|
\[ {}x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.196 |
|
|
\[ {}y {y^{\prime }}^{2}-{\mathrm e}^{2 x} = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
4.508 |
|
|
\[ {}y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y = 0 \] |
2 |
2 |
7 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
5.781 |
|
|
\[ {}9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y = 0 \] |
2 |
2 |
7 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
5.589 |
|
|
\[ {}a x y {y^{\prime }}^{2}-\left (a y^{2}+b \,x^{2}+c \right ) y^{\prime }+b x y = 0 \] |
2 |
1 |
0 |
[_rational] |
✓ |
✓ |
100.549 |
|
|
\[ {}y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y = 0 \] |
2 |
2 |
5 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
6.134 |
|
|
\[ {}\left (a^{2} \sqrt {x^{2}+y^{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a^{2} \sqrt {x^{2}+y^{2}}-y^{2} = 0 \] |
2 |
1 |
4 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
22.525 |
|
|
\[ {}f \left (x^{2}+y^{2}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+x y^{\prime }\right )^{2} = 0 \] |
2 |
1 |
5 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
4.023 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) f \left (\frac {x}{\sqrt {x^{2}+y^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+x y^{\prime }\right )^{2} = 0 \] |
2 |
1 |
1 |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
6.807 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) f \left (\frac {y}{\sqrt {x^{2}+y^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+x y^{\prime }\right )^{2} = 0 \] |
2 |
1 |
1 |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
7.245 |
|
|
\[ {}{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5} = 0 \] |
3 |
1 |
4 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
15.946 |
|
|
\[ {}x^{3} {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+\left (3 x y^{2}+x^{6}\right ) y^{\prime }-y^{3}-2 x^{5} y = 0 \] |
3 |
1 |
0 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
179.494 |
|
|
\[ {}2 \left (x y^{\prime }+y\right )^{3}-y y^{\prime } = 0 \] |
3 |
1 |
4 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
17.451 |
|
|
\[ {}y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \] |
3 |
1 |
7 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
81.011 |
|
|
\[ {}16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \] |
3 |
1 |
7 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
81.368 |
|
|
\[ {}x^{7} y^{2} {y^{\prime }}^{3}-\left (3 x^{6} y^{3}-1\right ) {y^{\prime }}^{2}+3 x^{5} y^{4} y^{\prime }-x^{4} y^{5} = 0 \] |
3 |
1 |
7 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
126.033 |
|
|
\[ {}{y^{\prime }}^{r}-a y^{s}-b \,x^{\frac {r s}{r -s}} = 0 \] |
0 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
1.43 |
|
|
\[ {}y \sqrt {1+{y^{\prime }}^{2}}-a y y^{\prime }-x a = 0 \] |
2 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
180.667 |
|
|
\[ {}a y \sqrt {1+{y^{\prime }}^{2}}-2 x y y^{\prime }+y^{2}-x^{2} = 0 \] |
2 |
2 |
2 |
[_rational] |
✓ |
✓ |
19.386 |
|
|
\[ {}y^{\prime } = F \left (\frac {y}{x +a}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.622 |
|
|
\[ {}y^{\prime } = 2 x +F \left (y-x^{2}\right ) \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
0.488 |
|
|
\[ {}y^{\prime } = -\frac {x a}{2}+F \left (y+\frac {x^{2} a}{4}+\frac {b x}{2}\right ) \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
0.688 |
|
|
\[ {}y^{\prime } = F \left (y \,{\mathrm e}^{-b x}\right ) {\mathrm e}^{b x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
0.648 |
|
|
\[ {}y^{\prime } = \frac {2 a}{y+2 F \left (y^{2}-4 x a \right ) a} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
0.882 |
|
|
\[ {}y^{\prime } = \frac {F \left (-\frac {-1+y \ln \left (x \right )}{y}\right ) y^{2}}{x} \] |
1 |
1 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
1.248 |
|
|
\[ {}y^{\prime } = \frac {-2 x^{2}+x +F \left (y+x^{2}-x \right )}{x} \] |
1 |
1 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
1.263 |
|
|
\[ {}y^{\prime } = \frac {2 a}{x^{2} \left (-y+2 F \left (\frac {x y^{2}-4 a}{x}\right ) a \right )} \] |
1 |
1 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
2.313 |
|
|
\[ {}y^{\prime } = \frac {y+F \left (\frac {y}{x}\right )}{-1+x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
1.589 |
|
|
\[ {}y^{\prime } = \frac {F \left (-\frac {-1+2 y \ln \left (x \right )}{y}\right ) y^{2}}{x} \] |
1 |
1 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
1.318 |
|
|
\[ {}y^{\prime } = -\frac {y^{2} \left (2 x -F \left (-\frac {x y-2}{2 y}\right )\right )}{4 x} \] |
1 |
1 |
2 |
[NONE] |
✓ |
✓ |
2.022 |
|
|
\[ {}y^{\prime } = \frac {\sqrt {y}}{\sqrt {y}+F \left (\frac {x -y}{\sqrt {y}}\right )} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.148 |
|
|
\[ {}y^{\prime } = \frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2 F \left (y \,{\mathrm e}^{-\frac {x^{2}}{4}}\right )\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2} \] |
1 |
1 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
1.669 |
|
|
\[ {}y^{\prime } = -\frac {-x^{2}+2 x^{3} y-F \left (\left (x y-1\right ) x \right )}{x^{4}} \] |
1 |
1 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.303 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.622 |
|
|
\[ {}y^{\prime } = \frac {1}{y+\sqrt {x}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
1.198 |
|
|
\[ {}y^{\prime } = \frac {1}{y+2+\sqrt {1+3 x}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
8.208 |
|
|
\[ {}y^{\prime } = \frac {x^{2}}{y+x^{\frac {3}{2}}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
8.038 |
|
|
\[ {}y^{\prime } = \frac {x^{\frac {5}{3}}}{y+x^{\frac {4}{3}}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
2.276 |
|
|
\[ {}y^{\prime } = \frac {\left (-1+y \ln \left (x \right )\right )^{2}}{x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
1.95 |
|
|
\[ {}y^{\prime } = \frac {x \left (-2+3 \sqrt {x^{2}+3 y}\right )}{3} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
2.971 |
|
|
\[ {}y^{\prime } = \frac {\left (-1+2 y \ln \left (x \right )\right )^{2}}{x} \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
2.034 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{b x}}{y \,{\mathrm e}^{-b x}+1} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
5.324 |
|
|
\[ {}y^{\prime } = \frac {x^{2} \left (1+2 \sqrt {x^{3}-6 y}\right )}{2} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
3.208 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{x}}{y \,{\mathrm e}^{-x}+1} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
6.884 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{\frac {2 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
5.501 |
|
|
\[ {}y^{\prime } = \frac {x \left (x +2 \sqrt {x^{3}-6 y}\right )}{2} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
3.243 |
|
|
\[ {}y^{\prime } = \left (-\ln \left (y\right )+x^{2}\right ) y \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.331 |
|
|
\[ {}y^{\prime } = \frac {x \left (-2+3 x \sqrt {x^{2}+3 y}\right )}{3} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
3.1 |
|
|
\[ {}y^{\prime } = \left (-\ln \left (y\right )+x \right ) y \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.007 |
