Solve the following initial value problem (DiracDelta function)

[IHave]

Homework Statement

y'' +4y = 2 delta(t - pi/4)

where y(0)=0 and y'(0)=0

Homework Equations

Laplace transform
Inverse Laplace transform

The Attempt at a Solution

after applying laplace tranform
Y(s)=2e^((-pi/4)*s) / s^(2)+4

as the final answer i have
y(t) = U(t-pi/4)*2sin(t-pi/4)

I'm not very comfortable with these types of problems yet, is my answer correct?

 

[dikmikkel]

I get the forward transform as:
s^2\tilde{y}(s) +4\tilde{y}(s) =2e^{-s\pi /4}
Then isolating i get the same as you. But you got something wrong, the product of two functions can't be inverse transformed generally. The result should be:
-\text{Heaviside}(t-\pi/4)\cos(2t)