Abstract
A generalization of the simplest equation method for finding exact solutions is presented. The basic idea of the method is to use simplest equations with function that is found during the calculations. Using our algorithm we consider two types of nonlinear ordinary differential equations of the second and the third order. The method is applied for finding exact solutions and first integrals. The exact solutions of some nonlinear differential equations are found. It is shown that the most methods that were used to construct exact solutions for differential equations are included in suggested approach.
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