Link to actual problem [11056] \[ \boxed {\left (x -a \right )^{2} \left (x -b \right )^{2} y^{\prime \prime }-y c=0} \]
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 &= y \left (x -b \right )^{\frac {b}{-b +a}} \left (x -a \right )^{-\frac {a}{-b +a}}, S \left (R \right ) &= \frac {-\ln \left (x -b \right )+\ln \left (x -a \right )}{-b +a}\right ] \\ \end{align*}