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Part BCSIR NET December 2024the-lipschitz-condition-is-in-y-not-x

The lipschitz condition is in y not x

The initial value problem dy/dx =√= \surd|x − 1| sin y, y(0) = 1 has

  1. A.a unique solution on R\mathbb{R}✓ Correct
  2. B.infinitely many solutions on the interval (−2, 2)
  3. C.a unique solution and its maximal interval of existence is (−∞,1)(-\infty, 1)
  4. D.no solution on the interval (−2, 2)

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, and why this one tests hypothesis dropped.

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50 are analysed free — try those first.

The trap it tests

Hypothesis dropped

A theorem applied without checking one of its preconditions.

Drill statements like this

Related counterexample: Every IVP has a unique solution

More on this topic

The chapter behind this: Existence, uniqueness and how far the solution extends — free to read

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

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