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A simple technique is introduced for calculating the kernels in the Volterra series expansion, which represents the solution of a large class of nonlinear differential equations. The Volterra series considered in previous discussions can represent only solutions with zero initial conditions. The scope is widened in this paper to allow representation of the general solution of nonlinear differential equations. The last section of the paper presents an adaptation of a technique commonly used in the analysis and design of linear systems to a nonlinear system through the use of the Volterra series.