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Research Paper | Mathematics | India | Volume 10 Issue 7, July 2021 | Popularity: 5.3 / 10
Study of Methods for Solving Second-Order ODEs with Constant Coefficient
Manjula B S
Abstract: The paper provides an in-depth analysis of various methods for solving second-order ordinary differential equations (ODEs) with constant coefficients, categorizing solutions based on the roots of the characteristic equation. Different real roots, complicated conjugate roots, and repetitive roots are the three primary types of roots that are covered by this. In the case of distinct real roots, the solution is a linear combination of exponential functions. On the other hand, complex conjugate roots result in solutions that include exponential and trigonometric functions. In order to assist students and researchers who are interested in understanding and solving second-order ordinary differential equations with constant coefficients with a roadmap that is both clear and succinct, the purpose of this work is to create such a guide. In the case of repeated roots, the solution uses a mix of exponential functions and a linear term to solve the problem. The formulation of the characteristic equation, the process of solving for roots, and the application of beginning conditions to find particular constants are all topics that are covered in this work. These approaches are shown using practical examples, which emphasize their usefulness in domains such as engineering, physics, and applied mathematics: these examples are offered to demonstrate these methods. In order to ensure that a full grasp of the topic is achieved, the study places an emphasis on the significance of these approaches in modeling a variety of physical processes and provides an organized approach to solving second-order ordinary differential equations.
Keywords: Second-order differential equations, Linear differential equations, Delay Differential Equations, DDEs
Edition: Volume 10 Issue 7, July 2021
Pages: 1550 - 1555
DOI: https://www.doi.org/10.21275/ES24928084917
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