Part BCSIR NET June 2024odd-parts-cancel-in-the-sum

Odd parts cancel in the sum

If u = u(x, t) is the solution of the initial value problem $u_{t} = u_{xx}$ for $x \in \mathbb{R}, t > 0$ , with u(x, 0) = sin(4x) + x + 1 for $x \in \mathbb{R}$ , satisfying |u(x, t)| $< 3e^(x^{2})$ for all $x \in \mathbb{R}$ and t > 0, then

A. $u(\pi/8, 1) + u(-\pi/8, 1) = 2$ ✓ Correct
B. $u(\pi/8, 1) = u(-\pi/8, 1)$
C. $u(\pi/8, 1) + 2u(-\pi/8, 1) = 2$
D. $u(\pi/8, 1) = -u(-\pi/8, 1)$

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 standard counterexample.

See pricing

50 are analysed free — try those first.

The trap it tests

Standard counterexample

There is a canonical object that settles this. Recognising it is the whole question.

Drill statements like this

Related counterexample: All the classical equations satisfy a maximum principle

Odd parts cancel in the sum

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