Link to actual problem [9240] \[ \boxed {y^{\prime }-\frac {-2 x \cos \left (x \right )+2 \sin \left (x \right ) x^{2}+2 x +2 y^{2}+4 y \cos \left (x \right ) x -4 x y+\cos \left (2 x \right ) x^{2}+3 x^{2}-4 x^{2} \cos \left (x \right )}{2 x}=0} \]
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*} \\ \\ \end{align*}