Differential equations: Learn what a differential equation

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. 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 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 ... In this section we study what differential equations are, how to verify their solutions, some methods that are used for solving them, and some examples of common and useful equations. Consider the equation y ′ = 3 x 2, which is an example of a differential equation because it includes a derivative.