$\mathrm{.}3$ The input, x$($t$),$ and output, y$($t$),$ of a causal, linear, time$-$invariant system satisfy the following differential equation:

frequency $!=2$ rad$/$sec$.$

Determine the impulse response of the system, h$($t$).$ Determine the output, y$($t$),$ if the input, x$($t$),$ is given by