Part CCSIR NET June 2025the-kernel-vanishes-on-the-diagonal-so-three-derivatives-give-a-clean-ode

The kernel vanishes on the diagonal so three derivatives give a clean ode

Let u(x) be the solution to the Volterra integral equation $u(x) = x^{2} + 4\int_{0}$ ˣ $(t - x)^{2}u(t)$ dt. Then which of the following statements are true?

A.u(0) = 0✓ Correct
B. $u(2\pi/\sqrt{3}) =$ $(1/6)(e^{4\pi/\sqrt{3}}$ − $e^{-2\pi/\sqrt{3}})$ ✓ Correct
C. $u(\pi/(2\sqrt{3})) =$ $(1/6)(e^{\pi/\sqrt{3}}$ $- \sqrt{3}$ $e^{-\pi/(2\sqrt{3})})$ ✓ Correct
D. $u(\pi/(2\sqrt{3})) =$ $(1/6)(e^{\pi/\sqrt{3}}$ $+ \sqrt{3}$ $e^{-\pi/\sqrt{3}})$

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 execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

The kernel vanishes on the diagonal so three derivatives give a clean ode

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