# Definition:Initial Value Problem

## 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 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.