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## Homework Statement

y'' + 4y' +4y = 5e^(-2x)

y''+9y=2sin(3x)

## Homework Equations

combined with 3

## The Attempt at a Solution

For the first one, I started off by finding the general solution.

r^2+4r+4=0

r=-2, double roots

y=c1*e^(-2x)+c2*x*e^(-2x)

And then when solving for the particular solution I end up with left side becoming 0.

The second problem I'm not sure if requires an annihilator or not, but I assume it does.

I get r=+/- 3i

y=c1*cos(3x)+c2*sin(3x)

and no idea what annihilator to use

In my entire DiffyEq book, the word "annihilator" is mentioned twice, and in both cases they just say to use it, but there's no explanation or anything. I looked online as well and couldn't fine anything helpful enough. Is there like some sort of table I need to use? How do I choose the annihilator?