Differential Equations

A differential equation is an equation that involves a derivative of one variable with respect to another — not just the variable itself, but how fast it is changing. Formally, an equation involving the derivative(s) of a dependent variable with respect to independent variable(s) is called a differential equation. When the equation involves derivatives of a dependent variable with respect to only one independent variable, it is called an ordinary differential equation (ODE) — the kind you will work with throughout this chapter.

Differential equations are not a purely abstract exercise: they are the natural language for describing how quantities change, and they appear across physics, chemistry, biology, economics, and even anthropology and geology wherever a rate of change matters. Because of this, the study of differential equations is central to modern scientific and quantitative modeling. …