What is the physical significance of differential equations?

Differential equations are fundamental in describing how physical quantities change over time or space, capturing the dynamics of systems in fields such as physics, engineering, and Biology. They model phenomena such as motion, heat transfer, and wave propagation, enabling us to predict behavior under varying conditions. By relating a function to its derivatives, these equations provide insights into rates of change and help solve real-world problems through mathematical analysis. Ultimately, they serve as a bridge between abstract mathematics and practical applications in understanding the natural world.