A New Method for the Exact Solution of Duffing Equation

Abstract

A lot of methods, such as Jacobian elliptic function analysis, are used to look for the explicit exact solution of Duffing differential equation. The key of the analysis is to construct quotient trigonometric function, and then nonlinear algebraic equation set theory and method are used for the solution of some kinds of nonlinear Duffing differential equation. In this paper, the exact solution of Duffing equation is obtained by using constant variation method, making use of the formula to solve cubic equations and general solution of the homogeneous equation of Duffing equation with appropriate Constant m and function f(t) .