Higher-Order Differential Equations with Variable Coefficients

Abstract

In the previous two chapters we studied differential equations having constant coefficients. The theory was straightforward, and, with the help of Mathematica, the solutions were easy to obtain—even when the order of the differential equations was rather large. The persistent difficulty was, when we needed the roots of a polynomial of degree five or more, we could not be certain that they could be obtained exactly. This opened up the possibility of needing approximations to the roots, which opened up the need for knowing how accurately those approximations could be obtained, which led to numerical analysis, etc. The difficulties lay outside the field of differential equations, so we did not press for a resolution of them.