Link to actual problem [8947] \[ \boxed {y^{\prime }-\frac {x +y+F \left (-\frac {-y+x \ln \left (x \right )}{x}\right ) x^{2}}{x}=0} \]
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 {y}{x}+1\right ] \\ \left [R &= -\frac {-y+x \ln \left (x \right )}{x}, S \left (R \right ) &= x\right ] \\ \end{align*}