Link to actual problem [9450] \[ \boxed {y^{\prime \prime } x -\left (x^{2}-x \right ) y^{\prime }+\left (x -1\right ) y=0} \]
type detected by program
{"kovacic", "second_order_change_of_variable_on_y_method_2"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x}\right ] \\ \end{align*}
\begin{align*} \\ \\ \end{align*}