order

A differential equation is a mathematical statement that includes one or more derivatives, representing the rates of change of continuously varying quantities. These equations are fundamental in science and engineering because they describe how systems change over time or space.1

Differential equations are classified into two main categories:
* Ordinary Differential Equations (ODEs): These involve a function of a single variable and its ordinary derivatives.21
* Partial Differential Equations (PDEs): These involve functions of multiple variables and their partial derivatives.31

The order of a differential equation is determined by the highest order of derivative it contains. For example, an equation with a third-order derivative but no higher would be a third-order differential equation. The degree refers to the power to which the highest-order derivative is raised. Solutions to differential equations often involve constants that are determined by auxiliary conditions, such as initial values or boundary values, which provide specific information about the system at a given point or time.214