| Abstract: |
Differential equations constitute one of the most powerful mathematical tools for modeling and analyzing real-world phenomena that involve change with respect to time, space, or other variables. From classical mechanics and electromagnetism to modern applications in biology, economics, engineering, and environmental sciences, differential equation models provide a rigorous framework for understanding dynamic systems. This paper presents a comprehensive study of differential equation models ordinary and partial and examines their formulation, classification, solution techniques, and wide-ranging applications in applied sciences. Emphasis is placed on how these models translate physical, biological, and socio-economic processes into mathematical language, enabling prediction, control, and optimization. The paper also discusses limitations of differential equation modeling and highlights emerging trends and interdisciplinary applications. |
