Link to actual problem [9651] \[ \boxed {y^{\prime \prime }-\frac {\left (5 x -4\right ) y^{\prime }}{x \left (x -1\right )}+\frac {\left (9 x -6\right ) y}{x^{2} \left (x -1\right )}=0} \]
type detected by program
{"kovacic", "second_order_change_of_variable_on_y_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 &= x, S \left (R \right ) &= \frac {y}{x^{3}}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x^{2} \left (x \ln \left (x \right )+1\right )}\right ] \\ \end{align*}