GATE 2026 MA – Question 61

Partial Differential Equations · Second Order Equations and Laplace Equation · 2 marks · Numerical answer

u is harmonic in the open unit disk and equals x²−y² on its boundary. Find $4[u(1/2,0)-u(0,1/2)]$ (integer).

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Correct answer: 2 to 2

Explanation

The polynomial x²−y² is harmonic because its second derivatives sum to 2−2=0. By uniqueness it equals u throughout the disk. Required value = 4[1/4−(−1/4)] = **2**.

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