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Counterexample

Is this true?

A locally unique solution exists for all time

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

See pricing

86 counterexamples are free — including most of the ones Part C leans on hardest.

Keep practicing

Existence vs uniqueness

A theorem giving one was read as giving both.

See real exam options built on this mistakeDrill statements like this
ODE

Go deeper· Explained in full in Existence, uniqueness and how far the solution extends· Asked in CSIR NET June 2025· From Ordinary Differential Equations › Existence–uniqueness, Picard, Lipschitz

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