Link to actual problem [11027] \[ \boxed {x \left (x -1\right ) \left (x -a \right ) y^{\prime \prime }+\left (\left (\alpha +\beta +1\right ) x^{2}-\left (\alpha +\beta +1+a \left (\gamma +d \right )-a \right ) x +a \gamma \right ) y^{\prime }+\left (\alpha \beta x -q \right ) y=0} \]
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 \(R,S\)