ABSTRACT
In Chapter 1, we discussed and illustrated the process and techniques of building mathematical models of physical and engineering systems. It has been found that modelling of many problems of practical interest leads to differential equations – ordinary (ODE) or partial (PDE) – with appropriate initial and boundary conditions. The solution of the model equation gives the explicit relationship between the variables and parameters, which is not only useful for quantitative understanding of the phenomenon but is helpful in design and optimization as well. As such, solution of differential equations is a very important part of application of mathematical methods for analysis of physical and engineering problems. However, there is no unique or universally applicable technique or methodology for analytical solution of an arbitrary differential equation. Solution of such equations is often a combination of art and mathematical skill, particularly when the equations are non-linear. In this chapter we shall review the techniques of analytical solution of ODEs with constant coefficients and illustrate their applications with a variety of examples. This will be followed by solution of secondorder ODEs with variable coefficients, which leads to special functions (Chapter 3).