|
|
\[ {}y^{\prime } = \frac {x^{3}+x^{2}+2 \sqrt {x^{3}-6 y}}{2 x +2} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
3.084 |
|
|
\[ {}y^{\prime } = -\frac {x}{4}+\frac {1}{4}+x \sqrt {x^{2}-2 x +1+8 y} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
3.399 |
|
|
\[ {}y^{\prime } = -\frac {x}{2}-\frac {a}{2}+x \sqrt {x^{2}+2 x a +a^{2}+4 y} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
3.252 |
|
|
\[ {}y^{\prime } = \frac {\left (\ln \left (y\right )+x^{2}\right ) y}{x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.096 |
|
|
\[ {}y^{\prime } = -\frac {x}{2}+1+x \sqrt {x^{2}-4 x +4 y} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
2.486 |
|
|
\[ {}y^{\prime } = -\frac {2 x^{2}+2 x -3 \sqrt {x^{2}+3 y}}{3 \left (1+x \right )} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
2.467 |
|
|
\[ {}y^{\prime } = \frac {y^{3} {\mathrm e}^{-\frac {4 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
4.551 |
|
|
\[ {}y^{\prime } = \frac {\left (\ln \left (y\right )+x^{3}\right ) y}{x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.328 |
|
|
\[ {}y^{\prime } = -\frac {x}{4}+\frac {1}{4}+x^{2} \sqrt {x^{2}-2 x +1+8 y} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
3.495 |
|
|
\[ {}y^{\prime } = -\frac {x^{2}-1-4 \sqrt {x^{2}-2 x +1+8 y}}{4 \left (1+x \right )} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
2.266 |
|
|
\[ {}y^{\prime } = -\frac {x a}{2}-\frac {b}{2}+x \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c} \] |
1 |
1 |
2 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
2.892 |
|
|
\[ {}y^{\prime } = -\frac {x}{2}-\frac {a}{2}+x^{2} \sqrt {x^{2}+2 x a +a^{2}+4 y} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
3.317 |
|
|
\[ {}y^{\prime } = -\frac {x a}{2}-\frac {b}{2}+x^{2} \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
3.178 |
|
|
\[ {}y^{\prime } = \frac {x}{2}+\frac {1}{2}+x^{2} \sqrt {x^{2}+2 x +1-4 y} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
2.891 |
|
|
\[ {}y^{\prime } = -\frac {x}{2}+1+x^{2} \sqrt {x^{2}-4 x +4 y} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
2.686 |
|
|
\[ {}y^{\prime } = \left (-\ln \left (y\right )+1+x^{2}+x^{3}\right ) y \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
2.563 |
|
|
\[ {}y^{\prime } = \frac {y^{3} {\mathrm e}^{-2 b x}}{y \,{\mathrm e}^{-b x}+1} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
1.837 |
|
|
\[ {}y^{\prime } = \frac {y^{3} {\mathrm e}^{-2 x}}{y \,{\mathrm e}^{-x}+1} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
4.694 |
|
|
\[ {}y^{\prime } = -\frac {x^{2}-x -2-2 \sqrt {x^{2}-4 x +4 y}}{2 \left (1+x \right )} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
2.381 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+2 x +1+2 \sqrt {x^{2}+2 x +1-4 y}}{2 x +2} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
2.301 |
|
|
\[ {}y^{\prime } = \frac {2 a}{x \left (-x y+2 a x y^{2}-8 a^{2}\right )} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.07 |
|
|
\[ {}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-2 b x}+y^{3} {\mathrm e}^{-3 b x}\right ) {\mathrm e}^{b x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
2.971 |
|
|
\[ {}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-\frac {4 x}{3}}+y^{3} {\mathrm e}^{-2 x}\right ) {\mathrm e}^{\frac {2 x}{3}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
3.481 |
|
|
\[ {}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-2 x}+y^{3} {\mathrm e}^{-3 x}\right ) {\mathrm e}^{x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
2.64 |
|
|
\[ {}y^{\prime } = \frac {\left (\ln \left (y\right )+x +x^{3}+x^{4}\right ) y}{x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.543 |
|
|
\[ {}y^{\prime } = -\frac {\left (-\ln \left (y-1\right )+\ln \left (y+1\right )+2 \ln \left (x \right )\right ) x \left (y+1\right )^{2}}{8} \] |
1 |
1 |
2 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
4.471 |
|
|
\[ {}y^{\prime } = \frac {\left (-\ln \left (y-1\right )+\ln \left (y+1\right )+2 \ln \left (x \right )\right )^{2} x \left (y+1\right )^{2}}{16} \] |
1 |
1 |
2 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
4.617 |
|
|
\[ {}y^{\prime } = \frac {-\ln \left (x \right )+{\mathrm e}^{\frac {1}{x}}+4 x^{2} y+2 x +2 x y^{2}+2 x^{3}}{\ln \left (x \right )-{\mathrm e}^{\frac {1}{x}}} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
10.543 |
|
|
\[ {}y^{\prime } = \frac {-y a b +b^{2}+a b +b^{2} x -b a \sqrt {x}-a^{2}}{a \left (-a y+b +a +b x -\sqrt {x}\, a \right )} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.737 |
|
|
\[ {}y^{\prime } = -\frac {x^{2}+x +x a +a -2 \sqrt {x^{2}+2 x a +a^{2}+4 y}}{2 \left (1+x \right )} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
2.842 |
|
|
\[ {}y^{\prime } = \frac {\left (18 x^{\frac {3}{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
4.141 |
|
|
\[ {}y^{\prime } = -\frac {y^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
2.492 |
|
|
\[ {}y^{\prime } = \frac {2 a}{y+2 a y^{4}-16 a^{2} x y^{2}+32 a^{3} x^{2}} \] |
1 |
1 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
0.999 |
|
|
\[ {}y^{\prime } = -\frac {y^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
2.178 |
|
|
\[ {}y^{\prime } = \frac {-\ln \left (x \right )+2 \ln \left (2 x \right ) x y+\ln \left (2 x \right )+\ln \left (2 x \right ) y^{2}+\ln \left (2 x \right ) x^{2}}{\ln \left (x \right )} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
3.72 |
|
|
\[ {}y^{\prime } = -\frac {y a b -b c +b^{2} x +b a \sqrt {x}-a^{2}}{a \left (a y-c +b x +\sqrt {x}\, a \right )} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.285 |
|
|
\[ {}y^{\prime } = \frac {1+2 y}{x \left (-2+x y^{2}+2 y^{3} x \right )} \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.129 |
|
|
\[ {}y^{\prime } = \frac {\left (-1+2 y \ln \left (x \right )\right )^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
2.694 |
|
|
\[ {}y^{\prime } = \frac {2 x^{2}+2 x +x^{4}-2 x^{2} y-1+y^{2}}{1+x} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
2.947 |
|
|
\[ {}y^{\prime } = \frac {2 a}{-x^{2} y+2 a y^{4} x^{2}-16 a^{2} x y^{2}+32 a^{3}} \] |
1 |
1 |
3 |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
2.482 |
|
|
\[ {}y^{\prime } = \frac {1+2 y}{x \left (-2+x y+2 x y^{2}\right )} \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.319 |
|
|
\[ {}y^{\prime } = \frac {\left (-1+y \ln \left (x \right )\right )^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
2.63 |
|
|
\[ {}y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x^{4}\right ) y}{x \left (1+x \right )} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
2.066 |
|
|
\[ {}y^{\prime } = \frac {y^{\frac {3}{2}}}{y^{\frac {3}{2}}+x^{2}-2 x y+y^{2}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
1.806 |
|
|
\[ {}y^{\prime } = \frac {-4 x y+x^{3}+2 x^{2}-4 x -8}{-8 y+2 x^{2}+4 x -8} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.186 |
|
|
\[ {}y^{\prime } = \frac {-4 x y-x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.204 |
|
|
\[ {}y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x \right ) y}{x \left (1+x \right )} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.83 |
|
|
\[ {}y^{\prime } = \frac {-8 x y-x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.227 |
