Solution of the Cauchy Problem for Oscillatory Equation with Delay

TL;DR

This paper addresses second-order delay differential equations by deriving an analytical solution using the method of steps, enhancing understanding of oscillatory equations with delays.

Contribution

It provides an explicit analytical representation for solutions of second-order delay differential equations, which was previously lacking.

Findings

Analytical solutions for oscillatory delay equations are derived.

The method of steps is effectively applied to second-order delay equations.

Results facilitate better analysis of oscillatory behavior with delays.

Abstract

Ordinary differential equations of the second order with one constant delay are considered in this paper. An analytical representation of the solution is obtained using the method of steps.