Part CCSIR NET December 2024the-eigenvalue-condition-forces-omega-to-be-an-integer

The eigenvalue condition forces omega to be an integer

Consider the boundary value problem (BVP $) d^{2} y /$ dx $^{2} + 4 ($ dy/dx $) + (λ + 2) y = 0, y (0) = y (π) = 0$ . Then which of the following statements are true?

A.The BVP has a non-zero solution if $λ = 2$
B.The BVP has a non-zero solution if $λ = 3$ ✓
C.The BVP has a non-zero solution y = y(x) satisfying $y (k π /2) = 0$ for every integer k if $λ = 6$ ✓
D.The BVP has a non-zero solution y = y(x) satisfying $y (k π /3) = 0$ for every integer k if $λ = 6$

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.

See pricing

50 are analysed free — try those first.

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

The eigenvalue condition forces omega to be an integer

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