Link to actual problem [9136] \[ \boxed {y^{\prime }+\frac {-\frac {1}{x}-f_{1} \left (y+\frac {1}{x}\right )}{x}=0} \]
type detected by program
{"unknown"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(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 {1}{x}\right ] \\ \left [R &= y+\frac {1}{x}, S \left (R \right ) &= \ln \left (x \right )\right ] \\ \end{align*}