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**1. Homework Statement**

Consider the initial value problem

y'' + 1/3y' + 4y = fk(t)

with y(0) = y'(0) = 0,

f

_{k}(t) = 1/2k for 4 - k < t < 4 + k

0 otherwise

and 0 < k < 4.

(a) Write fk(t) in terms of Heaviside step functions and then solve the initial value problem.

**3. The Attempt at a Solution**

I can convert it to a heaviside function and do the laplace transform and get

f

_{k}(t)= 1/2k H(t-(4-k)) - 1/2k H(t+(4-k))

and then taking the laplace transform of the entire equation get

Y(s) =

^{1}/

_{2k(s2+1/3 s + 4)}* (

^{e-(4-k)s}/

_{s}-

^{e-(4+k)s}/

_{s})

Im assuming this is corrent. But then how do I take the inverse laplace transform of this???