Part BCSIR NET June 2025a-separable-kernel-turns-the-equation-into-one-scalar-unknown

A separable kernel turns the equation into one scalar unknown

If y(x) is the solution of the integral equation $y (x) = x^{2} + 2 \int_{0}^{1}$ xt y(t) dt, then which of the following statements is true?

A.y(0) + y(1) = 1/2
B.y(−1) + y(1) = 1
C.y′(0) + y′(1) = 3/2
D.y′(−1) + y′(1) = 3✓

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 standard counterexample.

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50 are analysed free — try those first.

The trap it tests

Standard counterexample

There is a canonical object that settles this. Recognising it is the whole question.

Drill statements like this

A separable kernel turns the equation into one scalar unknown

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