|
|
\[ {}y^{\prime } = \frac {y \left (y+1\right )}{x \left (-y-1+x y\right )} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.378 |
|
|
\[ {}y^{\prime } = \frac {-4 a x y-a^{2} x^{3}-2 a \,x^{2} b -4 x a +8}{8 y+2 x^{2} a +4 b x +8} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.213 |
|
|
\[ {}y^{\prime } = \frac {x y+x +y^{2}}{\left (-1+x \right ) \left (x +y\right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.531 |
|
|
\[ {}y^{\prime } = \frac {-4 x y-x^{3}-2 x^{2} a -4 x +8}{8 y+2 x^{2}+4 x a +8} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.769 |
|
|
\[ {}y^{\prime } = \frac {x -y+\sqrt {y}}{x -y+\sqrt {y}+1} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
1.77 |
|
|
\[ {}y^{\prime } = \frac {y \left (y+1\right )}{x \left (-y-1+y^{4} x \right )} \] |
1 |
1 |
3 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.521 |
|
|
\[ {}y^{\prime } = \frac {x^{3} y+x^{3}+x y^{2}+y^{3}}{\left (-1+x \right ) x^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
✓ |
5.474 |
|
|
\[ {}y^{\prime } = \frac {-\sinh \left (x \right )+\ln \left (x \right ) x^{2}+2 y \ln \left (x \right ) x +\ln \left (x \right )+y^{2} \ln \left (x \right )}{\sinh \left (x \right )} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
41.107 |
|
|
\[ {}y^{\prime } = -\frac {\ln \left (x \right )-\sinh \left (x \right ) x^{2}-2 \sinh \left (x \right ) x y-\sinh \left (x \right )-\sinh \left (x \right ) y^{2}}{\ln \left (x \right )} \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
79.651 |
|
|
\[ {}y^{\prime } = -\frac {\ln \left (-1+x \right )-\coth \left (1+x \right ) x^{2}-2 \coth \left (1+x \right ) x y-\coth \left (1+x \right )-\coth \left (1+x \right ) y^{2}}{\ln \left (-1+x \right )} \] |
1 |
1 |
0 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
93.694 |
|
|
\[ {}y^{\prime } = -\frac {y \left (1+x y\right )}{x \left (x y+1-y\right )} \] |
1 |
1 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.964 |
|
|
\[ {}y^{\prime } = \frac {x^{3}+3 x^{2} a +3 x \,a^{2}+a^{3}+x y^{2}+a y^{2}+y^{3}}{\left (x +a \right )^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
✓ |
8.093 |
|
|
\[ {}y^{\prime } = \frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 x y^{2}+8 y^{3}}{\left (2 x -b \right )^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
✓ |
8.224 |
|
|
\[ {}y^{\prime } = \frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2+2 y^{2} {\mathrm e}^{-\frac {x^{2}}{2}}+2 y^{3} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2} \] |
1 |
1 |
1 |
[_Abel] |
✓ |
✓ |
29.868 |
|
|
\[ {}y^{\prime } = \frac {\left (1+2 y\right ) \left (y+1\right )}{x \left (-2 y-2+x +2 x y\right )} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.21 |
|
|
\[ {}y^{\prime } = \frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 x y^{2}+64 y^{3}}{\left (4 x -5\right )^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
✓ |
8.832 |
|
|
\[ {}y^{\prime } = \frac {y}{x \left (-1+x y+y^{3} x +y^{4} x \right )} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
4.684 |
|
|
\[ {}y^{\prime } = \frac {y \left (x^{3}+x^{2} y+y^{2}\right )}{x^{2} \left (-1+x \right ) \left (x +y\right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
7.444 |
|
|
\[ {}y^{\prime } = \frac {\left (1+2 y\right ) \left (y+1\right )}{x \left (-2 y-2+y^{3} x +2 y^{4} x \right )} \] |
1 |
1 |
3 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
7.243 |
|
|
\[ {}y^{\prime } = \frac {\left ({\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x +x^{2}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
5.023 |
|
|
\[ {}y^{\prime } = \frac {\left ({\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x +x^{3}\right ) {\mathrm e}^{\frac {y}{x}}}{x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
4.204 |
|
|
\[ {}y^{\prime } = \frac {b^{3}+y^{2} b^{3}+2 y b^{2} a x +b \,x^{2} a^{2}+y^{3} b^{3}+3 y^{2} b^{2} a x +3 y b \,a^{2} x^{2}+a^{3} x^{3}}{b^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Abel] |
✓ |
✓ |
3.258 |
|
|
\[ {}y^{\prime } = \frac {\alpha ^{3}+y^{2} \alpha ^{3}+2 y \alpha ^{2} \beta x +\alpha \,\beta ^{2} x^{2}+y^{3} \alpha ^{3}+3 y^{2} \alpha ^{2} \beta x +3 y \alpha \,\beta ^{2} x^{2}+\beta ^{3} x^{3}}{\alpha ^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Abel] |
✓ |
✓ |
3.256 |
|
|
\[ {}y^{\prime } = \frac {a^{3}+y^{2} a^{3}+2 y a^{2} b x +a \,b^{2} x^{2}+y^{3} a^{3}+3 y^{2} a^{2} b x +3 y a \,b^{2} x^{2}+b^{3} x^{3}}{a^{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Abel] |
✓ |
✓ |
3.294 |
|
|
\[ {}y^{\prime } = \frac {y \left ({\mathrm e}^{-\frac {x^{2}}{2}} x y+{\mathrm e}^{-\frac {x^{2}}{4}} x +2 y^{2} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2 y \,{\mathrm e}^{-\frac {x^{2}}{4}}+2} \] |
1 |
1 |
2 |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
5.991 |
|
|
\[ {}y^{\prime } = -\frac {2 x}{3}+1+y^{2}+\frac {2 x^{2} y}{3}+\frac {x^{4}}{9}+y^{3}+x^{2} y^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
2.798 |
|
|
\[ {}y^{\prime } = 2 x +1+y^{2}-2 x^{2} y+x^{4}+y^{3}-3 x^{2} y^{2}+3 x^{4} y-x^{6} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
2.392 |
|
|
\[ {}y^{\prime } = \frac {1+2 y}{x \left (-2+x +x y^{2}+3 y^{3} x +2 x y+2 y^{4} x \right )} \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
5.895 |
|
|
\[ {}y^{\prime } = -\frac {y^{2} \left (x^{2} y-2 x -2 x y+y\right )}{2 \left (-2+x y-2 y\right ) x} \] |
1 |
1 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
5.187 |
|
|
\[ {}y^{\prime } = \frac {-2 x y+2 x^{3}-2 x -y^{3}+3 x^{2} y^{2}-3 x^{4} y+x^{6}}{-y+x^{2}-1} \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
2.837 |
|
|
\[ {}y^{\prime } = -\frac {2 a}{-y-2 a -2 a y^{4}+16 a^{2} x y^{2}-32 a^{3} x^{2}-2 a y^{6}+24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.668 |
|
|
\[ {}y^{\prime } = \frac {-18 x y-6 x^{3}-18 x +27 y^{3}+27 x^{2} y^{2}+9 x^{4} y+x^{6}}{27 y+9 x^{2}+27} \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
2.931 |
|
|
\[ {}y^{\prime } = \frac {2 x^{2}-4 x^{3} y+1+x^{4} y^{2}+x^{6} y^{3}-3 x^{5} y^{2}+3 x^{4} y-x^{3}}{x^{4}} \] |
1 |
1 |
1 |
[_rational, _Abel] |
✓ |
✓ |
10.175 |
|
|
\[ {}y^{\prime } = \frac {6 x^{2} y-2 x +1-5 x^{3} y^{2}-2 x y+x^{4} y^{3}}{x^{2} \left (x^{2} y-x +1\right )} \] |
1 |
1 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
4.778 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{-\frac {2}{-y^{2}+x^{2}-1}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{-\frac {2}{-y^{2}+x^{2}-1}}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
6.133 |
|
|
\[ {}y^{\prime } = \frac {2 a \left (-y^{2}+4 x a -1\right )}{-y^{3}+4 a x y-y-2 a y^{6}+24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
4.06 |
|
|
\[ {}y^{\prime } = \frac {2 a x}{-x^{3} y+2 a \,x^{3}+2 a y^{4} x^{3}-16 y^{2} a^{2} x^{2}+32 a^{3} x +2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \] |
1 |
1 |
0 |
[_rational] |
✓ |
✓ |
7.266 |
|
|
\[ {}y^{\prime } = -\frac {-y^{3}-y+2 y^{2} \ln \left (x \right )-\ln \left (x \right )^{2} y^{3}-1+3 y \ln \left (x \right )-3 \ln \left (x \right )^{2} y^{2}+\ln \left (x \right )^{3} y^{3}}{y x} \] |
1 |
1 |
1 |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
4.983 |
|
|
