Publication Date



Characteristic equation; Repeated roots; Integrating factor


Most texts on elementary differential equations solve homogeneous constant coefficient linear equations by introducing the characteristic equation; once the roots of the characteristic equation are known the solutions to the differential equation follow immediately, unless there is a repeated root. In this paper we show how an integrating factor can be used to find all of the solutions in the case of a repeated root without depending on an assumption about the form that these solutions will take. We also show how an integrating factor can be used to explain the "extra" power of t which appears in the trial form of the solution when using the method of undetermined coefficients on a nonhomogeneous equation in the case where the right hand side is a polynomial multiple of the corresponding homogeneous solution.





To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.