The EulerLagrange(f, t, x(t)) command computes the Euler-Lagrange equations of a functional  subject to  and .

In general, the Euler-Lagrange equations are not independent.

The Euler-Lagrange equations are returned as expressions.

If they can be calculated, the trivial first integrals are also returned.

The first integrals are set equal to generated global indexed variables  that denote arbitrary constants.

For higher-order functionals, for example, f(t, y(t), y'(t), y''(t)), use variables to represent derivatives. For example, set x1(t) = y(t) and x2(t)=y'(t), and then determine the Euler-Lagrange equations of the functional f + L*( x1'(t) - x2(t) )^2. To find the equations for the higher-order problem, substitute x2(t) = x1'(t) into the result.