A study on solving Duffing – Van der Pol (DVP) differential equation by a second order nonlinear ordinary differential equation of Adomain's decomposition into the first order differential equations & solving them uses the same method. First the equation is converted into the first order differential equations and solving them using the same method. The Lindsted's method (LM) is used to compare the solutions of ADM and showing that converting the differential equation to the equations in Adomian's method, gives more accurate answers in a shorter of computations.