The system defined by the equation \( 2 \frac{d y(t)}{d t}=u(t)-4 y(t) \) is best described as: \( \begin{array}{ll}\text { (A) linear, time invariant \& dynamic } & \text { (B) nonlinear, time invariant \& dynamic } \\ \text { (C) linear, time invariant \& static } & \text { (D) nonlinear, time invariant \& static } \\ \text { (E) linear, time varying \& dynamic } & \text { (F) nonlinear, time varying \& static }\end{array} \)

The system described by the equation \( 2 \frac{d y(t)}{d t}=u(t)-4 y(t) \) is linear because it can be expressed in the form of a first-order linear differential equation, and it is time-invariant since the coefficients do not depend on \( t \). Furthermore, the presence of the derivative indicates that it is dynamic rather than static. Hence, the best choice is \( \text{(A) linear, time invariant \& dynamic} \). To provide some context, this kind of system can often be seen in control theory where the input \( u(t) \) affects the output \( y(t) \) over time. The structure of the differential equation reveals how past outputs influence future outputs, emphasizing the dynamic nature of the system.