Originally Posted by zzizi
Wiki explains it better than I can:
Recurrence relation - Wikipedia, the free encyclopedia
The equation in the above example was [[homogeneous differential equation|homogeneous]], in that there was no constant term. If one starts with the non-homogeneous recurrence
with constant term ''K'', this can be converted into homogeneous form as follows: The [[steady state]] is found by setting
Then the non-homogeneous recurrence can be rewritten in homogeneous form as
which can be solved as above.