Part BCSIR NET December 2024a-zero-boundary-value-reflects-oddly

A zero boundary value reflects oddly

Let u = u(x, t) be a solution of the wave equation $\partial^{2} u / \partial t^{2} - \partial^{2} u / \partial x^{2} = 0, x \in R, t > 0$ satisfying the condition u(0, t) = 0, ∀t ≥ 0. Then which of the following statements is true?

A.u(x, t) = 0, whenever x = t
B.u(x, t) = 0, whenever x = −t
C.u(−x, t) = u(x, t), whenever x > 0, t > 0
D.u(−x, t) = −u(x, t), whenever 0 < x ≤ t✓

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: All the classical equations satisfy a maximum principle

A zero boundary value reflects oddly

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