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 $u (x) = 3 + sin x + \int_{0}$ ˣ [(3 + sin x)/(3 + sin t)]u(t)dt, then

A. $u (π /2) = 4 e^{(} π /2)$ ✓
B. $u (π) = 3 e^{π}$ ✓
C. $u (- π) = 4 e^{(} - π)$
D. $u (- π /2) = 4 e^{π}$

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.

50 are analysed free — try those first.

Related counterexample: Every integral equation of the second kind has a unique solution

More on this topic

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volterra to odeDecember 2023
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one moment decides between none and infinitely manyDecember 2024
an antisymmetric kernel has no real eigenvalueDecember 2024

The chapter behind this: Integral equations: Fredholm vs Volterra — free to read

From Linear Integral Equations › Fredholm and Volterra equations

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