GATE 2026 MA – Question 44

Partial Differential Equations · Second Order Equations and Laplace Equation · 2 marks · Multiple choice

T is harmonic in 0 < x,y < 1, with T(x,0)=x, T(0,y)=y, T(x,1)=1+x, T(1,y)=1+y. Find T(1/2,1/3).

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Correct answer: (B) 5/6

Explanation

The function x+y is harmonic and agrees with all four boundary values. Uniqueness for the Dirichlet problem makes it the solution. Therefore T(1/2,1/3) = 1/2+1/3 = **5/6, B**.

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