# Definition:Initial Value Problem

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## Definition

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.

## Sources

- 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**initial value problem**