Link to actual problem [2608] \[ \boxed {y^{\prime }-\frac {\left (1-y \,{\mathrm e}^{y x}\right ) {\mathrm e}^{-y x}}{x}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 0] \end {align*}
type detected by program
{"exact"}
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 &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {{\mathrm e}^{-x y}}{x}\right ] \\ \\ \end{align*}