Link to actual problem [11039] \[ \boxed {x^{2} \left (x -a \right )^{2} y^{\prime \prime }+y b=0} \]
type detected by program
{"kovacic", "second_order_bessel_ode"}
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 &= \frac {y}{a -x}, S \left (R \right ) &= \frac {\ln \left (x -a \right )-\ln \left (x \right )}{a}\right ] \\ \end{align*}