Link to actual problem [1024] \[ \boxed {x \ln \left (x \right )^{2} y^{\prime }-\ln \left (x \right ) y-y^{2}=-4 \ln \left (x \right )^{2}} \]
type detected by program
{"riccati"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(y)]`], _Riccati]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\).\begin{align*} \\ \left [R &= \frac {y}{\ln \left (x \right )}, S \left (R \right ) &= \ln \left (\ln \left (x \right )\right )\right ] \\ \end{align*}