Link to actual problem [8690] \[ \boxed {\left (x \sin \left (y\right )-1\right ) y^{\prime }+\cos \left (y\right )=0} \]
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[[_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 [R &= y, S \left (R \right ) &= \frac {x}{\cos \left (y\right )}\right ] \\ \end{align*}