## Linear Difference Equation with Initial Conditions

Hello Everyone!

I'm having a bit of trouble solving this difference equation, well to be exact, I can't seem to introduce the initial conditions of the difference equation:

$y[n] -(1/2)y[n-1]=2(-1/2)^2 u[n]$ where $u[n]$ is the unit step function at the origin and $y[-1]=3$

Now using Z-Transform, we get:
$Y(z)=\frac{2}{(1-0.5z^{-1})(1+0.5z^{-1})}$. I do partial fraction expansion and then I'm stuck there. How can I introduce initial conditions?!