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Bressan Chow. Johnson P. Johnson Kloeden Advertisers Media Information. You can find the general solution to any separable first order differential equation by integration, or as it is sometimes referred to, by "quadrature". Thus you can apply the numerical techniques of the previous chapter to each of these directly and solve them numerically, if you cannot integrate them exactly.
Differential Equations — History & Overview
Suppose we have a first order differential equation that is not separable, so we cannot reduce its solution to quadratures directly. Can we apply the numerical techniques previously for doing integrals to the task of solving these equations? The answer is yes and we show how below. There is indeed a complication which we discuss next, but it can be overcome.
The implication of this fact is, that any system whose behavior can be modeled by a first order differential equation, or even by a set of linked first order equations, can be solved numerically to any desired accuracy by a modern computer very quickly.
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