Diff Eq- Convolutions and state-free solution

[giacomh]

Homework Statement

Find the state-free solution

yⁱⁱ+4yⁱ+29y=0
y²+4y+29=f(t)

Homework Equations

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

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

 

[vela]

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

 

[giacomh]

sorry, f(t) is y²+4y+29