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Is there any proof which would show that the uniqueness theorem does not imply complete uniqueness of a ODE solution?

Would it have any relation between the interval where uniqueness is assumed to exist and the maximal interval of existence?

Thanks :)

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Did you mean as in Theorem 2.4.1 or somethings else?. Regards –  Amzoti Feb 15 '13 at 23:46
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The usual example is something along the lines of $$ y' = 2 \sqrt y, \; \; y(0) = 0. $$ Then two legitimate solutions for $x \geq 0$ are $$ y = 0 $$ OR $$ y = x^2. $$

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