Enhancing Hospital Operations and Patient Care: The Role of AI in Smart Healthcare Systems

Abstract

This paper investigates the significance of differential equations in addressing complex engineering challenges, emphasizing their theoretical and practical roles in mechanical systems, fluid dynamics, electrical circuits, structural engineering, and control systems. The study utilizes a quantitative methodology to explore relationships between differential equation types and engineering outcomes such as model accuracy, system efficiency, and stability. Findings indicate that ordinary differential equations and partial differential equations are crucial in enhancing engineering solutions, testing hypotheses in different fields. These findings help bridge the gaps in research by pointing out the incorporation of differential equations into advanced models of engineering and future research directions to improve their applications in emerging technologies.