Link to actual problem [10855] \[ \boxed {y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (-x^{2 n} c +a \,x^{n +1}+b \,x^{n}+x^{n -1} n \right ) y=0} \]
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 \(R,S\)