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O within the rectangular region The solution of Laplace's equation Uzr + Uyy 0 < x < 5, 0 < y< 4, subject to the boundary conditions u(x, 0) = 0, u(x, 4) = 0, u(5, y) = 0, u(0, y) = 4y – y², has the form u(x, y) = a) (7) NAL E an sinh(nTI) sin("Ty n=1 b) None of these E an sinh () sin() 5 n=1 O d) 0 Èa, sinh sin("") 2] sin(² na(5-x) пту 4 n=1 e) пт(4-у) E a, sinh sin(") Σ αm sin (") 5 n=1

O within the rectangular region The solution of Laplace's equation Uzr + Uyy 0 < x < 5, 0 < y< 4, subject to the boundary conditions u(x, 0) = 0, u(x, 4) = 0, u(5, y) = 0, u(0, y) = 4y – y², has the form u(x, y) = a) (7) NAL E an sinh(nTI) sin("Ty n=1 b) None of these E an sinh () sin() 5 n=1 O d) 0 Èa, sinh sin("") 2] sin(² na(5-x) пту 4 n=1 e) пт(4-у) E a, sinh sin(") Σ αm sin (") 5 n=1

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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The solution of Laplace's equation Urx + Uyy 0 < x < 5, 0 < y < 4, subject to the boundary conditions u(x,0) = 0, u(x, 4) = 0, u(5, y) = 0, u(0, y) = 4y – y?, has the form u(x, y) = O within the rectangular region a) E an sinh(? ") sin(") 4 n=1 O b) None of these E an sinh () sin(") пту 5 n=1 d) nT(5-x) 2 an sinh sin(") NHY 4 4 n=1 e) пт(4—у) 2 an sinh sin ( ") 5 n=1
Transcribed Image Text:The solution of Laplace's equation Urx + Uyy 0 < x < 5, 0 < y < 4, subject to the boundary conditions u(x,0) = 0, u(x, 4) = 0, u(5, y) = 0, u(0, y) = 4y – y?, has the form u(x, y) = O within the rectangular region a) E an sinh(? ") sin(") 4 n=1 O b) None of these E an sinh () sin(") пту 5 n=1 d) nT(5-x) 2 an sinh sin(") NHY 4 4 n=1 e) пт(4—у) 2 an sinh sin ( ") 5 n=1
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