Conditions for the Boundness of the Solution for Second Order Linear Delay Differential Equations

It is well known that a solution to a second order differential equation with roots of its characteristic equation in the right half plane is unbounded. If a delay of the right magnitude is introduced into the equation the solution is bounded. This paper investigates this phenomenon by imbedding a second order differential equation with first order delay by embedding the equation in a field of equivalent classes of quotients of polynomials in the modified differential and delay operator over the real field. © 2022 World Scientific Publishing Company.