b) A boundary value problem that represents the potential distribution u(x, y) over a rectangular plate is given by J²u J²u + = 0, მ2 ay2 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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b)
A boundary value problem that represents the potential distribution
u(x, y) over a rectangular plate is given by
J²u
J²u
+
= 0,
მ2 ay2
0<x<2, 0< y < 2,
subject to the following conditions
u(0,y) = 0, u(2π, y) = 0,
u(x, 0) = 0, u(x, 2π) = π.
Use the method of separation of variables to determine the general
solution of this equation.
Transcribed Image Text:b) A boundary value problem that represents the potential distribution u(x, y) over a rectangular plate is given by J²u J²u + = 0, მ2 ay2 0<x<2, 0< y < 2, subject to the following conditions u(0,y) = 0, u(2π, y) = 0, u(x, 0) = 0, u(x, 2π) = π. Use the method of separation of variables to determine the general solution of this equation.
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