  In this Letter we identify special systems of (an arbitrary number) N of
first-order Ordinary Differential Equations with homogeneous polynomials of
arbitrary degree M on their right-hand sides, which feature very simple
explicit solutions; as well as variants of these systems--with right-hand sides
no more homogeneous--which feature periodic solutions. A novelty of these
findings is to consider special systems characterized by constraints involving
both their parameters and their initial data.
