Question 3: Solve the following two problems using the generalized d'Alambert formula: (Utt-Uxx = -2ecos (t), t> 0,x € (-00,00) x € (-00,00) (A) u(x,0) = cos (x) u₂(x,0) = 1 XE (-00,00) Utt-4uxx = x, t> 0, x € (-00,00) (B) u(x,0) = x x € (-00,00) . (u₂(x,0) = sin(x) XE (-CO, CO)

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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Question 3:
Solve the following two problems using the generalized d'Alambert formula:
(UttUxx = -2e-*cos (t), t> 0, x € (-00,00)
(A) u(x,0) = cos (x)
u₂(x,0) = 1
x € (-00,00)
F
XE (-00,00)
utt4uxx = x, t> 0, x € (-00,00)
(B)
u(x,0) = x
x € (-00,00)
F
(u₂(x,0) = sin(x)
x € (-00,00)
Transcribed Image Text:Question 3: Solve the following two problems using the generalized d'Alambert formula: (UttUxx = -2e-*cos (t), t> 0, x € (-00,00) (A) u(x,0) = cos (x) u₂(x,0) = 1 x € (-00,00) F XE (-00,00) utt4uxx = x, t> 0, x € (-00,00) (B) u(x,0) = x x € (-00,00) F (u₂(x,0) = sin(x) x € (-00,00)
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