What is an ordinary differential equation (ODE)?

An ordinary differential equation (ODE) is fundamentally characterized by its involvement of a function and its derivatives. This means that the equation relates a dependent variable, typically denoted as a function of one independent variable, to its rates of change, or derivatives. The nature of this relationship forms the crux of differential equations, where the objective is often to find the function that satisfies the equation based on given conditions.

In contrast, an equation that includes only constants or simply involves a function without derivatives does not meet the criteria to be classified as a differential equation. Additionally, while some ODEs may have multiple solutions, this is not a defining feature of what constitutes an ODE. Thus, the correct understanding hinges on recognizing the essential characteristics of how functions and their derivatives interact within the equation.