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GATE-Civil-Engg-2018-->View question

The solution at x = 1,t = 1 of the partial differential equation ∂ 2u ∂x 2 = 25 ∂ 2u ∂t 2 subject to initial conditions of u(0) = 3x and ∂u ∂t (0) = 3 is (GATE Civil engg 2018)

The solution at x = 1,t = 1 of the partial differential equation ∂2u∂x2 = 25 ∂2u∂t2 subject to initial conditions of u(0) = 3x and ∂u∂t (0) = 3 is ______
(A) 1 (B) 2  (C) 4 (D) 6


Asked On2019-06-05 01:26:43 by:gokilapriya

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Ans. (D) 
Sol. 
If the given one dimensional wave equation is of the form  - 8<x<8 and  c > 0 , 
satisfying the conditions u(x,0) = f(x) 
where f ( ) x , where & g x( ) are given functions representing the initial displacement and initial velocity, respectively then its general solution is given by
And we have given, 
Comparing the given problem with above general problem 
And f(x) = 3x  ,  g(y) = 3
 So by De-alemberts solution of wave equation. 
u(1,1) = 6
 

Answerd on:2019-06-07 Answerd By:Jaynil-Gaglani

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