Link to actual problem [9607] \[ \boxed {4 x^{2} y^{\prime \prime }+5 y^{\prime } x -y=\ln \left (x \right )} \]
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 &= x^{-\frac {1}{8}+\frac {\sqrt {17}}{8}}\right ] \\ \left [R &= x, S \left (R \right ) &= x^{\frac {1}{8}} x^{-\frac {\sqrt {17}}{8}} y\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= x^{-\frac {1}{8}-\frac {\sqrt {17}}{8}}\right ] \\ \left [R &= x, S \left (R \right ) &= x^{\frac {1}{8}} x^{\frac {\sqrt {17}}{8}} y\right ] \\ \end{align*}
\begin{align*} \\ \\ \end{align*}