Link to actual problem [2254] \[ \boxed {2 x^{2} y^{\prime \prime }-3 y^{\prime } x -18 y=\ln \left (x \right )} \]
type detected by program
{"kovacic", "second_order_euler_ode", "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 [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{x^{2}}\right ] \\ \\ \end{align*}
\begin{align*} \\ \left [R &= y+\frac {\ln \left (x \right )}{18}, S \left (R \right ) &= -\frac {\ln \left (x \right )}{18}\right ] \\ \end{align*}