Link to actual problem [1959] \[ \boxed {\cos \left (y\right )-\left (\sin \left (y\right ) x -y^{2}\right ) y^{\prime }=0} \]
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}{x \sin \left (y \right )-y^{2}}\right ] \\ \left [R &= x, S \left (R \right ) &= -x \cos \left (y\right )-\frac {y^{3}}{3}\right ] \\ \end{align*}