The Relation Between Boundedness and Oscillatory of First Order Neutral Delay Differential Equation

Abstract

 It is well known that all types of differential equations have wide range of applications in many areas. there is special type for differential equations that play important different theories of mechanical and electrical systems such by renaming the variables, this analogy has an important application the second order nonlinear differential equations with variables coefficients is of special interest, in this work we consider and give some sufficient conditions for oscillation of solutions of some types of neutral delay differential equations. and we made connection between oscillations and bondedness of the solution of the first order neutral delay differential equation of this form:

Where we will prove any oscillation solution of a differential equation is always bounded and the converse is not true.  And we use MATLAB software to solve examples on the previous equation.