  It is the aim of this work to identify and illustrate the potential and
weaknesses of the computer algebra system Maple in the area of the Calculus of
Variations: a classical area of mathematics that studies the methods for
finding maximum and minimum values of functionals of integral type. Variational
problems are usually solved with the help of the necessary optimality
conditions of Euler-Lagrange, which are, in general, nonlinear and difficult
second order differential equations to be solved. We show how the computer
algebra system Maple can be useful in the determination and resolution of these
equations. We will also present the solution to the celebrated brachistochrone
problem from the point of view of the calculus of variations and the Maple
system, and a reformulation of the classical problem obtained by restricting
the class of admissible functions.
