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Part CCSIR NET December 2023equilibria-trap-solutions

Equilibria trap solutions

Consider the problem y′=(1−y2)10cos⁡y,y(0)=0y' = (1 - y^{2})^{10} \cos y, y(0) = 0. Let J be the maximal interval of existence and K be the range of the solution. Which of the following statements are true?

  1. A.J=RJ = \mathbb{R}✓ Correct
  2. B.K = (−1, 1)✓ Correct
  3. C.J = (−1, 1)
  4. D.K = [−1, 1]

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 existence vs uniqueness.

See pricing

50 are analysed free — try those first.

The trap it tests

Existence vs uniqueness

A theorem giving one was read as giving both.

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

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

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