What is a Differential Equation? A differential equation is an equation involving the derivatives of the dependent variable concerning the independent variable. For example. d 2 y d x + x = 0 dxd2y + x = 0. Here, x is the independent variable, and y is the dependent variable. 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 ... 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.
