ABSTRACT
This chapter is concerned with the development of methods for the solution of the simplest classes of first-order differential equations for which solutions may always be obtained in an analytical form. The Bernoulli equation is considered because, although it is a nonlinear differential equation, a simple change of variable reduces it to a first-order linear differential equation so that its general solution can always be found. The chapter explores by means of a simple example how direct deductions can often be made from a differential equation without the necessity to solve it completely. The importance of the equation is that it arises in population growth studies, product marketing, ecological problems, the spread of epidemics, and the theory of learning and in certain nuclear problems.
