Find the solution formula of u(x, y) for Uxx + Uyy = 0, uy(2,0)=0, u(x,b)=0, u(0, y) = 0, u(a, y) = f(y), 6 Solve the problem in (b) when f(y) = 1. 0
Find the solution formula of u(x, y) for Uxx + Uyy = 0, uy(2,0)=0, u(x,b)=0, u(0, y) = 0, u(a, y) = f(y), 6 Solve the problem in (b) when f(y) = 1. 0
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
#30
Need C,D, E
![[30] (a) Find all nontrivial product solutions u(x, y) = X(x)Y(y) #0 of
0<x<a, 0<y<b,
0 < x <a,
0<y<b.
Uxx + Uyy = 0,
u,(2,0)=0, u(x,b)=0,
u(0, y) = 0,
(b) Find the solution formula of u(x, y) for
Uxx + Uyy = 0,
ủy(2,0)=0, u(x,b)=0,
u(0, y) = 0,
u(a, y) = f(y),
6
(c) Solve the problem in (b) when f(y) = 1.
(d) Using the formula you obtained in (b), solve the following problem:
Uxx + Uyy = 0,
uy(2,0) =0, u(x, b) = 0,
u(0, y) = f(y), u(a, y) = f2(y),
0<x<a, 0<y<b,
0 < x <a,
0<y<b.
u(x, b) = g(x),
u(a, y) = 0,
0<x<a, 0<y<b,
0 < x <a,
0 < y < b.
(e) Using the formula you obtained in (b), solve the following problem:
Uxx + Uyy = 0,
u(x,0) = 0,
ux(0, y) = 0,
0<x<a, 0 <y<b,
0 < x <a,
0 <y<b.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a4dcd82-baf4-45bc-b40b-693a3e683492%2F0987c11e-f971-44ec-aff9-006a9bff3c6d%2F4zg6ub_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[30] (a) Find all nontrivial product solutions u(x, y) = X(x)Y(y) #0 of
0<x<a, 0<y<b,
0 < x <a,
0<y<b.
Uxx + Uyy = 0,
u,(2,0)=0, u(x,b)=0,
u(0, y) = 0,
(b) Find the solution formula of u(x, y) for
Uxx + Uyy = 0,
ủy(2,0)=0, u(x,b)=0,
u(0, y) = 0,
u(a, y) = f(y),
6
(c) Solve the problem in (b) when f(y) = 1.
(d) Using the formula you obtained in (b), solve the following problem:
Uxx + Uyy = 0,
uy(2,0) =0, u(x, b) = 0,
u(0, y) = f(y), u(a, y) = f2(y),
0<x<a, 0<y<b,
0 < x <a,
0<y<b.
u(x, b) = g(x),
u(a, y) = 0,
0<x<a, 0<y<b,
0 < x <a,
0 < y < b.
(e) Using the formula you obtained in (b), solve the following problem:
Uxx + Uyy = 0,
u(x,0) = 0,
ux(0, y) = 0,
0<x<a, 0 <y<b,
0 < x <a,
0 <y<b.
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