An integrating factor is a mathematical tool used to solve certain types of differential equations, particularly first-order linear ordinary differential equations. It transforms the equation into a form that can be easily integrated. The integrating factor is typically a function of the independent variable, often denoted as μ(x), and is derived from the coefficient of the dependent variable in the equation. To apply the integrating factor, you multiply the entire differential equation by μ(x). This process simplifies the equation, allowing you to express it as the derivative of a product of functions. Once integrated, you can find the general solution to the original equation.