On the growth of solutions to non-homogeneous linear differential equations with entire coefficients having the same order

Abstract

In this paper, we investigate the order of solutions to the non-homogeneous linear differential equation f (k) + Bk−1 f (k−1) + · · · + Bl f (l) + · · · + B1 f + B0 f = F, where k 2, Bj (z)

j = 0, 1, . . . , k − 1

and F (z) are entire functions of finite order.