$3\mathrm{.}4$ The dynamic model for a process is given by

$\frac{d^{2}y}{d{t}^2}+6\frac{dy}{dt}+8y=3u(t)$

$\frac{d^{2}y}{d{t}^2}+6\frac{dy}{dt}+8y=3u(t)$

where $u(t)$ is the input function and $y(0)$ and $d\frac{y}{d}t(0)$ are both zero.

What are the functions of the time $(e,e,e^{-t^t})$ in the solution for each of the following cases?

a $u(t)=b{e}^{-2t}$

b$.u(t)=ct$

$b$ and $c$ are constants.

Note You do not have to find $y(t)$ in these cases. Just determine the functions of time that will appear in $y(t).$