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Solve Laplace's equation, . u(0, y) = 0, u(x, 0) = f(x), a²u a²u + = 0,0< x < a, 0 < y < b, (see (1) in Section 12.5) for a rectangular plate subject to the given boundary conditions. ду2 u(a, y) = 0 u(x, b) = 0 u(x, y) = 0 ax² + 00 Σ [A₂ ( n = 1 sin sinh ηπτ a ηπτ b nn (b-y) sinh a 2 )] where An where A₂ - ²*x) sin(x) dx f(x) a

Solve Laplace's equation, . u(0, y) = 0, u(x, 0) = f(x), a²u a²u + = 0,0< x < a, 0 < y < b, (see (1) in Section 12.5) for a rectangular plate subject to the given boundary conditions. ду2 u(a, y) = 0 u(x, b) = 0 u(x, y) = 0 ax² + 00 Σ [A₂ ( n = 1 sin sinh ηπτ a ηπτ b nn (b-y) sinh a 2 )] where An where A₂ - ²*x) sin(x) dx f(x) a

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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Solve Laplace's equation, . + u(0, y) = 0, u(x, 0) = f(x), a²ua²u u(x, y) = 0 ax² Əy² u(a, y) = 0 u(x, b) = 0 = 0, 0< x <a, 0 < y < b, (see (1) in Section 12.5) for a rectangular plate subject to the given boundary conditions. + Σ [A₂ ( ΣΑ n = 1 sin sinh ηπ a ηπτ b sinh (" (by)))] where Ap = f(x) sin(x) dx 름 a X
Transcribed Image Text:Solve Laplace's equation, . + u(0, y) = 0, u(x, 0) = f(x), a²ua²u u(x, y) = 0 ax² Əy² u(a, y) = 0 u(x, b) = 0 = 0, 0< x <a, 0 < y < b, (see (1) in Section 12.5) for a rectangular plate subject to the given boundary conditions. + Σ [A₂ ( ΣΑ n = 1 sin sinh ηπ a ηπτ b sinh (" (by)))] where Ap = f(x) sin(x) dx 름 a X
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