Link to actual problem [6039] \[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -4 \pi y=x} \]
type detected by program
{"kovacic", "second_order_euler_ode", "second_order_change_of_variable_on_x_method_1", "second_order_change_of_variable_on_x_method_2", "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*} \\ \left [R &= y+\frac {x}{4 \pi -1}, S \left (R \right ) &= -\frac {\ln \left (x \right )}{4 \pi -1}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= \frac {y}{x}, S \left (R \right ) &= \ln \left (x \right )\right ] \\ \end{align*}