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Part BCSIR NET December 2025differentiate-the-volterra-equation-twice-to-reach-a-plain-ode-then-add-not-subtract-to-cancel-e-to-minus-pi

Differentiate the volterra equation twice to reach a plain ode then add not subtract to cancel e to minus pi

Suppose u(x) is the solution of the integral equation u(x)=3+∫0u(x) = 3 + \int_{0}ˣ (x−t)u(t) dt. Then which of the following statements is true?

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

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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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