In this talk we consider a planar autonomous system of ODEs and look
for rational solutions of the system. Each of rational solutions of the
system forms a rational parametrization of a rational algebraic curve, which is
also known as an invariant algebraic curve of the system. So we will look for
the rational invariant algebraic curves of the system, then parametrize
the obtained curves by rational functions. Once the algebraic curve is
parametrizable by rational functions, it has infinitely many such
parametrizations. We choose the correct ones among those
parametrizations to be the rational solutions of the given system.