- #1

ultimatejulia

- 1

- 0

L[e

^{at}f(t)] = L[f(t)]

_{s-> s-a}

Here is a specific problem that applies it:

## Homework Statement

Y(s) = 4/(s+1)

^{3}+ 1/(s+1)

^{2}+ 2/(s+1)

I need to perform an inverse Laplace transform to find the solution to this initial value problem (beginning parts of the problem omitted).

## Homework Equations

L[e

^{at}f(t)] = L[f(t)]

_{s-> s-a}

## The Attempt at a Solution

let E = (s+1);

L

^{-1}(4/E

^{3}+ 1/E

^{2}+ 2/E) = 2t + t + 2

y(t) = 2t

^{2}e

^{-t}+ te

^{-t}+ 2e

^{-t}

... but why?