Definition:Initial Value Problem

Let $$y \left({x}\right)$$ be a solution to the first order ordinary differential equation:
 * $$\frac {dy} {dx} = f \left({x, y}\right)$$

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.