\[ {}y^{\prime } = \frac {2 a \left (x y^{2}-4 a +x \right )}{-x^{3} y^{3}+4 a \,x^{2} y-x^{3} y+2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \] |
1 |
1 |
1 |
[_rational] |
✓ |
✓ |
7.559 |
|
|
\[ {}y^{\prime } = -\frac {-y^{3}-y+4 y^{2} \ln \left (x \right )-4 \ln \left (x \right )^{2} y^{3}-1+6 y \ln \left (x \right )-12 \ln \left (x \right )^{2} y^{2}+8 \ln \left (x \right )^{3} y^{3}}{y x} \] |
1 |
1 |
1 |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
4.929 |
|
|
\[ {}y^{\prime } = \frac {y^{\frac {3}{2}} \left (x -y+\sqrt {y}\right )}{y^{\frac {3}{2}} x -y^{\frac {5}{2}}+y^{2}+x^{3}-3 x^{2} y+3 x y^{2}-y^{3}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
44.891 |
|
|
\[ {}y^{\prime } = \frac {y^{2}}{y^{2}+y^{\frac {3}{2}}+\sqrt {y}\, x^{2}-2 y^{\frac {3}{2}} x +y^{\frac {5}{2}}+x^{3}-3 x^{2} y+3 x y^{2}-y^{3}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
4.431 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{-2 \left (x -y\right ) \left (x +y\right )}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{-2 \left (x -y\right ) \left (x +y\right )}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
5.3 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{2 \left (x -y\right )^{2} \left (x +y\right )^{2}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{2 \left (x -y\right )^{2} \left (x +y\right )^{2}}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
5.895 |
|
|
\[ {}y^{\prime } = \frac {-8 x^{2} y^{3}+16 x y^{2}+16 y^{3} x -8+12 x y-6 x^{2} y^{2}+x^{3} y^{3}}{16 \left (-2+x y-2 y\right ) x} \] |
1 |
1 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
5.727 |
|
|
\[ {}y^{\prime } = -\frac {16 y^{3} x -8 y^{3}-8 y+8 x y^{2}-2 x^{2} y^{3}-8+12 x y-6 x^{2} y^{2}+x^{3} y^{3}}{32 y x} \] |
1 |
1 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
5.741 |
|
|
\[ {}y^{\prime } = \frac {-3 x^{2} y-2 x^{3}-2 x -x y^{2}-y+x^{3} y^{3}+3 x^{4} y^{2}+3 x^{5} y+x^{6}}{x \left (x y+x^{2}+1\right )} \] |
1 |
1 |
2 |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
8.714 |
|
|
\[ {}y^{\prime } = \frac {x}{2}+1+y^{2}+\frac {x^{2} y}{4}-x y-\frac {x^{4}}{8}+\frac {x^{3}}{8}+\frac {x^{2}}{4}+y^{3}-\frac {3 x^{2} y^{2}}{4}-\frac {3 x y^{2}}{2}+\frac {3 x^{4} y}{16}+\frac {3 x^{3} y}{4}-\frac {x^{6}}{64}-\frac {3 x^{5}}{32} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
3.691 |
|
|
\[ {}y^{\prime } = -\frac {x}{2}+1+y^{2}+\frac {7 x^{2} y}{2}-2 x y+\frac {13 x^{4}}{16}-\frac {3 x^{3}}{2}+x^{2}+y^{3}+\frac {3 x^{2} y^{2}}{4}-3 x y^{2}+\frac {3 x^{4} y}{16}-\frac {3 x^{3} y}{2}+\frac {x^{6}}{64}-\frac {3 x^{5}}{16} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
7.264 |
|
|
\[ {}y^{\prime } = -\frac {x}{4}+1+y^{2}+\frac {7 x^{2} y}{16}-\frac {x y}{2}+\frac {5 x^{4}}{128}-\frac {5 x^{3}}{64}+\frac {x^{2}}{16}+y^{3}+\frac {3 x^{2} y^{2}}{8}-\frac {3 x y^{2}}{4}+\frac {3 x^{4} y}{64}-\frac {3 x^{3} y}{16}+\frac {x^{6}}{512}-\frac {3 x^{5}}{256} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
3.816 |
|
|
|
||||||||
|
\[ {}y^{\prime } = \frac {-x^{2}+x +1+y^{2}+5 x^{2} y-2 x y+4 x^{4}-3 x^{3}+y^{3}+3 x^{2} y^{2}-3 x y^{2}+3 x^{4} y-6 x^{3} y+x^{6}-3 x^{5}}{x} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
7.046 |
|
|
\[ {}y^{\prime } = \frac {-32 x y+16 x^{3}+16 x^{2}-32 x -64 y^{3}+48 x^{2} y^{2}+96 x y^{2}-12 x^{4} y-48 x^{3} y-48 x^{2} y+x^{6}+6 x^{5}+12 x^{4}}{-64 y+16 x^{2}+32 x -64} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
5.046 |
|
|
\[ {}y^{\prime } = \frac {-32 x y-72 x^{3}+32 x^{2}-32 x +64 y^{3}+48 x^{2} y^{2}-192 x y^{2}+12 x^{4} y-96 x^{3} y+192 x^{2} y+x^{6}-12 x^{5}+48 x^{4}}{64 y+16 x^{2}-64 x +64} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
4.492 |
|
|
\[ {}y^{\prime } = -\frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{\frac {2 \left (x -y\right )^{3} \left (x +y\right )^{3}}{-y^{2}+x^{2}-1}}}{-y^{2}-2 x y-x^{2}+{\mathrm e}^{\frac {2 \left (x -y\right )^{3} \left (x +y\right )^{3}}{-y^{2}+x^{2}-1}}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
13.535 |
|
|
\[ {}y^{\prime } = \frac {-128 x y-24 x^{3}+32 x^{2}-128 x +512 y^{3}+192 x^{2} y^{2}-384 x y^{2}+24 x^{4} y-96 x^{3} y+96 x^{2} y+x^{6}-6 x^{5}+12 x^{4}}{512 y+64 x^{2}-128 x +512} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
4.328 |
|
|
\[ {}y^{\prime } = \frac {-32 a x y-8 a^{2} x^{3}-16 a \,x^{2} b -32 x a +64 y^{3}+48 x^{2} a y^{2}+96 y^{2} b x +12 y a^{2} x^{4}+48 y a \,x^{3} b +48 y b^{2} x^{2}+a^{3} x^{6}+6 a^{2} x^{5} b +12 a \,x^{4} b^{2}+8 b^{3} x^{3}}{64 y+16 x^{2} a +32 b x +64} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
4.367 |
|
|
\[ {}y^{\prime } = \frac {-32 x y-8 x^{3}-16 x^{2} a -32 x +64 y^{3}+48 x^{2} y^{2}+96 a x y^{2}+12 x^{4} y+48 y a \,x^{3}+48 a^{2} x^{2} y+x^{6}+6 x^{5} a +12 a^{2} x^{4}+8 a^{3} x^{3}}{64 y+16 x^{2}+32 x a +64} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
3.667 |
|
|
\[ {}y^{\prime } = \frac {x^{2} y+x^{4}+2 x^{3}-3 x^{2}+x y+x +y^{3}+3 x^{2} y^{2}-3 x y^{2}+3 x^{4} y-6 x^{3} y+x^{6}-3 x^{5}}{x \left (y+x^{2}-x +1\right )} \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
5.431 |
|
|
\[ {}y^{\prime } = -\frac {x a}{2}+1+y^{2}+\frac {a \,x^{2} y}{2}+b x y+\frac {a^{2} x^{4}}{16}+\frac {a b \,x^{3}}{4}+\frac {b^{2} x^{2}}{4}+y^{3}+\frac {3 x^{2} a y^{2}}{4}+\frac {3 y^{2} b x}{2}+\frac {3 y a^{2} x^{4}}{16}+\frac {3 y a \,x^{3} b}{4}+\frac {3 y b^{2} x^{2}}{4}+\frac {a^{3} x^{6}}{64}+\frac {3 a^{2} x^{5} b}{32}+\frac {3 a \,x^{4} b^{2}}{16}+\frac {b^{3} x^{3}}{8} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
3.684 |
|
|
\[ {}y^{\prime } = -\frac {x}{2}+1+y^{2}+\frac {x^{2} y}{2}+a x y+\frac {x^{4}}{16}+\frac {a \,x^{3}}{4}+\frac {a^{2} x^{2}}{4}+y^{3}+\frac {3 x^{2} y^{2}}{4}+\frac {3 a x y^{2}}{2}+\frac {3 x^{4} y}{16}+\frac {3 y a \,x^{3}}{4}+\frac {3 a^{2} x^{2} y}{4}+\frac {x^{6}}{64}+\frac {3 x^{5} a}{32}+\frac {3 a^{2} x^{4}}{16}+\frac {a^{3} x^{3}}{8} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
3.694 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{2+2 y^{4}-4 x^{2} y^{2}+2 x^{4}+2 y^{6}-6 y^{4} x^{2}+6 x^{4} y^{2}-2 x^{6}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{2+2 y^{4}-4 x^{2} y^{2}+2 x^{4}+2 y^{6}-6 y^{4} x^{2}+6 x^{4} y^{2}-2 x^{6}}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
7.367 |
|
|
\[ {}y^{\prime } = \frac {y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )-\sin \left (\frac {y}{x}\right ) y x -y \sin \left (\frac {y}{x}\right )+2 \sin \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x}{2 \cos \left (\frac {y}{x}\right ) \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right ) \left (1+x \right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
47.311 |
|
|
\[ {}y^{\prime } = \frac {\left (1+x y\right )^{3}}{x^{5}} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
30.454 |
|
|
\[ {}y^{\prime } = y \left (y^{2}+y \,{\mathrm e}^{b x}+{\mathrm e}^{2 b x}\right ) {\mathrm e}^{-2 b x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
19.244 |
|
|
\[ {}y^{\prime } = y^{3}-3 x^{2} y^{2}+3 x^{4} y-x^{6}+2 x \] |
1 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
4.408 |
|
|
\[ {}y^{\prime } = y^{3}+x^{2} y^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27}-\frac {2 x}{3} \] |
1 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
