Link to actual problem [9998] \[ \boxed {x^{2} y^{\prime \prime }+a \left (y^{\prime } x -y\right )^{2}=b \,x^{2}} \]
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*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x}\right ] \\ \end{align*}