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A- Show that the function u(x, y) e x/2 ycos ()- xsin( satisfies the Laplace %3D eqation and boundary conditions u(x, y) = 0 on y = o (x 2 0)(2-Ju(x, y)% = -xe 7on y = 1(x 2 0),3 u(x, y) ycos () On x = 0 (0 sy< 1),4- %3D u(x, y) 0 as x 00. B- Find the solution to the equation du = k satisfying the conditions ax2 1.S = 0 at x = 0 for all t,2 -u = 0 at x = 1 for all t, %3D 37u = acos(nx) cos (; x) for 0 sIs1 when t = 0.

A- Show that the function u(x, y) e x/2 ycos ()- xsin( satisfies the Laplace %3D eqation and boundary conditions u(x, y) = 0 on y = o (x 2 0)(2-Ju(x, y)% = -xe 7on y = 1(x 2 0),3 u(x, y) ycos () On x = 0 (0 sy< 1),4- %3D u(x, y) 0 as x 00. B- Find the solution to the equation du = k satisfying the conditions ax2 1.S = 0 at x = 0 for all t,2 -u = 0 at x = 1 for all t, %3D 37u = acos(nx) cos (; x) for 0 sIs1 when t = 0.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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A- Show that the function u(x, y) = e x/ 2ycos ()- xsin satisfies the Laplace eqation and boundary conditions u(x, y) = 0 on y = o (x2 0) 2-Ju(x, y) = -xe 7on y = 1(x 2 0),3u(x, y) ycos ( On x = 0 (0 sys 1),4- %3D %3D = ycos () On x = 0 (0 < y < 1),4- %3D u(x, y) 0 as x 0o. B- Find the solution to the equation = k dt satisfying the conditions ax2 1.S = 0 at x = 0 for all t.2 -u = 0 at x = 1 for all t, ax 37u = acos(nx) cos ( x) for 0 SIS1 when t = 0.
Transcribed Image Text:A- Show that the function u(x, y) = e x/ 2ycos ()- xsin satisfies the Laplace eqation and boundary conditions u(x, y) = 0 on y = o (x2 0) 2-Ju(x, y) = -xe 7on y = 1(x 2 0),3u(x, y) ycos ( On x = 0 (0 sys 1),4- %3D %3D = ycos () On x = 0 (0 < y < 1),4- %3D u(x, y) 0 as x 0o. B- Find the solution to the equation = k dt satisfying the conditions ax2 1.S = 0 at x = 0 for all t.2 -u = 0 at x = 1 for all t, ax 37u = acos(nx) cos ( x) for 0 SIS1 when t = 0.
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