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Part CCSIR NET December 2023volterra-to-ode

Volterra to ode

Let y be the solution to the Volterra integral equation y(x) = eˣ +∫0+ \int_{0}ˣ ((1+x2)/(1+t2))y(t)((1 + x^{2})/(1 + t^{2})) y(t) dt. Which of the following statements are true?

  1. A.y(1)=(1+π/4)ey(1) = (1 + \pi/4)e
  2. B.y(1)=(1+π/2)ey(1) = (1 + \pi/2)e✓ Correct
  3. C.y(3)=(1+y(\sqrt{3}) = (1 + 3π/4)e33\pi/4)e^{\sqrt{3}}
  4. D.y(3)=(1+y(\sqrt{3}) = (1 + 4π/3)e34\pi/3)e^{\sqrt{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 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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