An Easy Way to Teach First-Order Linear Differential and Difference Equations with a Constant Term and a Constant Coefficient

Abstract

We present a simple method of solving first-order linear differential and difference equations with a constant term and a constant coefficient. When solving such equations standard books in mathematical economics resort to a particular integral and a complementary function without further explaining those to beginning undergraduate students. We use the derivative and the difference, respectively, which give rise to a number of parental functions whose time path is studied by economic dynamics. A derived function is “shared” by multiple parental functions, but a number of parental functions give rise to one derived function. The method is smooth and easy to understand. Instead of spending time on complicated theoretical math techniques, the professor teaching quantitative methods could emphasize substantive economic models applying such simple equations.