# Diff Eq- Convolutions and state-free solution

1. Jul 18, 2012

### giacomh

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

Find the state-free solution

yii+4yi+29y=0
y2+4y+29=f(t)

2. Relevant equations

I know I have to find the impulse-response, e(t), which is 1/5e^-2t sin(5t).

3. The attempt at a solution

The state-free solutions is the convolution of e and f(t). This is the part I'm confused about, because there is only one example given in my book. Do I integrate the product of e(t-u) and f(u)?
1/5e-2t sin(5t)*y2 +4y2 +29y

Last edited: Jul 18, 2012
2. Jul 18, 2012

### vela

Staff Emeritus
What's f(t)? It seems to appear out of nowhere.

3. Jul 18, 2012

### giacomh

sorry, f(t) is y2+4y+29