# Substitution for impulse in recurrence equation

1. Apr 13, 2008

### yoran

Hi,

I was wondering what substitution to try when finding a particular solution for a recurrence equation with a linear combination of impulses on the right side of the equation. I think an example will clarify this.
Given the recurrence equation
$$y[k+2]-4y[k]=\delta [k] + 2\delta [k+1]$$
with $$\delta [k]$$ being the discrete impulse, i.e $$\delta [k] = 1$$ for $$k=0$$ and $$\delta [k] = 0$$ for $$k\neq 0$$.
First you must find a solution for the homogeneous equation. I have no problems with that. But I don't know what substitution to use for finding the particular solution? Can someone help me with that?

Thanks,

Yoran