Growth of solutions of higher-order linear differential equations

In this article, we study the growth of solutions of the linear differential equation $$ f^{(k)}+(A_{k-1}(z)e^{P_{k-1}(z)}+B_{k-1}(z)) f^{(k-1)}+dots +(A_0(z)e^{P_0(z)}+B_0(z))f=0, $$ where $kgeq 2$ is an integer, $P_j(z)$ are nonconstant polynomials and $A_j(z), B_j(z)$ are entire functions, not identically zero. We determine the hyper-order of these solutions, under certain conditions.