Link to actual problem [15437] \[ \boxed {x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x^{2} y^{\prime }+y x=2 \ln \left (x \right )} \] With initial conditions \begin {align*} [y \left (\infty \right ) = 0] \end {align*}
type detected by program
{"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 &= x, S \left (R \right ) &= \frac {y}{x}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\ln \left (x \right )}\right ] \\ \end{align*}