Application of First Order Linear Ordinary Differential Equations in Mechanics and Thermodynamics
Authors:- Jyotika Sa, Tejaswini Pradhan
Abstract- This comprehensive study explores the profound applications of first-order linear ordinary differential equations (ODEs) in the domains of classical mechanics and thermodynamics. These mathematical tools serve as vital instruments in modeling and analyzing real-world physical phenomena. In particular, this research focuses on Newton’s Second Law of Motion and Newton’s Law of Cooling, both of which are quintessential examples of how first-order linear ODEs can effectively describe dynamic systems. The paper provides an in-depth explanation of the formulation, derivation, and solution of these equations, supported by descriptive illustrations and analytical interpretations. Emphasis is placed on demonstrating the solution techniques such as the integrating factor method, and the separation of variables method, while linking their mathematical elegance to practical engineering, environmental, and forensic applications. The ultimate objective is to illuminate how first-order linear ODEs not only simplify complex physical laws but also enable predictions that are essential in technological and scientific advancements.
