# Definition:Initial Value Problem

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## Definition

Let $y \left({x}\right)$ be a solution to the first order ordinary differential equation:

- $\dfrac {\mathrm d y} {\mathrm d x} = f \left({x, y}\right)$

which is subject to an initial condition: $\left({a, b}\right)$.

That is, it is required that $y = b$ when $x = a$, i.e. $y \left({a}\right) = b$.

The finding of this 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.