On the order of growth of solutions to complex non-homogeneous linear differential equations

Abstract

In this paper, we study the order of growth of solutions to the non-homogeneous linear differential equation f(k) + Ak-1eazf(k-1) +...+ A1eazf' + A0eazf = F1eaz + F2ebz; where Aj (z) (≢ 0) (j = 0, 1,..., k - 1), Fj (z) (≢ 0) (j = 1, 2) are entire functions and a, b are complex numbers such that ab (a - b) ≠ 0.