2. Consider a system governed by the following differential equation:
$2\dot{y}(t) + 4y(t) = 4x(t)$, with zero initial conditions.
a) Find its unit step response, $y_s(t)$, and unit ramp response, $y_r(t)$.
b) In terms of your answers to part (a) above, write down the response of the above system due to the
following input, $x(t)$:
$x(t)$
c) Using the final value theorem, find the steady state response (if it exists) of the above system due to the
following inputs:
i) $x(t) = 4u(t-1)$, ii) $x(t) = 2u(t) + 2r(t)$
