Differential equations: In calculus

In calculus, a differential equation is an equation that involves the derivative (derivatives) of the dependent variable with respect to the independent variable (variables). Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Learn what a differential equation is, how to classify it by order, degree and type, and how to solve it using different methods. Explore the real-world examples and applications of differential equations in physics, engineering, biology and more. Differential equations A differential equation is an equation involving a function and its derivative (or derivatives). Our goal is to find the function, if one exists, that satisfies the given differential equation. For example, y = sin (x) is a solution to the ordinary differential equation, To show this, we can find the derivative of the solution, y' (x), and substitute it, as well as y (x), into the differential equation. Differentiating y = sin (x) yields y' = cos (x). Substituting ...