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In this paper, we have characterized the nature and form of solutions of thefollowing non-linear delay-differential equation:$$f^{n}(z)+\sum_{i=1}^{n-1}b_{i}f^{i}(z)+q(z)e^{Q(z)}L(z,f)=P(z),$$ where$b_i\in\mathbb{C}$, $L(z,f)$ be a linear delay-differential polynomial of $f$;$n$ be positive integers; $q$, $Q$ and $P$ respectively be non-zero,non-constant and any polynomials. Different special cases of our result willaccommodate all the results of ([J. Math. Anal. Appl., 452(2017), 1128-1144.],[Mediterr. J. Math., 13(2016), 3015-3027], [Open Math., 18(2020), 1292-1301]).Thus our result can be considered as an improvement of all of them. We havealso illustrated a handful number of examples to show that all the cases asdemonstrated in our theorem actually occurs and consequently the same areautomatically applicable to the previous results.

Characterization of exponential polynomial as solution of certain type of non-linear delay-differential equation