GATE 2021 MA – Question 17

Partial Differential Equations · Heat and Wave Equations · 1 mark · Multiple choice

For u_tt=u_xx on x∈ℝ,t>0, u(x,0)=0 and u_t(x,0)=4xe^(−x²), find u(5,5).

Show answer and explanation

Correct answer: (A) 1−e^(−100)

Explanation

D’Alembert’s formula gives u(x,t)=(1/2)∫_(x−t)^(x+t)4s e^(−s²)ds. At (5,5), this equals [−e^(−s²)]₀¹⁰=**1−e^(−100), A**.

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