Part BCSIR NET December 2023

Sturm–Liouville problems and Green's functions

The smallest real number $\lambda$ for which the problem $-y'' + 3y = \lambda{}y, y(0) = 0, y(\pi) = 0$ has a non-trivial solution is

A.3
B.2
C.1
D.4✓ 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.

50 are analysed free — try those first.

Related counterexample: Every boundary value problem has a Green's function

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The chapter behind this: Sturm–Liouville problems and Green's functions — free to read

From Ordinary Differential Equations › Sturm–Liouville problems and Green's functions

Last revised 7 Sept 2026. Found a mistake? Tell us — corrections are the fastest thing we act on.

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