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Part CCSIR NET December 2024a-separable-kernel-makes-it-a-differential-equation

A separable kernel makes it a differential equation

If u is the solution of the Volterra integral equation u(x)=3+sin⁡x+∫0u(x) = 3 + \sin x + \int_{0}ˣ [(3 + sin x)/(3 + sin t)]u(t)dt, then

  1. A.u(π/2)=4e(π/2)u(\pi/2) = 4e^(\pi/2)✓ Correct
  2. B.u(π)=3eπu(\pi) = 3e^\pi✓ Correct
  3. C.u(−π)=4e(−π)u(-\pi) = 4e^(-\pi)
  4. D.u(−π/2)=4eπu(-\pi/2) = 4e^\pi

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

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

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