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 Existence and Uniqueness True-or-False

 1 . An equation has a unique local solution if there is some interval I containing t0 on which there is exactly one solution y. [Hint]  True  False 2 . If there is a unique solution on I, then there is not a unique solution on any subinterval I. [Hint]  True  False 3 . A maximal solution is a soultion whose only continuation is itself. [Hint]  True  False 4 . The concept of uniqueness is closely tied to the local nature of the solution. [Hint]  True  False 5 . Any continuation of y defined on an interval I, must equal y on this interval. [Hint]  True  False 6 . The graph of any continuation of y is a subset of the graph of y. [Hint]  True  False 7 . A solution defined on the whole real line is called a local solution. [Hint]  True  False 8 . The solution normally means the unique maximal solution. [Hint]  True  False 9 . Theorem 1 is our local existence and uniqueness theorem. [Hint]  True  False 10 . Theorem 1 requires the function and the derivative to be continuous on some open rectangle. [Hint]  True  False

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