  In this paper we study some solution techniques of differential-difference
equation $$ y'(x) = y(x + 1/2)- y(x- 1/2),$$ first without an initial condition
and then with some initial function $h$ defined on the unit interval $ [-1/2,
1/2]$. We show some sufficient conditions that an initial function $h$ is
admissible, i.e., it yields a unique continuous solution on some symmetric
interval about $0$.
