John D. Cook • 3/2/2026

Differential equation with a small delay

This technical article examines delay-differential equations, specifically x′(t) = a x(t) + b x(t − τ). It discusses a theorem proving that sufficiently small delays do not change the qualitative behavior of the solution compared to the non-delayed case, and provides the mathematical conditions for 'small enough' delays. The author illustrates the concept with a concrete example, computational results using Mathematica, and a reference to a peer-reviewed paper.

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#mathematical modeling #Numerical Analysis #Differential Equations