Definition:Initial Value Problem

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Let $\map y x$ be a solution to the first order ordinary differential equation:

$\dfrac {\d y} {\d x} = \map f {x, y}$

which is subject to an initial condition: $\tuple {a, b}$.

That is, it is required that $y = b$ when $x = a$, that is $\map y a = b$.

The finding of the resulting particular solution is known as an initial value problem.

Also known as

This is sometimes found abbreviated as I.V.P. or IVP, but beware of getting this confused with Intermediate Value Property.