Unstability of Zero Solution of a Class Nonautonomous
Differential Equation

Yaxin Guo

doi:https://doi.org/10.14445/22315373/IJMTT-V69I8P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 69 | Issue 8 | Year 2023 | Article Id. IJMTT-V69I8P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I8P503

Unstability of Zero Solution of a Class Nonautonomous Differential Equation

Yaxin Guo

Received	Revised	Accepted	Published
08 Jun 2023	24 Jul 2023	07 Aug 2023	24 Aug 2023

Citation :

Yaxin Guo, "Unstability of Zero Solution of a Class Nonautonomous Differential Equation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 8, pp. 25-29, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I8P503

Abstract

In this paper, we consider a class of one-dimensional nonautonomous differential equation. Under certain conditions, we construct the general solution and prove that the zero solution x = 0 are unstable. The differential equations of mechanics arises from the variational problems of the laws of nature, thus, the study about stability or the unstability of the special solutions, such as the zero solution, attracts many researchers. The novelty of this paper is that the system we consider is nonautonimous with the vector field being the polynomial of any order and prove that the zero solution is unstable. Our result will throw light on the research of the dynamics of celestial mechanics and enrich the differential equation theory.

Keywords

Nonautonomous differential equation, General solution, Unstability, Zero solution.

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