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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

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

The kind of mistake this is

Existence vs uniqueness

A theorem giving one was read as giving both.

Drill statements like this

Others that fail the same way

From Ordinary Differential Equations › Existence–uniqueness, Picard, Lipschitz

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