Link to actual problem [5303] \[ \boxed {y+\left (y x +x -3 y\right ) y^{\prime }=0} \]
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\).\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {x y -3 y +3}{x y +x -3 y}\right ] \\ \\ \end{align*}