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Solve the boundary value problem ( 37/201 a²u 1 du - 2² r ər at² + = ar² 00 with u(3,t)=0, t> o, and u(r,0) = 0, u₁(r,0)=2, 0

Solve the boundary value problem ( 37/201 a²u 1 du - 2² r ər at² + = ar² 00 with u(3,t)=0, t> o, and u(r,0) = 0, u₁(r,0)=2, 0

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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Solve the boundary value problem 2²u at²' a²u 1 ди + ar² r ar 0<r<3, t>0 with u(3,t)=0, t> o, and u(r,0) = 0, u₁(r,0)=2, 0<r<3 which of the following are correct: (1) Using separation of variable, we get r² R" + rR' + (r² = n²) R = 0 and T" + 3XT=0 (II) The general solution is u(r,t) = Σ [Ancos(3αnt) + B₂sin(3αnt)]Jo(ar) n=1 (III) An = 0 and Bn O A. (II) only O B. (II) and (III) only O C. (III) only O D. (I) only O E. (I) and (II) only = 2 3x² Jo(4αn)
Transcribed Image Text:Solve the boundary value problem 2²u at²' a²u 1 ди + ar² r ar 0<r<3, t>0 with u(3,t)=0, t> o, and u(r,0) = 0, u₁(r,0)=2, 0<r<3 which of the following are correct: (1) Using separation of variable, we get r² R" + rR' + (r² = n²) R = 0 and T" + 3XT=0 (II) The general solution is u(r,t) = Σ [Ancos(3αnt) + B₂sin(3αnt)]Jo(ar) n=1 (III) An = 0 and Bn O A. (II) only O B. (II) and (III) only O C. (III) only O D. (I) only O E. (I) and (II) only = 2 3x² Jo(4αn)
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