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(c) The solution of the following problem for the wave equation on the half-line: Utt = Ugr, x > 0, t> 0, u(x, 0) = x², u(x, 0) = 0, x> 0, u(0, t) = 0, t> 0. for x-t20 is given by u(r, t) = (A) [(z +t)2 + (z - 1)기 = 22 + P (B) 하-(#+1) Gr+)? - (r - t)°] = -x² – t² (D) (2 + t)* – (x – t)*) = 2rt

(c) The solution of the following problem for the wave equation on the half-line: Utt = Ugr, x > 0, t> 0, u(x, 0) = x², u(x, 0) = 0, x> 0, u(0, t) = 0, t> 0. for x-t20 is given by u(r, t) = (A) [(z +t)2 + (z - 1)기 = 22 + P (B) 하-(#+1) Gr+)? - (r - t)°] = -x² – t² (D) (2 + t)* – (x – t)*) = 2rt

Advanced Engineering Mathematics
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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(c) The solution of the following problem for the wave equation on the half-line: x > 0, t> 0, u(x,0) = x, u(x, 0) = 0, x> 0, u(0, t) = 0, t> 0. Utt = Urx, %3D for x-t>0 is given by u(x, t) = (A) 히(z + t)2 + (2-1)2 = 22 + P (B)하-(z +t)2 + (2-기 = -2t (C)-(z+ t)* - ( - 1}1 = -r² - (D)( +)p - (2 - t)9] = 2xt
Transcribed Image Text:(c) The solution of the following problem for the wave equation on the half-line: x > 0, t> 0, u(x,0) = x, u(x, 0) = 0, x> 0, u(0, t) = 0, t> 0. Utt = Urx, %3D for x-t>0 is given by u(x, t) = (A) 히(z + t)2 + (2-1)2 = 22 + P (B)하-(z +t)2 + (2-기 = -2t (C)-(z+ t)* - ( - 1}1 = -r² - (D)( +)p - (2 - t)9] = 2xt
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