A differential equation is a mathematical formula common in science and engineering that seeks to find the rate of change in one variable to other variables. Differential equations use derivatives, which are variables that represent change of a functional dependence of one variable upon another. In many differential equations, you will see the derivatives expressed in x and y terms. Differential equations are used in areas of quantitative study because they help scientists and engineers find solutions that may be used to predict the behavior of an original system. These solutions, called functions, show rates of change in matters that can be directly observed and measured.