Counterexample

Is this true?

A continuous right-hand side gives a unique solution

No — it is false.

The counterexample

y′ = $y^{1/3}$ , y(0) = 0

Why it fails

Not Lipschitz at 0: y ≡ 0 and y = $(2x/3)^{3/2}$ both solve it, as do infinitely many hybrids.

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Keep practicing

Existence vs uniqueness

A theorem giving one was read as giving both.

See real exam options built on this mistake Drill statements like this

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

Published 23 Aug 2026. Found a mistake? Tell us — corrections are the fastest thing we act on.

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