Problem $2[50\%]$

a$)$ Use the linearity property to find the Laplace transform of $($t$)=$ Acos$($t$).$ Hint: recall that cos$(0)=($ej$+$e$-1$o$).$

b$)$ Compute the Laplace transform of v$($t$),$ when

dv$($t$)$

$+6$v$($t$)=4$u$($t$),$ v$(0)=3$V$.$

dt

c$)$ Find the Laplace transform of the following signal v$($t$)=7$u$($t$),$ where u$($t$)$ is a step function