1. ## dirac delta functions...

ok im doing this problem and its not working out for me and i was wondering if someone could look it over...let y(0)=1 and y'(0)=0

$y''+4y'+13y=\delta (t-\pi )\delta +(t-3\pi )$

$s^2Y(s)-s+4sY(s)+13Y(s)=e^{-\pi s}+e^{-3\pi s}$

and so i got...

$Y(s)=\frac{e^{-\pi s}+e^{-3\pi s}+s}{s^2+4s+13}$

according to my text, this is wrong...

any help would be appreciated..

2. I don't think you're taking the LT of the LHS correctly. The second derivative has two terms, one of which vanishes. The first derivative also has one term that does NOT vanish.

3. yeah i caught it, i see my mistake....the numerator should have a +4 on the end...

thanks

4. You're welcome!