Link to actual problem [10953] \[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } a x +\left (-b^{2} x^{2}+a \left (a +1\right )\right ) y=0} \]
type detected by program
{"kovacic", "second_order_bessel_ode", "second_order_change_of_variable_on_y_method_1"}
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 &= x, S \left (R \right ) &= \frac {x^{-a} y}{\sinh \left (b x \right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {x^{-a} y}{\cosh \left (b x \right )}\right ] \\ \end{align*}