Link to actual problem [12049] \[ \boxed {\left (\cos \left (t \right ) t -\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right )=0} \] Given that one solution of the ode is \begin {align*} x_1 &= t \end {align*}
type detected by program
{"reduction_of_order"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)