Hi Guys,

Could you give my work a quick check... I'm hoping im doing this correctly :0

Find the solution to the following IVP using Laplace transforms:

y' + 3y = 2e^-4t with y(0) = 2

First, take the Laplace transform of both sides:

L[y'+3y] = L[2e^-4t]

sL{y} - y(0) + 3L{y} = 2/(s+4)

L{y} (s + 3) = 2/(s+4) + 2

taking the inverse laplace transform of both sides.

2/(s+3)(s+4) = A/(s+3) + B/(s+4)

A(s+4) + B(s+3) = 2

s=-4 s=-3

-B = 2 A = 1

Therefore, our transform equation becomes:

Taking the inverse laplace transform of both sides, we get: