Category:Definitions/Initial Conditions

This category contains definitions related to Initial Conditions.
Related results can be found in Category:Initial Conditions.

Let $\Phi = \map F {x, y, y', y, \ldots, y^{\paren n} }$ be an ordinary differential equation.

An initial condition is an ordered pair $\tuple {x_0, y_0}$ which any solution of $\Phi$ must satisfy.

That is, an initial condition is the additional imposition that a solution $y = \map y x$ of $\Phi$ satisfy:

$\map y {x_0} = y_0$