ABSTRACT
In the preceding chapters we studied a few restricted types of differential equations that can be solved in terms of familiar elementary functions. The methods we developed require considerable skill in the techniques of integration, and their many interesting applications have a tasty flavor of practicality. Unfortunately, however, it must be admitted that this part of the subject tends to be a miscellaneous bag of tricks, and conveys little insight into the general nature of differential equations and their solutions. In the present chapter we discuss an important class of equations with a rich and far-reaching theory. We shall see that this theory can be given a coherent and satisfying structure based on a few simple principles.
