Link to actual problem [5423] \[ \boxed {\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-y^{\prime } \cos \left (x \right ) x +y \cos \left (x \right )=x} \]
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 \(R,S\)