Link to actual problem [9774] \[ \boxed {y^{\prime \prime }+\frac {b^{2} y}{\left (-a^{2}+x^{2}\right )^{2}}=0} \]
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}{\sqrt {-a^{2}+x^{2}}}, S \left (R \right ) &= -\frac {-\ln \left (x -a \right )+\ln \left (x +a \right )}{2 a}\right ] \\ \end{align*}