In this article, the solutions of Bessel’s differential equations (DEs) by variable change method are formulated. To do so, we have considered the first and second kind of Bessel’s functions which are obtained as solutions of Bessel’s equations and it is used to determine the solutions of the lengthening pendulum (LP). To solve the given equations, we have used Frobenius theorem and the gamma function and hence, apply the obtained results to solve the LP. The finding reveals that Bessel’s functions establish the solutions of LP equations. The solutions obtained for lengthening the pendulum are illustrated graphically using the computer software of MathLab. The graphical results show that the sinusoidal wave natures are compressed or extended based on the chosen parameter k . Finally, it is concluded that the obtained method gives an effective, efficient, and systematic method.

Beyalfew Anley

Daba Meshesha Gusu

Tolosa Nigussie

Abstract and Applied Analysis

ABSTRACT AND APPLIED ANALYSIS 是一本专门致力于发表抽象和应用分析领域的高质量研究论文的数学期刊。重点放在经典分析、线性和非线性泛函分析、常微分方程和偏微分方程、优化理论和控制理论方面的重要发展。摘要和应用分析支持出版涉及上述学科重大问题的完整解决方案的原始材料。摘要和应用分析还鼓励就分析理论和应用的当前趋势发表及时而全面的调查文章。

Abstract and Applied Analysis is a mathematical journal dedicated to publishing high-quality research papers in the field of abstract and applied analysis. The journal focuses on significant developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimization theory, and control theory. Abstract and Applied Analysis supports the publication of original materials that provide comprehensive solutions to major problems in these disciplines. Additionally, the journal encourages timely and comprehensive survey articles on current trends in analysis theory and applications.

《Abstract and Applied Analysis》是一本专注于发表抽象与应用分析领域高质量研究论文的数学期刊。期刊重点关注经典分析、线性与非线性泛函分析、常微分方程与偏微分方程、优化理论及控制理论等领域的重要发展。《Abstract and Applied Analysis》支持发表涉及上述学科重大问题的完整解决方案的原创研究材料。同时，期刊也鼓励发表关于分析理论与应用当前趋势的及时而全面的综述文章。

Solutions of Bessel’s Differential Equations by Variable Change Method

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