Link to actual problem [5829] \[ \boxed {x^{2} \left (-1+\ln \left (x \right )\right ) y^{\prime \prime }-y^{\prime } x +y=x \left (-\ln \left (x \right )+1\right )^{2}} \]
type detected by program
{"second_order_change_of_variable_on_y_method_2", "second_order_ode_non_constant_coeff_transformation_on_B"}
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*}