Weierstrass Integrability of Complex Differential Equations

Abstract

We characterize the complex differential equations of the form $${{dy} \over {dx}} = {a_n}(x){y^n} + {a_{n - 1}}(x){y^{n - 1}} + \cdots + {a_1}(x)y + {a_0}(x),$$ where aj(x) are meromorphic functions in the variable x for j = 0,…,n that admit either a Weierstrass first integral or a Weierstrass inverse integrating factor.