Differential equations are mathematical equations that relate a function to its derivatives. They are used to describe how things change over time or space, such as the motion of a falling object or the growth of a population. By solving these equations, we can predict future behavior based on current conditions. 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 essential in various fields, including physics, engineering, and economics, helping us model complex systems and understand their dynamics.