Exercise $4$: Applying the eigenfunction theorem of LTI systems:

a$)$Determine the response of an analog LTI system with impulse response h$($t$)=(1/3)^$t u$($t$)$to the input signal x$($t$)=$cosh$^2($t$),$simplifying the result as much as possible.

b$)$Determine the value of the constant k that appears in the impulse response of the discrete system h$[$n$]=$k$$u$[$n$],$knowing that the response of this system to the input signal x$[$n$]=2$e$^4$n is y$[$n$]=3$e$^4$n