# Solve the following initial value problem (DiracDelta function)

1. Apr 27, 2012

### IHave

1. The problem statement, all variables and given/known data
y'' +4y = 2 delta(t - pi/4)

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

2. Relevant equations
Laplace transform
Inverse Laplace transform

3. 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?

2. Apr 27, 2012

### 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 cant be inverse transformed generally. The result should be:
$-\text{Heaviside}(t-\pi/4)\cos(2t)$