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## Homework Statement

Determine whether existence of at least one solution of the given initial value problem is guaranteed and, if so, whether uniqueness of the solution is guaranteed.

dy/dx=y^(1/3); y(0)=0

## Homework Equations

Existence and Uniqueness of Solutions Theorem:

Suppose that both the function ƒ

*(x,y)*and its partial derivative [D][/y]

*f*(x,y) are continuous on some rectangle R in the xy-plane that contains the point (a,b) in its interior. Then, for some open interval I containing the point a, the initial value problem

dy/dx=ƒ(x,y), y(a)=b

has one and only one solution that is defined on the interval I.

## The Attempt at a Solution

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