Link to actual problem [11234] \[ \boxed {{y^{\prime }}^{2} x^{2}-2 y y^{\prime } x +y^{2}-x^{2} y^{2}=x^{4}} \]
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*}