... determine the constants or functions by the aid of the given conditions It often happens, however, that the general solution of the differential equation in question cannot be obtained, and then, ... treatment of our subject will require the investigation of the properties and relations of certain new and important functions, as well as the consideration of methods of developing in terms of them ... INTRODUCTION 16 Since the first member of (2) does not contain x, and the second member does not contain y, and the two members must be identically equal, neither of them can contain either x or y, and...