Consider a causal LTI (Linear-time invariant) system described by the following differential equation:
\(\frac{d^2}{dt^2}y(t) + 5\frac{d}{dt}y(t) + 6y(t) = \frac{d}{dt}x(t) + x(t)\)
a) Determine the transfer function of this system.
b) Determine the impulse response of this system.
c) Sketch the poles and zeros on the s-plane and determine the BIBO stability of the system.
d) What is the steady-state value (when t > 0) of the output y(t) if the input is a unit step signal?