A differential equation is a mathematical equation that relates a function to its derivatives. It describes how a quantity changes over time or space, making it essential in various fields such as physics, engineering, and biology. By solving a differential equation, one can find the original function that represents a system's behavior. There are two main types of differential equations: ordinary differential equations (ODEs), which involve functions of a single variable, and partial differential equations (PDEs), which involve multiple variables. These equations are crucial for modeling real-world phenomena, such as population growth, heat transfer, and motion in mechanics.