Link to actual problem [3452] \[ \boxed {x y^{\prime }-y-\sqrt {x^{2}+y^{2}}\, x=0} \]
type detected by program
{"unknown"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(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 &= 1, \underline {\hspace {1.25 ex}}\eta &= \frac {y}{x}\right ] \\ \left [R &= \frac {y}{x}, S \left (R \right ) &= x\right ] \\ \end{align*}