Definition:Initial Value Problem

Definition

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

$\dfrac {dy} {dx} = f \left({x, y}\right)$

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.

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