I am trying to solve

$\displaystyle y''+4y=0, 0<t<a; exp(-t), t>a $

using Laplace transforms.

I end up with

$\displaystyle H(t-a)(exp(-(t-a))-cos(2(t-a))+1/2sin(2(t-a))$

where H(t-a) is the Heaviside/unit step function. Is this correct? If not, where have I gone wrong?

Cheers,

Ben