Is the following statement true? Every IVP has a unique solution

No. y′ = y^{1/3}, y(0) = 0 Not Lipschitz at 0; y ≡ 0 and y = (2x/3)^{3/2} both solve it.

Counterexample

Is this true?

Every IVP has 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.

Keep practicing

Existence vs uniqueness

A theorem giving one was read as giving both.

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