Link to actual problem [4517] \[ \boxed {\left (x -\cos \left (y\right )\right ) y^{\prime }+\tan \left (y\right )=0} \] With initial conditions \begin {align*} \left [y \left (1\right ) = \frac {\pi }{6}\right ] \end {align*}
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}{\sin \left (y \right )}, \underline {\hspace {1.25 ex}}\eta &= 0\right ] \\ \\ \end{align*}