5.1 Solutions about Ordinary Points

5.2 Solutions about Singular Points

5.3 Special Functions

Chapter 5 in Review

Up to this point we primarily have solved linear differential equations of order two (or higher) with constant coefficients. The Cauchy–Euler equations in Section 3.6 were the only exception. In applications, linear high-order equations with variable coefficients are just as important as DEs with constant coefficients. In this chapter we will see that the same ease with which we solved Cauchy–Euler equations does not carry over to a simple second-order equation with variable coefficients such as y″ − xy = 0. We will see that solutions of this equation are functions defined by infinite series.