$($a$)$ Consider the system described by the differential equation $0\mathrm{.}5y^{}(t)+y(t)=2u(t),$ 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 $y(t),t0.,(20\%)$

$($b$)$ Plot the time response function $y(t)$ versus time $t,$ and specify the initial value $y(0),$ the time constant $,$

the value of $y(),$ and the steady$-$state value of $y()$ on the graph. $(20\%)$