Advanced Techniques in Solving First-Order Linear Ordinary Differential Equations

Dr. Raman

Differential equations, ordinary differential equations (ODEs), partial differential equations (PDEs), discuss analytical and numerical solution techniques.

This paper explores the fundamental concepts, methodologies, and applications of differential equations in various scientific and engineering fields. Differential equations, being pivotal in modeling the behavior of dynamic systems, provide essential tools for understanding and predicting the evolution of natural and man-made systems. We investigate both ordinary differential equations (ODEs) and partial differential equations (PDEs), discuss analytical and numerical solution techniques, and highlight recent advancements and applications in areas such as physics, biology, and finance. Our findings underscore the versatility and significance of differential equations in solving complex real-world problems.