The Growth of Solutions of Higher Order Differential Equations with Coefficients Having the Same Order

In this paper, we consider the growth of solutions of some homogeneous and non- homogeneous higher order differential equations. It is proved that under some conditions for entire functions F, Aji and polynomials Pj（z）, Oj（z） （j = 0, 1,..., k - 1; i = 1, 2） with degree n ≥ 1, the equation f（k） ＋ （Ak-l,1 （z）e pk-l（z） ＋Ak-1,2 （z）eQk-l（z））f（x-1） ＋...＋ （A0,1 （z）eP0（z） ＋ A0,2（z）eQ0（z））f = F, where k ≥ 2, satisfies the properties： When F ≡ 0, all the non-zero solu- tions are of infinite order; when F ≠ 0, there exists at most one exceptional solution f0 with finite order, and all other solutions satisfy -λ（f） = A（f） = σ（f） = ∞.