Can anyone do a very comprehensive breakdown of the Laplace translation property for me? I don't understand how to apply it: L[eat f(t)] = L[f(t)] s-> s-a Here is a specific problem that applies it: 1. The problem statement, all variables and given/known data 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). 2. Relevant equations L[eat f(t)] = L[f(t)] s-> s-a 3. The attempt at a solution let E = (s+1); L-1 (4/E3 + 1/E2 + 2/E) = 2t + t + 2 y(t) = 2t2e-t + te-t + 2e-t ... but why?