Link to actual problem [11037] \[ \boxed {x^{4} y^{\prime \prime }+2 x^{2} \left (x +a \right ) y^{\prime }+y b=0} \]
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 {1}{x}\right ] \\ \end{align*}