4.05 |
|
|
\[ {}y^{\prime } = \frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x}{x} \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], _rational, _Abel] |
✓ |
✓ |
1.503 |
|
|
\[ {}y^{\prime } = \frac {y \,{\mathrm e}^{-\frac {x^{2}}{2}} \left (2 y^{2}+2 y \,{\mathrm e}^{\frac {x^{2}}{4}}+2 \,{\mathrm e}^{\frac {x^{2}}{2}}+x \,{\mathrm e}^{\frac {x^{2}}{2}}\right )}{2} \] |
1 |
1 |
1 |
[_Abel] |
✓ |
✓ |
68.025 |
|
|
\[ {}y^{\prime } = \frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x^{2}}{\left (-1+x \right ) \left (1+x \right )} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
5.314 |
|
|
\[ {}y^{\prime } = \frac {\left (1+x y\right ) \left (x^{2} y^{2}+x^{2} y+2 x y+1+x +x^{2}\right )}{x^{5}} \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
3.867 |
|
|
\[ {}y^{\prime } = \frac {\left (y-x +\ln \left (1+x \right )\right )^{2}+x}{1+x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
2.306 |
|
|
\[ {}y^{\prime } = f \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.033 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}+b \,x^{-2-n} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
2.179 |
|
|
\[ {}x^{2} y^{\prime } = x^{2} a y^{2}+b \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
4.039 |
|
|
\[ {}x^{4} y^{\prime } = -x^{4} y^{2}-a^{2} \] |
1 |
1 |
1 |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
2.489 |
|
|
\[ {}\left (x^{2} a +b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0 \] |
1 |
1 |
1 |
[_rational, _Riccati] |
✓ |
✓ |
6.493 |
|
|
\[ {}x y^{\prime } = a \,x^{n} y^{2}+b y+c \,x^{-n} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
3.868 |
|
|
\[ {}\left (x a +c \right ) y^{\prime } = \alpha \left (b x +a y\right )^{2}+\beta \left (b x +a y\right )-b x +\gamma \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
5.273 |
|
|
\[ {}x^{2} y^{\prime } = x^{2} a y^{2}+b x y+c \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
4.879 |
|
|
\[ {}\left (x^{2} a +b \right ) y^{\prime }+y^{2}-2 x y+\left (1-a \right ) x^{2}-b = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
4.773 |
|
|
\[ {}\left (x^{2} a +b x +c \right ) y^{\prime } = y^{2}+\left (2 \lambda x +b \right ) y+\lambda \left (\lambda -a \right ) x^{2}+\mu \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
6.681 |
|
|
\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime }+y^{2}+k \left (y+x -a \right ) \left (y+x -b \right ) = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
5.77 |
|
|
\[ {}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+b y+c \,{\mathrm e}^{-\lambda x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
2.21 |
|
|
\[ {}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+b \,{\mathrm e}^{-\lambda x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
2.273 |
|
|
\[ {}x y^{\prime } = \left (a y+b \ln \left (x \right )\right )^{2} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
1.66 |
|
|
\[ {}y y^{\prime }-y = A x +B \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
19.496 |
|
|
\[ {}y y^{\prime } = \frac {y}{\sqrt {x a +b}}+1 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
18.811 |
|
|
\[ {}y y^{\prime } = \left (3 x a +b \right ) y-a^{2} x^{3}-a \,x^{2} b +c x \] |
1 |
1 |
1 |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.573 |
|
|
\[ {}\left (y A +B x +a \right ) y^{\prime }+B y+k x +b = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.462 |
|
|
\[ {}\left (y+x a +b \right ) y^{\prime } = \alpha y+\beta x +\gamma \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
9.039 |
|
|
\[ {}\frac {y^{2}-2 x^{2}}{x y^{2}-x^{3}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
6.898 |
|
|
\[ {}\frac {1}{\sqrt {x^{2}+y^{2}}}+\left (\frac {1}{y}-\frac {x}{y \sqrt {x^{2}+y^{2}}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.803 |
|
|
\[ {}6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.003 |
|
|
\[ {}2 x^{2} y+3 y^{3}-\left (x^{3}+2 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.087 |
|
|
\[ {}4 x +3 y+1+\left (1+x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.957 |
|
|
\[ {}4 x -y+2+\left (x +y+3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.927 |
|
|
\[ {}2 x +y-\left (4 x +2 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.305 |
|
|
\[ {}y+2 x y^{2}-x^{2} y^{3}+2 x^{2} y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.801 |
|
|
\[ {}2 y+3 x y^{2}+\left (2 x^{2} y+x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.91 |
|
|
\[ {}y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.565 |
|
|
\[ {}y^{\prime }-\frac {y+1}{1+x} = \sqrt {y+1} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.266 |
|
|
\[ {}x^{4} y \left (3 y+2 x y^{\prime }\right )+x^{2} \left (4 y+3 x y^{\prime }\right ) = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
9.448 |
|
|
\[ {}2 x^{3} y-y^{2}-\left (2 x^{4}+x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.711 |
|
|
\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.5 |
|
|
\[ {}3 x^{2}+6 x y+3 y^{2}+\left (2 x^{2}+3 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.418 |
|
|
\[ {}y^{2}-x^{2}+2 m x y+\left (m y^{2}-m \,x^{2}-2 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
11.212 |
|
|
\[ {}x +y y^{\prime }+y-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.106 |
|
|
\[ {}\left (y-x \right )^{2} y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.933 |
|
|
\[ {}\left (y-x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.315 |
|
|
\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.91 |
|
|
\[ {}-y+x y^{\prime } = \sqrt {x^{2}-y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.668 |
|
|
\[ {}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.359 |
|
|
\[ {}x -2 y+5+\left (2 x -y+4\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.618 |
|
|
\[ {}x y^{2} \left (3 y+x y^{\prime }\right )-2 y+x y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.125 |
|
|
\[ {}5 x y-3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.938 |
|
|
\[ {}2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.217 |
|
|
\[ {}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.365 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) \left (x +y y^{\prime }\right )+\sqrt {1+x^{2}+y^{2}}\, \left (y-x y^{\prime }\right ) = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
2.616 |
|
|
\[ {}1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.179 |
|
|
\[ {}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.38 |
|
|
\[ {}y^{\prime }+2 x y = x^{2}+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
2.116 |
|
|
\[ {}y = -x y^{\prime }+x^{4} {y^{\prime }}^{2} \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
5.934 |
|
|
\[ {}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0 \] |
3 |
1 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
136.206 |
|
|
\[ {}x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+x = 0 \] |
2 |
2 |
6 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
10.509 |
|
|
\[ {}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \] |
3 |
1 |
7 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
133.768 |
|
|
\[ {}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+1 = 0 \] |
2 |
2 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
