Differential Equations: The Mathematical Framework for Modelling Dynamic Systems

Abstract

Differential equations are essential tools in the mathematical Modelling of dynamic systems, providing a framework for describing phenomena that evolve over time or space. These equations are used across diverse fields, including physics, engineering, biology, economics, and social sciences, to capture the behavior of systems governed by rates of change. This paper explores the role of differential equations in Modelling dynamic systems, presents different types of differential equations, discusses solution methods, and examines the applicability and challenges associated with their use. Through this discussion, we aim to highlight the fundamental importance of differential equations in understanding and predicting the behavior of real-world systems.