Link to actual problem [10988] \[ \boxed {\left (a^{2}+x^{2}\right ) y^{\prime \prime }+2 b x y^{\prime }+b \left (b -1\right ) y=0} \]
type detected by program
{"kovacic"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \\ \end{align*}
\begin{align*} \\ \left [R &= y \left (a^{2}+x^{2}\right )^{-\frac {1}{2}+\frac {b}{2}}, S \left (R \right ) &= \frac {\arctan \left (\frac {x}{a}\right )}{a}\right ] \\ \end{align*}