Link to actual problem [9650] \[ \boxed {y^{\prime \prime }+\frac {2 \left (x -2\right ) y^{\prime }}{x \left (x -1\right )}-\frac {2 \left (x +1\right ) y}{x^{2} \left (x -1\right )}=0} \]
type detected by program
{"kovacic", "exact linear second order ode", "second_order_integrable_as_is", "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*} \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{x^{2}}\right ] \\ \\ \end{align*}