In this work we will study the Bessel Differential Equation and its resolution using the Frobenius
method, thus obtaining the solutions of the First and Second Kind of Bessel Functions. The motivation for the study object of this work arose because Bessel's Ordinary Differential Equation is one of the most important Ordinary Differential Equations in advanced studies of mathematics applied to Physics and Engineering. This study was developed in a bibliographical sequence, higher education books on Differentiable Equations with Application in Modeling, scientific articles and academic works were used as a research source for bibliographical complementation. Initially, we recalled some concepts considered prerequisites to the topic of the work, then several important topics were covered about the power series method, which is a fundamental tool for obtaining the solution of a differential equation. Subsequently, based on the content exposed in the initial chapters, the Bessel Differential Equation was solved and, thus, the First and Second Species Functions were obtained and in the final part an application that can be found in [11] was shown. Finally, the present work contributes to the presentation of teaching material that complements the study of Ordinary Second Order Differential Equations and serves as support for the development of knowledge about Bessel Functions.
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