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fter separation of variables, the general solution of Laplace's equation V-V ertain scenario is written as follows: (,y,z) = U for a X(x) = Aekx + Be¬kx %3D Y(y) = C cos ly + D sin ly Z(z) = E cos mz + F sin mz %3D -here k² = 1² + m² . Find the solution of the Laplace's equation by applying the following oundary conditions: (1) V (x = 0) = .(y) %3D (2) V(x = –∞) = 0 (3) V(y = 0) = 0 (4) V(y = a) = 0 (5) V(z = 0) = 0 (6) V(z = a) = 0

fter separation of variables, the general solution of Laplace's equation V-V ertain scenario is written as follows: (,y,z) = U for a X(x) = Aekx + Be¬kx %3D Y(y) = C cos ly + D sin ly Z(z) = E cos mz + F sin mz %3D -here k² = 1² + m² . Find the solution of the Laplace's equation by applying the following oundary conditions: (1) V (x = 0) = .(y) %3D (2) V(x = –∞) = 0 (3) V(y = 0) = 0 (4) V(y = a) = 0 (5) V(z = 0) = 0 (6) V(z = a) = 0

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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After separation of variables, the general solution of Laplace's equation V²V(x, y, z) = 0 for a certain scenario is written as follows: %3D X(x) = Aek* + Be¬kx I| Y(y) = C cos ly + D sin ly Z(z) = E cos mz + F sin mz where k2 = 12 + m². Find the solution of the Laplace's equation by applying the following boundary conditions: (1) V (x = 0) = V,(y) (2) V(x = -) = 0 (3) V(y = 0) = 0 (4) V(y = a) = 0 (5) V(z = 0) = 0 (6) V(z = a) = 0 %3D
Transcribed Image Text:After separation of variables, the general solution of Laplace's equation V²V(x, y, z) = 0 for a certain scenario is written as follows: %3D X(x) = Aek* + Be¬kx I| Y(y) = C cos ly + D sin ly Z(z) = E cos mz + F sin mz where k2 = 12 + m². Find the solution of the Laplace's equation by applying the following boundary conditions: (1) V (x = 0) = V,(y) (2) V(x = -) = 0 (3) V(y = 0) = 0 (4) V(y = a) = 0 (5) V(z = 0) = 0 (6) V(z = a) = 0 %3D
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