Link to actual problem [11057] \[ \boxed {\left (x -a \right )^{2} \left (x -b \right )^{2} y^{\prime \prime }+\left (x -a \right ) \left (x -b \right ) \left (2 x +\lambda \right ) y^{\prime }+\mu y=0} \]
type detected by program
{"kovacic", "second_order_change_of_variable_on_x_method_2"}
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, S \left (R \right ) &= -\frac {\ln \left (x -b \right )}{-b +a}+\frac {\ln \left (x -a \right )}{-b +a}\right ] \\ \end{align*}