GATE 2025 MA – Question 40

Partial Differential Equations · Heat and Wave Equations · 2 marks · Multiple choice

u_tt−9u_xx=0 on ℝ,t>0, with u(x,0)=eˣ and u_t(x,0)=sinx. Find u(π/2,π/6).

Show answer and explanation

Correct answer: (C) $(e^\pi+5/3)/2$

Explanation

D’Alembert gives $u=[e^{x+3t}+e^{x-3t}]/2+(1/6)\int_{x-3t}^{x+3t}\sin s\,ds$. Here endpoints are 0,π. Thus u=(e^π+1)/2+2/6=(e^π+5/3)/2. **C**.

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