The exact meromorphic solutions of some nonlinear differential equations

We find the exact forms of meromorphic solutions of the nonlinear differential equations fn+q(z)eQ(z)f(k)=p1eα1z+p2eα2z,n≥3,k≥1,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f^n} + q(z){{\rm{e}}^{Q(z)}}{f^{(k)}} = {p_1}{{\rm{e}}^{{\alpha _1}z}} + {p_2}{{\rm{e}}^{{\alpha _2}z}},\,\,\,\,n \ge 3,\,\,\,k \ge 1,$$\end{document} where q, Q are nonzero polynomials, Q ≡ Const., and p1, p2, α1, α2 are nonzero constants with α1 ≠ α2. Compared with previous results on the equation p(z)f3 + q(z)f″ = − sin α(z) with polynomial coefficients, our results show that the coefficient of the term f(k) perturbed by multiplying an exponential function will affect the structure of its solutions.