ANALYSIS OF THE DIFFERENTIAL-DIFFERENCE EQUATION y(x+12)−y(x−12)=y′(x)

In this paper we study some solution techniques of solving the differential-difference equation y′(x)=y(x+12)−y(x−12), first without an initial condition and then with some initial function h defined on the unit interval [−12,12]. 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.