Link to actual problem [11021] \[ \boxed {\left (a \,x^{3}+b \,x^{2}+c x \right ) y^{\prime \prime }+\left (n \,x^{2}+m x +k \right ) y^{\prime }+\left (k -1\right ) \left (\left (-a k +n \right ) x +m -b k \right ) y=0} \]
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 \(R,S\)