Solution of the Cubic Duffing Equation via the Differential Transform Method

In this work, we review the dimensional differential transform and introduce a formula for the cubic

non-linear term .  Then, we use the differential transform method, with this formula, to solve the well-known cubic Duffing’s equation.  Next, with the help of Maple program tools, we show that the series solutions obtained by the differential transform method converge rapidly to the Alvaro and Jairo exact solutions, which given in term of the Jacobian elliptic functions.  This shows that the differential transform method is capable to solve non-linear ordinary differential equations, when the non-linear term is given as a polynomial of degree higher than three.