Link to actual problem [15060] \[ \boxed {y^{\prime } \cos \left (y\right )+\sin \left (y\right )=x +1} \]
type detected by program
{"exactWithIntegrationFactor"}
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}{\cos \left (y \right )}\right ] \\ \\ \end{align*}