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Parametric conditions and exact solution for the Duffing-Van der Pol class of equations

Dao Huy Bich, Nguyen Dang Bich


This paper presents a methodology to find the exact solution and respective parametric conditions to the Duffing-Van der Pol class of equations. The supposed method in this paper is different from the Prelle and Singer method and the Lie symmetry method. The main idea of the supposed method is implemented in finding the first integrals of the original equation and leading this equation to a solved equation of lower order to which the exact solution can be obtained. As results the parametric conditions and the exact solutions in parametric forms are indicated. The algorithm for determining integral constants and the investigation of solution characteristics are considered.


parametric conditions; Prelle and Singer method; Lie symmetry method; exact solutions; Duffing-Van der Pol equation; Riccati equation; hypergeometric functions

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