Question: Consider the Cauchy problem for the autonomous system : x' = f(x), r(to) = To , in which f : $2 -> R is a

Consider the Cauchy problem for the autonomous system : x' = f(x), r(to) = To , in which f : $2 -> R" is a Lipschitz function and $ is an open set of R". a) Show that if f is also bounded in ? then the problem has an unique so- lution define in some open set Ia(to) for any (to, To) E R" x Rn

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