Methods for solving ordinary differential equations of second order with coefficients that is constant

Shohal Hossain¹ , Samme Akter Mithy²

Section:Research Paper, Product Type: Journal-Paper
Vol.10 , Issue.2 , pp.9-16, Apr-2023

Online published on Apr 30, 2023

Copyright © Shohal Hossain, Samme Akter Mithy . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
This article provides a detailed overview of the techniques and methods used to solve second-order ordinary differential equations having coefficients that remain constant. The article begins by introducing the general form of 2nd-order differential equations and explaining the concept of constant coefficients. Next, the article presents the characteristic of equation and its roots, which are used to determine the nature of the solutions. The article then goes on to discuss the three possible cases: distinct and real roots, complex conjugate roots, and repeated roots, and present the general solution for each case, including examples to illustrate the application of the method. The article concludes with a brief discussion of applications of second-order differential equations in engineering and physics. The aim of this article is to provide a clear and concise guide for students and researchers interested in this important topic.

Key-Words / Index Term :
Second-order differential equations, Constant coefficients, Homogeneous linear equations Real and distinct roots, Complex conjugate roots, Repeated roots

References :
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