My question is this: 

In with(DifferentialGeometry): with(JetCalculus) with(Physics):

I work with the following Jet Bundle:

DGsetup([x], [u, psi], E, 40), 

where psi is declared anticommuting with Setup(anticommutativeprefix={psi}). 

When I work with expressions that are differential polynomials in u with coefficients arbitrary functions of u, the EulerLagrange operator behaves correctly. The same is true if I multiply these expressions by psi or by psi_1 ...