f) Consider the wave equation unt=4urr, t>0, with boundary conditions u(0, t)=0= u(2,t) Заг for all t20 and initial conditions u(x, 0) = sin u(x,0)=0. Which of the following is 2 a solution of this problem? Answers: (A) u(x, t) = cos 3rt sin (B) u(x, t) = cos (C) u(x, t) = sin 3nt 2 3nt 2 sin sin 3x 2 (D) u(x, t) = sin 3nt sin (E) None of the above. Злт 2 3x 2 Зах 2
f) Consider the wave equation unt=4urr, t>0, with boundary conditions u(0, t)=0= u(2,t) Заг for all t20 and initial conditions u(x, 0) = sin u(x,0)=0. Which of the following is 2 a solution of this problem? Answers: (A) u(x, t) = cos 3rt sin (B) u(x, t) = cos (C) u(x, t) = sin 3nt 2 3nt 2 sin sin 3x 2 (D) u(x, t) = sin 3nt sin (E) None of the above. Злт 2 3x 2 Зах 2
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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Jj.196.
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Transcribed Image Text:e) Let f be defined by f(x) =
F(5)=
Answers:
fr+2, -2<r<1
1 < x < 2.
(A) 1
(B) 2
(C) 3
(D) 0
(E) None of the above.
f) Consider the wave equation ut=4urr, t> 0, with boundary conditions u(0, t) = 0 = u(2,t)
ue(x,0) = 0. Which of the following is
Зит
for all t> 0 and initial conditions u(x, 0) = sin
2
a solution of this problem?
Answers:
(A) u(x, t) = cos 3rt sin
3nt
(B) u(x, t) = cos sin
2
(C) u(x, t) = sin sin
3nt
2
(D) u(x, t) = sin 3nt sin
(E) None of the above.
Зах
2
3nx
2
Зах
2
If F(x) is the Fourier series for f(r), then
Зах
2
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