Link to actual problem [562] \[ \boxed {\left (-\sin \left (y\right )+\frac {x}{y}\right ) y^{\prime }=-1} \]
type detected by program
{"exact", "differentialType"}
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 [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{y \sin \left (y \right )-x}\right ] \\ \\ \end{align*}