Gözen, M.2025-05-102025-05-1020232705-106410.37256/cm.44202330452-s2.0-85180833422https://doi.org/10.37256/cm.4420233045This paper deals with a nonlinear ordinary differential system of second order. In the paper, qualitative properties of solutions of the system called asymptotic stability (AS), uniform stability (US), boundedness, ultimately boundedness (UB) and integrability of solutions, are investigated by using the second method of Lyapunov. We give four new qualitative results and an example as a numerical application of the results. The results of this article extend and improve some earlier ones in the literature. © 2023 Melek Gözen.eninfo:eu-repo/semantics/closedAccessBoundednessDifferential SystemIntegrabilitySecond OrderStabilityThe Second Method Of LyapunovArticle