Link to actual problem [9323] \[ \boxed {y^{\prime }+F \left (x \right ) \left (-y^{2}+2 y x^{2}+1-x^{4}\right )=2 x} \]
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 &= x, S \left (R \right ) &= \frac {\ln \left (-x^{2}+y-1\right )}{2}-\frac {\ln \left (-x^{2}+y+1\right )}{2}\right ] \\ \end{align*}