Applied Mathematical Methods

32

First Order Ordinary Differential Equations

In earlier chapters, we have studied numerical methods for solving ordinary differential equations (ODE’s). Those methods have general applicability. In the present and following chapters, we study some special classes of ODE’s that can be solved or analyzed by known analytical means, without reference to ‘numerical values'. Analytical solutions, whenever applicable, provide us with richer information regarding the properties and behaviour of the solution function, besides simplifying their evaluation.

In this chapter, we first have a brief look at the way ODE’s are formed to represent classes of functions, and also discuss a few important terms to be used in these chapters. Next, we concentrate ...