\begin{definition}[Definition:Initial Value Problem]
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'''.
\end{definition}