Differential equations are fundamental mathematical tools used to describe how quantities change in relation to each other. They involve rates of change and are expressed in terms of derivatives. These equations are prevalent in various scientific fields, including physics, engineering, biology, economics, and more, as they model dynamic systems and their behaviors. A differential equation typically contains an unknown function and its derivatives. The goal is to find a function that satisfies the equation, thereby uncovering the relationship between the function and its derivatives. Differential equations come in various forms, such as ordinary differential equations (ODEs) involving single-variable functions and their derivatives with respect to one independent variable, and partial differential equations (PDEs) involving multivariable functions and their partial derivatives.
