Link to actual problem [10629] \[ \boxed {y^{\prime }-g \left (x \right ) \left (-f \left (x \right )+y\right )^{2}=f^{\prime }\left (x \right )} \]
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 [\underline {\hspace {1.25 ex}}\xi &= \frac {1}{g \left (x \right )}, \underline {\hspace {1.25 ex}}\eta &= \frac {f^{\prime }\left (x \right )}{g \left (x \right )}\right ] \\ \\ \end{align*}