Consider an LTIC system described by the following differential equation [ frac{d^{2} y(t)}{d t^{2}}+frac{d y(t)}{d t}-6 y(t)=X(s)

Question:

Consider an LTIC system described by the following differential equation

\[
\frac{d^{2} y(t)}{d t^{2}}+\frac{d y(t)}{d t}-6 y(t)=X(s)
\]

Determine

(a) the system transfer function.

(b) impulse response of the system if it is causal.

(c) Impulse response of the system if the system is stable.

(d) Impulse response of the system if it is neither causal nor stable.