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: