Part BCSIR NET June 2025dalembert-averages-the-displacement-and-integrates-the-velocity-over-the-cone

Dalembert averages the displacement and integrates the velocity over the cone

Let u = u(x, t) be the solution of $\partial^{2} u / \partial t^{2} - \partial^{2} u / \partial x^{2} = 0, x \in R, t > 0, u (x, 0) = 1 + x^{2}, x \in R, \partial u / \partial t (x, 0) = x + 1, x \in R$ . Then the value of u(1, 1) is

A.2
B.3
C.4
D.5✓

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 execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: All the classical equations satisfy a maximum principle

Dalembert averages the displacement and integrates the velocity over the cone

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