Find the solution of Laplace's equation u + Uyy = 0 within the rectangle 0 < x < 2, 0 < y < 4, which satisfies the boundary conditions u(0, y) = 0, u(2, y) = 0, u(x,0) = 0, u(x,4) = 3. Write down the complete solution u(x, y) and give the first two non-zero terms of the series.
Find the solution of Laplace's equation u + Uyy = 0 within the rectangle 0 < x < 2, 0 < y < 4, which satisfies the boundary conditions u(0, y) = 0, u(2, y) = 0, u(x,0) = 0, u(x,4) = 3. Write down the complete solution u(x, y) and give the first two non-zero terms of the series.
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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![4. [12 marks] The solution of Laplace's equation upr + Uyy = 0, 0 <x < L, 0 < y < M,
satisfying the boundary conditions u(0, y) = 0, u(L, y) = 0, u(x, 0) = 0, u(x, M) = f(x),
has the form
6.
u(r, y):
. Σ α
NTY
E an sinh
n=1
Find the solution of Laplace's equation uær + Uyy
0 < y < 4, which satisfies the boundary conditions u(0, y) = 0, u(2, y) = 0, u(x,0) = 0,
u(x, 4) = 3. Write down the complete solution u(x, y) and give the first two non-zero
terms of the series.
= 0 within the rectangle 0 < x < 2,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b3a0573-47cf-4847-8e28-bcfe5be0f8d4%2Fb8ab191f-1360-4916-b1b8-64cbe7276c50%2Fr0301et_processed.png&w=3840&q=75)
Transcribed Image Text:4. [12 marks] The solution of Laplace's equation upr + Uyy = 0, 0 <x < L, 0 < y < M,
satisfying the boundary conditions u(0, y) = 0, u(L, y) = 0, u(x, 0) = 0, u(x, M) = f(x),
has the form
6.
u(r, y):
. Σ α
NTY
E an sinh
n=1
Find the solution of Laplace's equation uær + Uyy
0 < y < 4, which satisfies the boundary conditions u(0, y) = 0, u(2, y) = 0, u(x,0) = 0,
u(x, 4) = 3. Write down the complete solution u(x, y) and give the first two non-zero
terms of the series.
= 0 within the rectangle 0 < x < 2,
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