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

Analysis of the Differential-Difference Equation $y(x+1/2)-y(x-1/2) = y'(x)$