Link to actual problem [10156] \[ \boxed {\left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y^{\prime \prime } y\right )^{2}-4 x y \left (y^{\prime } x -y\right )^{3}=0} \]
type detected by program
{"unknown"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \\ \end{align*}
\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*}