# Inverse Laplace

1. Mar 16, 2008

### pooface

1. The problem statement, all variables and given/known data
Inverse laplace transforms

F(s)=$$\frac{5s-2}{s^{2}(s-1)(s+2)}$$

2. Relevant equations
Residue technique

3. The attempt at a solution

F(s)=$$\frac{5s-2}{s^{2}(s-1)(s+2)} = \frac{k1}{s^{2}} + \frac{k2}{s-1} + \frac{k3}{s+2}$$

I solved for K1,K2, and K3, which all came to be 1.

answer=$$e^{t}+e^{-2t}+t$$
textbook answer = $$e^{t}+e^{-2t}+t -2$$

Can someone explain to me how did the -2 come?

Last edited: Mar 16, 2008
2. Mar 17, 2008

### pooface

It is very important that I know this. I was told that there was a k4 at the end but for problems we did in control theory class k4 was said to be 0 always and we took it as a rule.

So I need to know where this -2 came from.