Link to actual problem [9657] \[ \boxed {y^{\prime \prime }+\frac {\left (A \,x^{2}+B x +C \right ) y^{\prime }}{\left (x -a \right ) \left (x -b \right ) \left (x -c \right )}+\frac {\left (\operatorname {DD} x +E \right ) y}{\left (x -a \right ) \left (x -b \right ) \left (x -c \right )}=0} \]
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 \(R,S\)