Link to actual problem [2721] \[ \boxed {y \cos \left (y x \right )+x \cos \left (y x \right ) y^{\prime }=\sin \left (x \right )} \]
type detected by program
{"exact"}
type detected by Maple
[_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
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 \cos \left (x y \right )}\right ] \\ \\ \end{align*}