well dont worry i found out a way anyways.
so i got:
L(y) = 8/s(s^2 + 4) + (11s + 5)/(s^2 + 4)
i wont type it all out cause it's annoying, but what i did was i partial fraction decomposed 8/s(s^2 + 4) and i expanded all the terms and equated coeficcients cause i hate dealing with complex...
find solution using laplace transforms
y'' + 4y = 8
alright, so i did the laplace transform of both sides and i get
(s^2 + 4)L(y) - 11s - 5 = 8/s
so i isolate L(y) and i get this expression:
L(y) = (11s^2 + 5s + 8)/(s*(s^2 + 4))
however, the textbook...