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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section: Chapter Questions
Problem 7RE
Related questions
Question
![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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ddc0d11-139d-4179-848e-9946b62b5a81%2F5ac80439-3d8e-4c90-a89c-a1eed016359b%2Fp8j36zl_processed.jpeg&w=3840&q=75)
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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