Consider the differential equation y$+6$y$+5$y$=3($followed by that greek letter that looks like a fancy d or s$)($t$-4)$ with initial conditions y$(0)=5$and y$(0)=2.$

a$)$ Take the Laplace transform of the differential equation and solve for Y$($s$).$ Use partial fraction expansion $($PFE$)$ to simplify your answer. Show all your work.

b$)$ Find the solution of the differential equation by computing y$($t$)=$Laplace inverse $($Y$($s$)).$ Show all your work.