Part BCSIR NET June 2024non-lipschitz-at-one-height-only

Non lipschitz at one height only

Consider the initial value problem (IVP $) y^{'} (x) = \sqrt$ | $y (x) + ε$ |, $x \in R, y (0) = y_{0}$ . Consider the following statements: S1: There is an $ε > 0$ such that for all $y_{0} \in R$ , the IVP has more than one solution. S2: There is $a y_{0} \in R$ such that for all $ε > 0$ , the IVP has more than one solution. Then

A.both $S_{1}$ and $S_{2}$ are true
B. $S_{1}$ is true but $S_{2}$ is false
C. $S_{1}$ is false but $S_{2}$ is true
D.both $S_{1}$ and $S_{2}$ are false✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Related counterexample: Every IVP has a unique solution

Non lipschitz at one height only

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