A new trend in complex differential equations: Quasimeromorphic solutions

Complex differential equations study analytic or meromorphic solutions of equations. We start a new trend by considering quasimeromorphic solutions for generalized algebraic differential equations of the first order. Particularly, the classical Goldberg's result that any meromorphic solution of a first order algebraic differential equation must be of finite order has been extended to any $K(r)$-quasimerormorphic (in $\Bbb{C}$) solutions of first order generalized algebraic differential equation.