(a) Consider the system described by the differential equation $0.5\dot{y}(t) + y(t) = 2u(t)$, where $u(t)$ and $y(t)$ are the input and the output of the system, respectively. Assume the initial condition $y(0) = 0$ and the input is $u(t) = u_s(t)$, which is the unit step function. Find the time response function $y(t)$, $t \ge 0$. (20%)
(b) Plot the time response function $y(t)$ versus time $t$, and specify the initial value $y(0)$, the time constant $\tau$, the value of $y(\tau)$, and the steady-state value of $y(\infty)$ on the graph. (20%)
