existence and uniqueness theorem

Also known as the Picard-Lindelof theorem or the Cauchy-Lipschitz theorem

A differential equation of the form

Has a unique solution y on the interval (x0−a,x0+a) with a>0 if f:D→R where D is an open set that contains (x0,y0) is lipschitz continuous.

The larger the lipschitz constant, the smaller this bound for a unique solution becomes.