Solving y''+y=δ(t-2π)cos(t) with Laplace transform

[polarbears]

Homework Statement

$$y''+y=\delta (t-2\pi )cos(t)$$
$$y(0)=0,y'(0)=1$$

Homework Equations

The Attempt at a Solution

The left side is (s^2+1)Y(s)-1=RHS

My problem is the fact that cosine is being multiplied by the delta function. I put it in the form of an intergral but I don't know what to do from there.

 

[HallsofIvy]

Well, good! Delta functions usually make integrals trivial. What integral did you get?

 

[annoymage]

hmm, i don't know what is this question, may i know, what topic should i study for this question?

 

[polarbears]

Differential Equations -Laplace transforms

OHHHH waitttt does the delta function just determine the bound of my intergral?