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 $) + (\lambda + 2)y = 0, y(0) = y(\pi) = 0$ . Then which of the following statements are true?

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

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, and why this one tests boundary and endpoint.

See pricing

50 are analysed free — try those first.

The trap it tests

Boundary and endpoint

The statement turns at the edge of the interval, the domain, or the parameter range.

Drill statements like this

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

The eigenvalue condition forces omega to be an integer

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