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GATE 2018 CE (CE1) – Question 47

Engineering Mathematics · PDE: Fourier series, separation of variables, diffusion, wave and Laplace equations · 2 marks · Multiple choice

For $\partial^2u/\partial x^2=25\,\partial^2u/\partial t^2$ with initial data $u(x,0)=3x$ and $\partial u/\partial t(x,0)=3$, find u at x = 1, t = 1.

  1. 1
  2. 2
  3. 4
  4. 6

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Correct answer: (D) 6

Explanation

The equation is $u_{tt}=u_{xx}/25$. The function $u(x,t)=3x+3t$ satisfies both initial conditions and has both second derivatives zero. Thus $u(1,1)=6$ (D).