In this article, we analyze meromorphic solutions of the following nonlinear complex differential equation of the form \(\begin{aligned} f^{n}+P_d(z,f)=p_{1}e^{\alpha _{1}z^{k}}+p_{2}e^{\alpha _{2}z^{k}}+p_{3}e^{\alpha _{3}z^{k}}, \end{aligned}\) where n and \(k\ge 1\) are integers, f is a meromorphic function, \(P_d(z,f)\) is a differential polynomial in f of degree d with rational functions of f as the coefficients, \(\alpha _{1},~\alpha _{2},~\alpha _{3},~p_{1},~p_{2},~p_{3}\) are nonzero constants. For \(n\ge 3,~d\le n-2~or~n\ge 3,~d=n-1~or~n\ge 5,~d\le n-4,\) we present the expressions of meromorphic solutions of the above equation under the conditions on the ratios between \(\alpha _{1}\) , \(\alpha _{2}\) and \(\alpha _{3}.\) Furthermore, we give some examples to show the accuracy of our results.
