Skip to content
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)=x2+2∫01y(x) = x^{2} + 2\int_{0}^{1} xt y(t) dt, then which of the following statements is true?

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

See pricing

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

Related counterexample: Volterra equations have eigenvalues just like Fredholm equations

More on this topic

The chapter behind this: Separable kernels and resolvent kernels — free to read

From Linear Integral Equations › Separable kernels and resolvent kernels

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

ShareWhatsAppTelegram