# Laplace Transformation Convolution Integral

1. Sep 18, 2013

### bmb2009

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

I need to find the laplace transformation of the following function (and it's ok to leave it expressed as an integral). After doing the initial steps and algebra I got

Y(s)= g(t)/(s+2)^2 + 7(1/(s+2)^2)+ 2(1/(s+2)^2)

the answer is y(t)=2e^-2t +te^-2t +∫(t-τ)e^-2(t-τ) g(τ) dτ

We are allowed to use laplace transformation tables but what I don't understand is how to factor the terms in the Y(s) equation into a form which correlates in the base transformations. Any help would be great. Thanks

2. Relevant equations

3. The attempt at a solution

2. Sep 18, 2013

### LCKurtz

Why is there a $t$ variable in your expression for $Y(s)$?

3. Sep 18, 2013

### bmb2009

My bad it's G(s) which is not explicitly defined

4. Sep 19, 2013

### vela

Staff Emeritus
Is there some reason you didn't combine the last two terms into 9/(s+2)2?

If this is the answer, you need to recheck your earlier work for errors.