6.652 |
|
|
\[ {}\left (-y+x y^{\prime }\right ) \left (x +y y^{\prime }\right ) = a^{2} y^{\prime } \] |
2 |
1 |
0 |
[_rational] |
✓ |
✓ |
72.443 |
|
|
\[ {}y = x y^{\prime }+\frac {y {y^{\prime }}^{2}}{x^{2}} \] |
2 |
2 |
7 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
8.293 |
|
|
\[ {}3 x +2 y+\left (y+2 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.587 |
|
|
\[ {}\frac {3-y}{x^{2}}+\frac {\left (y^{2}-2 x \right ) y^{\prime }}{x y^{2}} = 0 \] |
1 |
1 |
1 |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
5.309 |
|
|
\[ {}\frac {1+8 x y^{\frac {2}{3}}}{x^{\frac {2}{3}} y^{\frac {1}{3}}}+\frac {\left (2 x^{\frac {4}{3}} y^{\frac {2}{3}}-x^{\frac {1}{3}}\right ) y^{\prime }}{y^{\frac {4}{3}}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
4.96 |
|
|
\[ {}y+x \left (x^{2}+y^{2}\right )^{2}+\left (y \left (x^{2}+y^{2}\right )^{2}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
1.89 |
|
|
\[ {}2 x y+3 y^{2}-\left (x^{2}+2 x y\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}\left (2 s^{2}+2 s t +t^{2}\right ) s^{\prime }+s^{2}+2 s t -t^{2} = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.428 |
|
|
\[ {}x^{3}+y^{2} \sqrt {x^{2}+y^{2}}-x y \sqrt {x^{2}+y^{2}}\, y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.595 |
|
|
\[ {}\sqrt {x +y}+\sqrt {x -y}+\left (\sqrt {x -y}-\sqrt {x +y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
7.445 |
|
|
\[ {}2 x -5 y+\left (4 x -y\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}x y^{\prime }+y = \left (x y\right )^{\frac {3}{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
21.659 |
|
|
\[ {}y^{\prime } = \left (1-x \right ) y^{2}+\left (2 x -1\right ) y-x \] |
1 |
1 |
1 |
[_Riccati] |
✓ |
✓ |
3.596 |
|
|
\[ {}y^{\prime } = -8 x y^{2}+4 x \left (1+4 x \right ) y-8 x^{3}-4 x^{2}+1 \] |
1 |
1 |
1 |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
3.138 |
|
|
\[ {}\left (3 x^{2} y^{2}-x \right ) y^{\prime }+2 y^{3} x -y = 0 \] |
1 |
1 |
6 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
3.475 |
|
|
\[ {}3 x -5 y+\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.6 |
|
|
\[ {}2 x^{2}+x y+y^{2}+2 x^{2} y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
4.295 |
|
|
\[ {}y^{\prime } = \frac {4 x^{3} y^{2}-3 x^{2} y}{x^{3}-2 x^{4} y} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.252 |
|
|
\[ {}y^{\prime } = \frac {2 x -7 y}{3 y-8 x} \] |
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 |
|
|
\[ {}y^{\prime } = \frac {2 x +7 y}{2 x -2 y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.665 |
|
|
\[ {}2 x y^{2}+y+\left (2 y^{3}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_rational] |
✓ |
✓ |
2.313 |
|
|
\[ {}4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.113 |
|
|
\[ {}8 x^{2} y^{3}-2 y^{4}+\left (5 x^{3} y^{2}-8 y^{3} x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.99 |
|
|
\[ {}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.466 |
|
|
\[ {}3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.452 |
|
|
\[ {}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.211 |
|
|
\[ {}10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.471 |
|
|
\[ {}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
9.043 |
|
|
\[ {}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.579 |
|
|
\[ {}2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.896 |
|
|
\[ {}4 x +3 y+1+\left (1+x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
13.358 |
|
|
\[ {}x y+y^{2}+x^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.543 |
|
|
\[ {}x^{\prime } = \frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{x t} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.396 |
|
|
\[ {}12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.199 |
|
|
\[ {}x y^{\prime } = y+\sqrt {x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.964 |
|
|
\[ {}y-x y^{\prime } = x^{2} y y^{\prime } \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.868 |
|
|
\[ {}x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
5.086 |
|
|
\[ {}y^{\prime } = \frac {y}{x +y^{3}} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.094 |
|
|
\[ {}y^{\prime } = \frac {2 y-x -4}{2 x -y+5} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.189 |
|
|
\[ {}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.65 |
|
|
\[ {}y^{\prime } = \left (x -5 y\right )^{\frac {1}{3}}+2 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
4.777 |
|
|
\[ {}y^{\prime } = \frac {3 x -4 y-2}{3 x -4 y-3} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.773 |
|
|
\[ {}y = x^{2}+2 x y^{\prime }+\frac {{y^{\prime }}^{2}}{2} \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
3.135 |
|
|
\[ {}3 y^{2}-x +2 y \left (y^{2}-3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
7.424 |
|
|
\[ {}y^{\prime } = \frac {x +y-3}{-x +y+1} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.433 |
|
|
\[ {}\left (4 y+2 x +3\right ) y^{\prime }-2 y-x -1 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.665 |
|
|
\[ {}\left (-x^{2}+y^{2}\right ) y^{\prime }+2 x y = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.112 |
|
|
\[ {}y^{\prime } = \cos \left (x +y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.796 |
|
|
\[ {}x y \left (1-{y^{\prime }}^{2}\right ) = \left (x^{2}-y^{2}-a^{2}\right ) y^{\prime } \] |
2 |
1 |
0 |
[_rational] |
✓ |
✓ |
71.363 |
|
|
\[ {}y-x +\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.889 |
|
|
\[ {}x +y+\left (y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.426 |
|
|
\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.636 |
|
|
\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.751 |
|
|
\[ {}2 \sqrt {s t}-s+t s^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.618 |
|
|
\[ {}x \cos \left (\frac {y}{x}\right ) \left (x y^{\prime }+y\right ) = y \sin \left (\frac {y}{x}\right ) \left (-y+x y^{\prime }\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.424 |
|
|
\[ {}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.181 |
|
|
\[ {}x +2 y+1-\left (4 y+2 x +3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.838 |
|
|
\[ {}\frac {y-x y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
25.151 |
|
|
\[ {}\frac {x +y y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
3.546 |
|
|
\[ {}y+\frac {x}{y^{\prime }} = \sqrt {x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.977 |
|
|
\[ {}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.635 |
|
|
\[ {}\left (y^{3}-x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
2.472 |
|
|
\[ {}\frac {x}{\left (x +y\right )^{2}}+\frac {\left (y+2 x \right ) y^{\prime }}{\left (x +y\right )^{2}} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.196 |
|
|
\[ {}x +y y^{\prime } = \frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
1.104 |
|
|
\[ {}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.849 |
|
|
\[ {}y^{\prime } = \ln \left (x +y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.801 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{x +3 y} \] |
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 |
|
|
\[ {}y^{\prime } = \left (x y\right )^{\frac {1}{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
96.204 |
|
|
