Link to actual problem [8770] \[ \boxed {x^{2} {y^{\prime }}^{2}-2 y x y^{\prime }+y \left (y+1\right )=x} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _rational]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \\ \end{align*}