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Part CCSIR NET December 2024one-moment-decides-between-none-and-infinitely-many

One moment decides between none and infinitely many

The integral equation u(x)=f(x)+(2/π)∫0πcos⁡(x+t)u(t)u(x) = f(x) + (2/\pi)\int_{0}^\pi \cos(x + t)u(t)dt has infinitely many solutions if

  1. A.f(x) = cos x
  2. B.f(x) = cos 5x✓ Correct
  3. C.f(x) = sin x✓ Correct
  4. D.f(x) = sin 5x✓ Correct

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 integral equation of the second kind has a unique solution

More on this topic

The chapter behind this: Integral equations: Fredholm vs Volterra — free to read

From Linear Integral Equations › Fredholm and Volterra equations

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

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