Link to actual problem [8920] \[ \boxed {y^{\prime }-\frac {F \left (\frac {y}{\sqrt {x^{2}+1}}\right ) x}{\sqrt {x^{2}+1}}=0} \]
type detected by program
{"unknown"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(y)]`]]
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 &= x +\frac {1}{x}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \left [R &= \frac {y}{\sqrt {x^{2}+1}}, S \left (R \right ) &= \frac {\ln \left (x^{2}+1\right )}{2}\right ] \\ \end{align*}