Link to actual problem [6228] \[ \boxed {\left ({\mathrm e}^{x} \cot \left (y\right )+2 y \csc \left (y\right )\right ) y^{\prime }=-{\mathrm e}^{x}} \]
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 [\underline {\hspace {1.25 ex}}\xi &= \frac {{\mathrm e}^{-x}}{\sin \left (y \right )}, \underline {\hspace {1.25 ex}}\eta &= 0\right ] \\ \\ \end{align*}