\[ {}y^{\prime } = \sqrt {\frac {y-4}{x}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.463 |
|
|
\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.729 |
|
|
\[ {}y^{\prime } = -\frac {y \left (y+2 x \right )}{x \left (2 y+x \right )} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.775 |
|
|
\[ {}y^{\prime } = \frac {y^{2}}{1-x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.053 |
|
|
\[ {}y^{\prime } = \frac {y}{y-x} \] |
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 |
|
|
\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.59 |
|
|
\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.036 |
|
|
\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.143 |
|
|
\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \] |
1 |
1 |
3 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.897 |
|
|
\[ {}y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \] |
1 |
1 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.395 |
|
|
\[ {}y^{\prime } = \sin \left (x +y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.269 |
|
|
\[ {}y^{\prime } = \frac {1}{\left (3 x +3 y+2\right )^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.151 |
|
|
\[ {}y^{\prime } = \frac {\left (3 x -2 y\right )^{2}+1}{3 x -2 y}+\frac {3}{2} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.398 |
|
|
\[ {}\cos \left (-4 y+8 x -3\right ) y^{\prime } = 2+2 \cos \left (-4 y+8 x -3\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
42.072 |
|
|
\[ {}y^{\prime } = 1+\left (y-x \right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.104 |
|
|
\[ {}\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right ) = 1+\sin \left (\frac {y}{x}\right ) \] |
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 |
|
|
\[ {}3 y^{\prime } = -2+\sqrt {2 x +3 y+4} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.576 |
|
|
\[ {}y^{\prime } = 4+\frac {1}{\sin \left (4 x -y\right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.558 |
|
|
\[ {}\left (y-x \right ) y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.053 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = y \] |
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 |
|
|
\[ {}y^{\prime } = 2 \sqrt {2 x +y-3}-2 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.504 |
|
|
\[ {}y^{\prime } = 2 \sqrt {2 x +y-3} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
2.576 |
|
|
\[ {}-y+x y^{\prime } = \sqrt {x y+x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.937 |
|
|
\[ {}y^{\prime } = \left (3+x -y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.824 |
|
|
\[ {}y^{\prime }+2 x = 2 \sqrt {y+x^{2}} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.547 |
|
|
\[ {}y^{\prime } = x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.08 |
|
|
\[ {}2 x y+y^{2}+\left (x^{2}+2 x y\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}1+\ln \left (x y\right )+\frac {x y^{\prime }}{y} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
✓ |
2.614 |
|
|
\[ {}{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_exponential_symmetries], _exact] |
✓ |
✓ |
0.989 |
|
|
\[ {}y+\left (y^{4}-3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.097 |
|
|
\[ {}\frac {2 y}{x}+\left (4 x^{2} y-3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
8.607 |
|
|
\[ {}2 y^{3}+\left (4 x^{3} y^{3}-3 x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
6.408 |
|
|
\[ {}4 x y+\left (3 x^{2}+5 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.204 |
|
|
\[ {}6+12 x^{2} y^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.278 |
|
|
\[ {}x y y^{\prime }-y^{2} = \sqrt {x^{4}+x^{2} y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.862 |
|
|
\[ {}y^{\prime } = x^{2}-2 x y+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.462 |
|
|
\[ {}y^{\prime } = \frac {2 y+x}{x +2 y+3} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.162 |
|
|
\[ {}y^{\prime } = \frac {2 y+x}{2 x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.306 |
|
|
|
||||||||
|
\[ {}1-\left (2 y+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.086 |
|
|
\[ {}x y y^{\prime } = x^{2}+x y+y^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.259 |
|
|
\[ {}x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
2.127 |
|
|
\[ {}\left (y-x +3\right )^{2} \left (y^{\prime }-1\right ) = 1 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class C‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
1.268 |
|
|
\[ {}y^{\prime } = \tan \left (6 x +3 y+1\right )-2 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
498.314 |
|
|
\[ {}2 x -y-y y^{\prime } = 0 \] |
1 |
1 |
9 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.731 |
|
|
\[ {}3 y \left (t^{2}+y\right )+t \left (t^{2}+6 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.441 |
|
|
\[ {}2 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.77 |
|
|
\[ {}y^{\prime } = \sqrt {\frac {y}{t}} \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
123.202 |
|
|
\[ {}y^{\prime } = \frac {x +y+3}{3 x +3 y+1} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.496 |
|
|
\[ {}y^{\prime } = \frac {x -y+2}{2 x -2 y-1} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.58 |
|
|
\[ {}y^{\prime } = \frac {1}{x +y^{2}} \] |
1 |
1 |
1 |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
0.976 |
|
|
\[ {}y-\left (x +3 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.014 |
|
|
\[ {}y^{2}-\frac {y}{2 \sqrt {t}}+\left (2 t y-\sqrt {t}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
13.151 |
|
|
\[ {}\ln \left (t y\right )+\frac {t y^{\prime }}{y} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
✓ |
3.692 |
|
|
\[ {}-\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
1.446 |
|
|
\[ {}2 t y+\left (t^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
10.187 |
|
|
\[ {}2 t y^{3}+\left (1+3 t^{2} y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
3.243 |
|
|
\[ {}\left (3+t \right ) \cos \left (t +y\right )+\sin \left (t +y\right )+\left (3+t \right ) \cos \left (t +y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
10.316 |
|
|
\[ {}-\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}1+5 t -y-\left (t +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.456 |
|
|
\[ {}\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}\cos \left (\frac {t}{t +y}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime } = 0 \] |
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 |
|
|
\[ {}2 t +\left (y-3 t \right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.185 |
|
|
\[ {}t y-y^{2}+t \left (t -3 y\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}y^{\prime } = \frac {4 y+t}{4 t +y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.911 |
|
|
\[ {}y+\left (t +y\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}y+2 \sqrt {t^{2}+y^{2}}-t y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
5.359 |
|
|
\[ {}y^{2} = \left (t y-4 t^{2}\right ) y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.947 |
|
|
\[ {}y-\left (3 \sqrt {t y}+t \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.876 |
|
|
\[ {}\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y = 0 \] |
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 |
|
|
\[ {}t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime } = y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.945 |
