7ty xsin() satisfies the Laplace ycos equation and boundary conditions u(x, y) = 0 on y = o (x 2 0)(2-u(x, y) A- Show that the function u(x, y) = ex/2 On x = 0 (0 sys 1),4- %3D -xe 7on y == 1(x 2 0),3 -u(x, y) ycos u(x, y) - 0 as x co.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A- Show that the function u(x, y) = e-x/2 ycos () - xsin() satisfies the Laplace
equation and boundary conditions u(x, y) = 0 on y = o (x 2 0) 2-Ju(x, y)
2
%3D
%3D
ny
-xe 2 on y == 1(x 2 0),3 u(x, y) ycos ( On x = 0 (0 sy< 1),4-
u(x, y) 0 as x→ 00.
Transcribed Image Text:A- Show that the function u(x, y) = e-x/2 ycos () - xsin() satisfies the Laplace equation and boundary conditions u(x, y) = 0 on y = o (x 2 0) 2-Ju(x, y) 2 %3D %3D ny -xe 2 on y == 1(x 2 0),3 u(x, y) ycos ( On x = 0 (0 sy< 1),4- u(x, y) 0 as x→ 00.
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