Stability of solutions of certain third order non-autonomous ordinary differential equations

Sufficient criteria were established to ensure the stability of solutions of certain third order nonlinear non-autonomous ordinary differential equations of the form x...+(a(t,x,x˙,x¨)+m(t,x,x˙,x¨))x¨+b(t)ϕ(x,x˙)+c(t,x,x˙,x¨)h(x)=p(t,x,x˙,x¨).\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {\mathop {x}\limits ^{...}}+(a(t,x,\dot{x},\ddot{x})+m(t,x,\dot{x},\ddot{x})) \ddot{x}+b(t)\phi (x,\dot{x})+c(t,x,\dot{x},\ddot{x})h(x)= p(t,x,\dot{x},\ddot{x}). \end{aligned}$$\end{document}By using Lyapunov’s direct method, we obtained new result on the subject being considered. An example is hereby introduced to illustrate the importance of the result obtained with graphical representation.