|
|
\[ {}t y^{\prime }-y-\sqrt {t^{2}+y^{2}} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.808 |
|
|
\[ {}t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
5.021 |
|
|
\[ {}t y^{3}-\left (t^{4}+y^{4}\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}t -2 y+1+\left (4 t -3 y-6\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.077 |
|
|
\[ {}5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.359 |
|
|
\[ {}3 t -y+1-\left (6 t -2 y-3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.536 |
|
|
\[ {}2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.532 |
|
|
\[ {}t^{\frac {1}{3}} y^{\frac {2}{3}}+t +\left (t^{\frac {2}{3}} y^{\frac {1}{3}}+y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
5.841 |
|
|
\[ {}y \sin \left (\frac {t}{y}\right )-\left (t +t \sin \left (\frac {t}{y}\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.586 |
|
|
\[ {}3 t +\left (t -4 y\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}x^{\prime } = \frac {5 t x}{t^{2}+x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.543 |
|
|
\[ {}2 x -y-2+\left (2 y-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
7.896 |
|
|
\[ {}\cos \left (t -y\right )+\left (1-\cos \left (t -y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
9.635 |
|
|
\[ {}y^{\prime } = \sqrt {x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
7.889 |
|
|
\[ {}y^{\prime } = \sqrt {x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
5.955 |
|
|
\[ {}y^{\prime } = \sqrt {x^{2}-y}-x \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
15.783 |
|
|
\[ {}y^{\prime } = \frac {y+1}{x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.871 |
|
|
\[ {}y^{\prime } = \left (3 x -y\right )^{\frac {1}{3}}-1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
4.842 |
|
|
\[ {}y^{\prime } = \cos \left (x -y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
2.09 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.728 |
|
|
\[ {}y^{\prime } = \sin \left (x -y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
2.056 |
|
|
\[ {}\left (x +y\right )^{2} y^{\prime } = a^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.625 |
|
|
\[ {}x y^{\prime } = y \left (\ln \left (y\right )-\ln \left (x \right )\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
6.031 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}-x y+x^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.745 |
|
|
\[ {}x y^{\prime } = y+\sqrt {-x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.697 |
|
|
\[ {}2 x^{2} y^{\prime } = x^{2}+y^{2} \] |
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 |
|
|
\[ {}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.897 |
|
|
\[ {}x +y-2+\left (-y+4+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.743 |
|
|
\[ {}x +y+\left (x -y-2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.56 |
|
|
\[ {}2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.665 |
|
|
\[ {}8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.536 |
|
|
\[ {}x -2 y-1+\left (3 x -6 y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.121 |
|
|
\[ {}x +y+\left (x +y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.97 |
|
|
\[ {}2 x y^{\prime } \left (x -y^{2}\right )+y^{3} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.533 |
|
|
\[ {}y \left (1+\sqrt {y^{4} x^{2}+1}\right )+2 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
2.709 |
|
|
\[ {}x +y^{3}+3 \left (y^{3}-x \right ) y^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
2.108 |
|
|
\[ {}\left (2 x -y^{2}\right ) y^{\prime } = 2 y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.271 |
|
|
\[ {}y^{\prime } = \frac {y}{2 y \ln \left (y\right )+y-x} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.484 |
|
|
\[ {}\left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime } = 3 x^{2} \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.671 |
|
|
\[ {}x \left (2 x^{2}+y^{2}\right )+y \left (x^{2}+2 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
3.869 |
|
|
\[ {}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0 \] |
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 |
|
|
\[ {}3 y^{2}-x +\left (2 y^{3}-6 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
4 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
8.741 |
|
|
\[ {}x -x y+\left (y+x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.663 |
|
|
\[ {}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0 \] |
2 |
2 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
9.56 |
|
|
\[ {}{y^{\prime }}^{2}-4 x y^{\prime }+2 y+2 x^{2} = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
3.668 |
|
|
\[ {}x y^{\prime }-y^{2}+\left (2 x +1\right ) y = x^{2}+2 x \] |
1 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
0.905 |
|
|
\[ {}x^{2} y^{\prime } = x^{2} y^{2}+x y+1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
0.944 |
|
|
\[ {}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0 \] |
3 |
1 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
90.18 |
|
|
\[ {}\left (x y^{\prime }+y\right )^{2}+3 x^{5} \left (x y^{\prime }-2 y\right ) = 0 \] |
2 |
2 |
5 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
69.164 |
|
|
\[ {}y \left (y-2 x y^{\prime }\right )^{2} = 2 y^{\prime } \] |
2 |
2 |
7 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.633 |
|
|
\[ {}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0 \] |
2 |
2 |
3 |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.18 |
|
|
\[ {}y^{\prime } = \left (x -y\right )^{2}+1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.559 |
|
|
\[ {}x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime } = 0 \] |
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 |
|
|
\[ {}y^{\prime } = \frac {1}{2 x -y^{2}} \] |
1 |
1 |
1 |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
0.829 |
|
|
\[ {}\frac {1}{y^{2}-x y+x^{2}} = \frac {y^{\prime }}{2 y^{2}-x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
16.427 |
|
|
\[ {}x -y+3+\left (3 x +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.276 |
|
|
\[ {}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
7.802 |
|
|
\[ {}x -y+2+\left (3+x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.623 |
|
|
\[ {}\left (x -2 x y-y^{2}\right ) y^{\prime }+y^{2} = 0 \] |
1 |
1 |
1 |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.728 |
|
|
\[ {}2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.443 |
|
|
\[ {}x^{2} y^{n} y^{\prime } = 2 x y^{\prime }-y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.296 |
|
|
\[ {}\left (3 x +3 y+a^{2}\right ) y^{\prime } = 4 x +4 y+b^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.179 |
|
|
\[ {}\left (5 x -7 y+1\right ) y^{\prime }+x +y-1 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.893 |
|
|
\[ {}x +y+1+\left (2 x +2 y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.923 |
|
|
\[ {}y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.227 |
|
|
\[ {}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
1.625 |
|
|
\[ {}4 x^{2} {y^{\prime }}^{2}-y^{2} = y^{3} x \] |
2 |
2 |
3 |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
45.149 |
|
|
|
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