(a) The eigenvalues of the following eigenvalue problem:0 = (1),X = (0),Xare given by An =(B) n², n=1, 2,3, -..(D) (n7)², n = 1,2, 3, - ..(A) n², n= 0, 1, 2, 3, ..(C) (nT)², n = 0,1,2, 3, - -.

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Answered: (a) The eigenvalues of the following…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Problem 1RQ

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PART 1 (MCQ: 8 Marks): 1. Choose the most appropriate answer. (a) The eigenvalues of the following eigenvalue problem: are given by An = 0 = (1),X = (0),x '0= xY+ „X (A) n², n=0, 1, 2, 3, - - - (C) (na)², n = 0,1, 2, 3, · - . (B) n², n=1,2,3, - - - (D) (n7)², n= 1, 2, 3, · - - (b) At x = 0, the Fourier series of x - 2, = (x)f I 5x > 0 converges to: (A) -2 (B) –1 (D) 1 (c) The solution of the following Cauchy problem: '00 > x > - u(x, 0) = 0, 4 (x, 0) = x, *00 > x > o0- is given by u(x, t) = (A) [(z+ t)? – (2 – t)*] = ct (B) (7 + t) + (x – t)] =: (C) (z +t)² + (x – t)*] = (2² + t*) 1=(9-2) -0+0)은 (a) (d) Let o(x) = x² + x, x > 0. If defines an even extension of ø to the entire real line, then for x < 0, (x) = (C) -a2 +x (A) x² +x X - „x ()
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(a) The eigenvalues of the following eigenvalue problem: 0= (1X = (0),x '0=xY+ „X are given by An = (A) n², n=0, 1, 2, 3, .. (B) n², n = 1,2,3, .- (C) (n7)², n = 0,1, 2, 3, - (D) (n7)², n= 1,2, 3, - -