Part CCSIR NET June 2025on-the-unit-circle-x-squared-times-y-squared-peaks-at-one-quarter

On the unit circle x squared times y squared peaks at one quarter

Suppose u = u(x, y) is the solution of the boundary value problem $\partial^{2} u / \partial x^{2} + \partial^{2} u / \partial y^{2} + \partial u / \partial x = 0$ in { $(x, y) \in R^{2} : x^{2} + y^{2} < 1$ }, $u (x, y) = 1 + 2 x^{2} y^{2}$ on { $(x, y) \in R^{2} : x^{2} + y^{2} = 1$ }. Then which of the following statements are true?

A.The minimum value of u is 1✓
B.The maximum value of u is 3
C.The minimum value of u is 2
D.The maximum value of u is 3/2✓

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

On the unit circle x squared times y squared peaks at one quarter

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