An analytic study on the Euler-Lagrange equation arising in calculus of variations

The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the di erential transformation method (DTM) for nding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an in nite power series with easily computable components. Several illustrative examples are given to demonstrate the e ectiveness of the present method.