Link to actual problem [8771] \[ \boxed {x^{2} {y^{\prime }}^{2}-2 y x y^{\prime }+y^{2} \left (-x^{2}+1\right )=x^{4}} \]
type detected by program
{"unknown"}
type detected by Maple
[_rational, [_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*}