Explicit and exact solutions to cubic Duffing and double-well Duffing equations

In this paper, a kind of explicit exact solution of nonlinear differential equations is obtained using a new approach applied in this case to look for exact solutions of the Duffing and double-well Duffing equations. The new proposed procedure is applied by using a quotient trigonometric function expansion method. The method can also be easily applied to solve other nonlinear differential equations.