1.2 Initial-Value Problems


We are often interested in problems in which we seek a solution y(x) of a differential equation so that y(x) satisfies prescribed side conditions—that is, conditions that are imposed on the unknown y(x) or on its derivatives. In this section we examine one such problem called an initial-value problem.

Initial-Value Problem

On some interval I containing x0, the problem

Solve: (1)

Subject to:

where y0,

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