There is a method to solve the delay differential equation, which is called Method of steps you can look on the book of Driver for delay differential equations. You start by a function \phai on the interval [-\tau,0] and then integrate and then consider [\tau, 2\tau] and so on  (like proving continuation of solution of first order differential equations)

"Numerical Methods for Delay Differential Equations" by A.Bellen and M.Zennaro, Oxford UP, 2005 - https://global.oup.com/academic/product/numerical-methods-for-delay-differential-equations-9780199671373?cc=lt&lang=en&

You can use MathLab: 

https://se.mathworks.com/help/matlab/delay-differential-equations.html?requestedDomain=www.mathworks.com

http://se.mathworks.com/matlabcentral/fileexchange/3899-tutorial-on-solving-ddes-with-dde23

“Stability of Linear Delay Differential Equations. A Numerical Approach with MATLAB” by Dimitri Breda, Stefano Maset, Rossana Vermiglio, 2015

http://www.springer.com/us/book/9781493921065

See also Kęstutis Pyragas papers: 

http://pyragas.pfi.lt/eng/publications/pdf_recent.html

 Method of steps.

Dear Thirunavukarasu,

Classical methods for solving Delay diff.Eqns are: ,

I) Method of Steps  is one of the method as said by Dr.Samir I would like add one more

II) Adomian Decomposition Method

Best luck

DNYAN