Link to actual problem [5315] \[ \boxed {\sin \left (y\right )-\left (2 y \cos \left (y\right )-x \left (\sec \left (y\right )+\tan \left (y\right )\right )\right ) y^{\prime }=-1} \]
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 {1}{\sec \left (y \right )+\tan \left (y \right )}, \underline {\hspace {1.25 ex}}\eta &= 0\right ] \\ \\ \end{align*}