Link to actual problem [11083] \[ \boxed {\left (a \,x^{n +1}+b \,x^{n}+c \right )^{2} y^{\prime \prime }+\left (\alpha \,x^{n}+\beta \,x^{n -1}+\gamma \right ) y^{\prime }+\left (n \left (-n a -a +\alpha \right ) x^{n -1}+\left (n -1\right ) \left (-b n +\beta \right ) x^{-2+n}\right ) y=0} \]
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 \(R,S\)