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Part CCSIR NET December 2023linear-growth-global-existence

Linear growth global existence

Consider the initial value problem y′ = y + ½|sin⁡(y2)\sin(y^{2})|, x > 0, y(0) = −1. Which of the following statements are true?

  1. A.There exists an α∈(0,∞)\alpha \in (0, \infty) such that limx→α−lim_{x\to\alpha^{-}} |y(x)| =∞= \infty.
  2. B.y(x) exists on (0,∞)(0, \infty) and it is monotone.✓ Correct
  3. C.y(x) exists on (0,∞)(0, \infty), but not bounded below.✓ Correct
  4. D.y(x) exists on (0,∞)(0, \infty), but not bounded above.

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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