We study the set of T-periodic solutions of a class of T-periodically
perturbed Differential-Algebraic Equations with separated variables. Under
suitable hypotheses, these equations are equivalent to separated variables ODEs
on a manifold. By combining known results on Differential-Algebraic Equations,
with an argument about ODEs on manifolds, we obtain a global continuation
result for the T-periodic solutions to the considered equations. As an
application of our method, a multiplicity result is provided
