  The explicit solution of the initial-values problem is exhibited of a
subclass of the autonomous system of 2 coupled first-order ODE s with
second-degree polynomial right-hand sides, hence featuring 12 a prior arbitrary
(time-independent) coefficients. The solution is explicitly provided if the 12
coefficients are expressed by explicitly provided formulas in terms of 10 a
prior arbitrary parameters; the inverse problem to express these 10 parameters
in terms of the 12 coefficients is also explicitly solved, but it is found to
imply as it were, a posterior that the 12 coefficients must then satisfy 4
algebraic constraints, which are explicitly exhibited.Special sub cases are
also identified the general solutions of which are completely periodic with a
period independent of the initial data, or are characterized by additional
restrictions on the coefficients which identify particularly interesting
models.
