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Abstract:The problem of find approximate solution for the first order linear ordinary delay differentialequations by using two of the special cases of the weighted residual method which are the leastsquares method and Petrov-Galerkin method with compare between these methods for which the bestapproximate solution near to the exact solution, also numerical applications are considered in thiswork.

Keywords: Delay differential equation --- weighted residual method --- least squares method --- Petrov- Galerkin method.