Link to actual problem [9195] \[ \boxed {y^{\prime }+\frac {\left (-\frac {y \,{\mathrm e}^{\frac {1}{x}}}{x}-f_{1} \left ({\mathrm e}^{\frac {1}{x}} y\right )\right ) {\mathrm e}^{-\frac {1}{x}}}{x}=0} \]
type detected by program
{"unknown"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
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 &= x, \underline {\hspace {1.25 ex}}\eta &= \frac {y}{x}\right ] \\ \left [R &= y \,{\mathrm e}^{\frac {1}{x}}, S \left (R \right ) &= \ln \left (x \right )\right ] \\ \end{align*}