Tunc, Cemil2025-05-102025-05-1020142325-039910.12785/amis/0801492-s2.0-84890086197https://doi.org/10.12785/amis/080149https://hdl.handle.net/20.500.14720/20337Kroopnick (2010) discussed the bounded solutions of certain non-autonomous differential equations of the second order by using the integral test. In this paper, instead of the integral test, we study the results of Kroopnick [9] by using the Liapunov's function approach. We compare the established results with that of Kroopnick [9]. We also give some additional results on the equi-bounded solutions and uniformly-bounded solutions, and an example is given for the illustrations.eninfo:eu-repo/semantics/closedAccessNon-AutonomousDifferential EquationSecond OrderBounded SolutionsArticle