## Fourteen

CONTINUOUS TIME: FIRST-ORDER DIFFERENTIAL EQUATIONS

In the Domar growth model, we have solved a simple differential equation by direct integration. For more complicated differential equations, there are various established methods of solution. Even in the latter cases, however, the fundamental idea underlying the methods of solution is still the techniques of integral calculus. For this reason, the solution to a differential equation is often referred to as the integral of that equation.

Only first-order differential equations will be discussed in the present chapter. In this context, the word order refers to the highest order of the derivatives (or differentials) appearing in the differential equation; thus a first-order differential equation can contain only the first derivative, say, dy/dt.

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