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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.
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
has one and only one solution that is defined on the interval I.
The Attempt at a Solution