For a particular situation that we might wish to investigate, our first task is to write an equation (or equations) that best describes the phenomenon.Suppose that we wish to study how a population $$P(t)$$ grows with time $$t\text$$ We might make the assumption that a constant fraction of population is having offspring at any particular time.In addition, the theory of the subject has broad and important implications.¶We begin our study of ordinary differential equations by modeling some real world phenomena.