Modelling with Differential Equations
In most of the examples of Chapter 8 we were given or assumed that our variable was modelled by a particular function of time, y = f(t), and then we found the rate of change, y′ = f′(t). Very often our modelling assumptions are expressed in terms of rates of change. For example, we may assume that the rate of change, y′, is related to the value of y itself at any time t. The rate of change of the size of a population, for example, clearly depends on the existing size of the population. This gives us the problem of working back from y′ to find y. (Note that in all the examples in this chapter we use ′ to stand for d/dt.)
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