1. The problem statement, all variables and given/known data Given: dx/dt + 3*x = exp(-3*t) and all initial conditions are zero. 2. Relevant equations Laplace 3. The attempt at a solution L[dx/dt + 3*x = exp(-3*t)] s*X(s) + 3*X(s) = 1 / (s + 3) X(s) = 1 / (s + 3)^2 So here is where I get mixed up. For some reason, I thought I was supposed to use a partial fraction expansion here. But those of you who know better will probably get a good chuckle out of hearing about how I did do the partial fraction expansion only to re-discover that X(s) = 1 / (s + 3)^2 So....2 questions: 1) Do you know why I thought I needed a PFE? 2) I have a list of Laplaces and their inverses. 1 / (s + a)^n is NOT one of them. 1 / (s + a) IS one of them. I presume I am supposed to use this rule in conjunction with some other rule to find the inverse Laplace of 1 / (s + a)^n . Can I get a hint on how to do this?