where \(\left\{q,p\right\}\equiv qp+pq\) represents the anti-commutator. The r.h.s. of these equations fail to be purely quadratic forms, because of the presence of the driving force. This situation is corrected with the use of the equations of motion (\ref{eq:02}) themselves.
Now we take a set of time-dependent functions \(c_i=\left(c_1,c_2,c_3,c_4,c_5\right)\), build a linear combination of (\ref{eq:02}) and (\ref{eq:16}), and collect the total time derivative. The result is given by