An LTIC system is described by the following differential equation [ frac{d^{2} y(t)}{d t^{2}}+4 frac{d y(t)}{d t}+3

Question:

An LTIC system is described by the following differential equation

\[
\frac{d^{2} y(t)}{d t^{2}}+4 \frac{d y(t)}{d t}+3 y(t)=\frac{d x(t)}{d t}+4 x(t)
\]

The system is in the initial state of $y\left(0^{-}ight)=2$ and $\dot{y}\left(0^{-}ight)=1$. The system is excited with the input $x(t)=e^{-5 t}$. Determine

(a) The natural response of the system.

(b) The forced response of the system.

(c) Total response of the system. Use Laplace transform method.