This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

EulerEquations

EulerEquations[f, u[x], x]
returns the Euler-Lagrange differential equation obeyed by u[x] derived from the functional f, where f depends on the function u[x] and its derivatives as well as the independent variable x.
EulerEquations[f, u[x, y, ...], {x, y, ...}]
returns the Euler-Lagrange differential equation obeyed by u[x, y, ...].
EulerEquations[f, {u[x, y, ...], v[x, y, ...], ...}, {x, y, ...}]
returns a list of Euler-Lagrange differential equations obeyed by u[x, y, ...], v[x, y, ...], ....