Pólya’s Looking Back: an Example with Leibniz’s Integrating Factor and Second Order Linear Differential Equations

Abstract

A teacher who wants to present ordinary differential equation subjects with P´olya’s flavour has had a hard time on finding good examples which fits that aim. It might be due the fact that many well-done solutions obtained by using P´olya’s approach, for some reason, were never even submitted for publishing by its authors. Here we describe how looking back at Leibniz’s integrating factor lead us to an integrating factor method for nonhomogeneous second order linear equations. This approach avoids the need of knowledge on complex number’s topics such as Euler’s identity and complex exponential.