Consider the Boundary Value problem Using the separation of variables method, the solution z(x, y), is given by the series where b - 8²u g²u + = 0, dx² Əy² u(x,0) = x(7x), u(0,y) = 0, u(7,y) = 0, &(r,Y) = 0
Consider the Boundary Value problem Using the separation of variables method, the solution z(x, y), is given by the series where b - 8²u g²u + = 0, dx² Əy² u(x,0) = x(7x), u(0,y) = 0, u(7,y) = 0, &(r,Y) = 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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Transcribed Image Text:Consider the Boundary Value problem
Using the separation of variables method, the solution z(x, y), is given by the series
where
ba
-
8²u
2²u
+ = 0, 0<x, y<7
dx² Əy²
u(x,0) = x(7x), u(x,7)=0, 0<x<7
u(0,y) = 0, u(7,y) = 0, 0<y<7
u(r.Y)
-=[b, sin (172)
b₁
=
sinh (n (7 – 8))
sinh(nữ)
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![[(49*pi)/[2*(n^2)]]*sinh(n*pi)+[1-cosh(n*pi)]*
[49/(n^3)]
The answer above is NOT correct.
Entered
where
b₁ =
Consider the Boundary Value problem
J²u
2²u
+ = 0, 0<x, y <7
02² dy²
u(x,0) = x(7x), u(x, 7) = 0, 0<x<7
u(0,y) = 0, u(7,y)=0, 0<y<7
49x
Using the separation of variables method, the solution u(x, y), is given by the series
म
sinh (n (7 - 3))
sinh(na)
2n
49T
21²
- sinh(m) + (1 – cosh(n))
Answer Preview
sinh(nr)+ (1 – cosh(n))
u(x, y) =[b, sin (n 7 z).
n=1
49
49
723
Result
incorrect](https://content.bartleby.com/qna-images/question/94884f69-365e-43dc-a457-f3f8066ccdfc/2f6551b1-8a3b-4106-a6c4-1d02dfe7cf8b/bbnuiop_processed.png)
Transcribed Image Text:[(49*pi)/[2*(n^2)]]*sinh(n*pi)+[1-cosh(n*pi)]*
[49/(n^3)]
The answer above is NOT correct.
Entered
where
b₁ =
Consider the Boundary Value problem
J²u
2²u
+ = 0, 0<x, y <7
02² dy²
u(x,0) = x(7x), u(x, 7) = 0, 0<x<7
u(0,y) = 0, u(7,y)=0, 0<y<7
49x
Using the separation of variables method, the solution u(x, y), is given by the series
म
sinh (n (7 - 3))
sinh(na)
2n
49T
21²
- sinh(m) + (1 – cosh(n))
Answer Preview
sinh(nr)+ (1 – cosh(n))
u(x, y) =[b, sin (n 7 z).
n=1
49
49
723
Result
incorrect
Solution
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