Link to actual problem [10493] \[ \boxed {y^{\prime } x -a \,x^{n} \left (y+b \ln \left (x \right )\right )^{2}=-b} \]
type detected by program
{"riccati"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\).\begin{align*} \\ \left [R &= y+b \ln \left (x \right ), S \left (R \right ) &= \frac {x^{n}}{n}\right ] \\ \end{align*}