Link to actual problem [5261] \[ \boxed {-2 \sin \left (y\right )+\left (2 x -4 \sin \left (y\right )-3\right ) \cos \left (y\right ) y^{\prime }=-x -3} \]
type detected by program
{"unknown"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(y)]`]]
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 &= 1, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{2 \cos \left (y \right )}\right ] \\ \\ \end{align*}