Link to actual problem [14635] \[ \boxed {\left (\sin \left (t \right )-t \cos \left (t \right )\right ) y^{\prime \prime }-t \sin \left (t \right ) y^{\prime }+\sin \left (t \right ) y=t} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{4}\right ) = 0, y^{\prime }\left (\frac {\pi }{4}\right ) = 0\right ] \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 \(R,S\)