Part CCSIR NET December 2024an-antisymmetric-kernel-has-no-real-eigenvalue

An antisymmetric kernel has no real eigenvalue

The integral equation $u (x) = f (x) + (2/ π) \int_{0}^{π} sin (x - t) u (t)$ dt has a unique solution if

A.f(x) = cos x✓
B.f(x) = cos 5x✓
C.f(x) = sin x✓
D.f(x) = sin 5x✓

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.

50 are analysed free — try those first.

Related counterexample: Every integral equation of the second kind has a unique solution

More on this topic

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a separable kernel makes it a differential equationDecember 2024

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

From Linear Integral Equations › Fredholm and Volterra equations

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