On the Polynomial Solutions of the Polynomial Differential Equations y y ' = a(0)(x) plus a(1)(x) y plus a(2)(x) y(2) + horizontal ellipsis plus a(n)(x) y(n)

Abstract

In this paper we deal with differential equations of the form yy ' = P(x, y) where y ' = dy/dx and P(x, y) is a polynomial in the variables x and y of degree n in the variable y. We provide an upper bound for the number of polynomial solutions of this class of differential equations, and for some particular classes we study properties of their polynomial solutions.