(a) The eigenvalues of the following eigenvalue problem: %3D 0= (1),X = (0),X 0= XX+ „X are given by An = (B) n², n = 1,2,3, --. (A) n², n=0, 1, 2, 3, -.. (C) (na)², n = 0,1, 2, 3, - .. ... (D) (n7)², n=1,2,3, - --
(a) The eigenvalues of the following eigenvalue problem: %3D 0= (1),X = (0),X 0= XX+ „X are given by An = (B) n², n = 1,2,3, --. (A) n², n=0, 1, 2, 3, -.. (C) (na)², n = 0,1, 2, 3, - .. ... (D) (n7)², n=1,2,3, - --
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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 ()](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71744873-9728-4f8c-b9eb-07350292a1e1%2Ffb5b8472-320c-4848-a1b0-9264806d5633%2F5epght4n_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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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