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## Homework Statement

Use Laplace transforms to solve the initial value problem:

f''(y) + 4f'(y) +8y = u(t-1) where y(0) = 1 and y'(0) = -1

Solve this problem using laplace transforms, showing all steps in your reasoning. State the solution y(t) for each of 0<t<1 and t>1, then sketch it over the range 0<= t <= 10, noting its main features.

## Homework Equations

## The Attempt at a Solution

I have gotten up to F(Y) = (e^-s + s^2 + 3s)/(s(s^2 + 4s+8))

However, from here i am not sure what to do. I tried taking the partial fractions of:

1/(s(s^2 + 4s+8))

but am getting very confused. Again any help would be much appreciated. Cheers