Link to actual problem [13440] \[ \boxed {\sin \left (y\right )+\left (x +y\right ) \cos \left (y\right ) y^{\prime }=0} \]
type detected by program
{"exact"}
type detected by Maple
[_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
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 {1}{\cos \left (y \right ) \left (x +y \right )}\right ] \\ \\ \end{align*}