Link to actual problem [9696] \[ \boxed {y^{\prime \prime }+\frac {a y}{\left (x^{2}-1\right )^{2}}=0} \]
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 {-1+x}\, \sqrt {1+x}}, S \left (R \right ) &= -\operatorname {arctanh}\left (x \right )\right ] \\ \end{align*}