  We study a particular class of autonomous Differential-Algebraic Equations
that are equivalent to Ordinary Differential Equations on manifolds. Under
appropriate assumptions we determine an easy-to-use straightforward formula for
the computation of the degree of the associated tangent vector field that does
not require any explicit knowledge of the manifold. We use this formula to
study the set of harmonic solutions to periodic perturbations of our equations.
Two different classes of applications are provided.
