Link to actual problem [9182] \[ \boxed {y^{\prime }-f_{1} \left (y-\ln \left (\sinh \left (x \right )\right )\right )=\frac {\cosh \left (x \right )}{\sinh \left (x \right )}} \]
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 {\cosh \left (x \right )}{\sinh \left (x \right )}\right ] \\ \\ \end{align*}