On the growth of meromorphic solutions of some higher order linear differential equations

Let $k,m,n $ be integers such that $k\geq 1$, $n\geq 2$ and $1\leq m\leq n$. In this article we study the order $\rho(f)$ and the hyperorder $\rho_2(f)$ of nonzero meromorphic solutions $f$ of the differential equation $$\sum_{j=1,j\ne m}^{n}A_j(z)f^{(j)}(z)+A_m(z)e^{p_m(z)}f^{(m)}(z)+\left(A_0(z)e^{p(z)}+B_0(z)e^{q(z)}\right)f(z)=0,$$ where $B_0(z)$, $A_0(z), \cdots, A_n(z)$ are meromorphic functions such that $A_0A_mA_nB_0\not\equiv 0$, $\max\{\rho(B_0), \rho(A_0), \cdots,\rho(A_n)\}