A system described by the following differential equation $\frac{d^{2} y}{d t^{2}}+3 \frac{d y}{d t}+2 y=x(t)$ is initially at rest. For input $x(t)=2 u(t)$, the output $y(t)$ is
- $\left(1-2 e^{-t}+e^{-2 t}\right) u(t)$
- $\left(1+2 e^{-t}-2 e^{-2 t}\right) u(t)$
- $\left(0.5+e^{-t}+1.5 e^{-2 t}\right) u(t)$
- $\left(0.5+2 e^{-1}+2 e^{-2 t}\right) u(t)$