(adsbygoogle = window.adsbygoogle || []).push({}); 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 Ididdo the partial fraction expansion only to re-discover that

X(s) = 1 / (s + 3)^2

So....2 questions:

1) Doyouknow 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?

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# Homework Help: Solve Diff EQ using Laplace

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