Link to actual problem [8915] \[ \boxed {y^{\prime }-\frac {1+2 F \left (\frac {1+4 x^{2} y}{4 x^{2}}\right ) x}{2 x^{3}}=0} \]
type detected by program
{"unknown"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(x)]`]]
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 &= 2 x^{2}, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{x}\right ] \\ \left [R &= y+\frac {1}{4 x^{2}}, S \left (R \right ) &= -\frac {1}{2 x}\right ] \\ \end{align*}