Link to actual problem [8061] \[ \boxed {x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (4 x +1\right ) y=0} \]
type detected by program
{"kovacic", "second_order_change_of_variable_on_y_method_2"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries]]
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}\right ] \\ \\ \end{align*}