We shall now discuss the manner in which the earlier techniques can be extended in two ways: to systems of equations and to equations of higher order. The order of an equation is the order of the highest derivative appearing in it. We will assume that it can be written in the form

(4.1)

where satisfies a Lipschitz constant in each of the

A system of equations involves are independent variable t and more than one dependent variable. Thus,

(4.2)

is a system of two first order equations.