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What is an initial-value problem?

What is an initial-value problem? Here are some definitions.

Noun
  1. (calculus) the problem of solving a (set of) ordinary differential equations accompanied by the requirement that the function sought (and possibly also one or more of its derivatives), taken for some value, equals some other specific value; graphically, (for example) the problem of finding that antiderivative of some function that passes through a particular point
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