A continuous time $\text{LTI}$ system is described by
\[ \frac{d^{2} y(t)}{d t^{2}}+4 \frac{d y(t)}{d t}+3 y(t)=2 \frac{d x(t)}{d t}+4 x(t) \]
Assuming zero initial conditions, the response $y(t)$ of the above system for the input $x(t)=e^{-2 t} u(t)$ is given by
- $\left(e^{t}-e^{3t)}\right) u(t)$
- $\left(e^{-t}-e^{-3 t}\right) u(t)$
- $\left(e^{-t}+e^{-3t}\right) u(t)$
- $\left(e^{t}+e^{3 t}\right) u(t)$