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The bounded solution of Laplace's equation Upr +Ur + uge = O outside the circle r 3 which satisfies the boundary condition u(3,0) = 3+ 2 sin(40) – 3 cos(20) is u(r, 0) = + E r-" [a, cos(no) + bn sin(n0)], where ao 2 n=1 O a) None of these b) ao 2 6, а2 3, b4 = 1, an = O otherwise c) ao = 6, a2 = -27, b4 = 162, an 162, ат = bn = 0 otherwise d) ao = 6, a2 = -3, b4 = 2, an = bn = 0 otherwise 2, аn e) ao = 3, a2 = -27, b4 = 162, an = bn O otherwise

The bounded solution of Laplace's equation Upr +Ur + uge = O outside the circle r 3 which satisfies the boundary condition u(3,0) = 3+ 2 sin(40) – 3 cos(20) is u(r, 0) = + E r-" [a, cos(no) + bn sin(n0)], where ao 2 n=1 O a) None of these b) ao 2 6, а2 3, b4 = 1, an = O otherwise c) ao = 6, a2 = -27, b4 = 162, an 162, ат = bn = 0 otherwise d) ao = 6, a2 = -3, b4 = 2, an = bn = 0 otherwise 2, аn e) ao = 3, a2 = -27, b4 = 162, an = bn O otherwise

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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The bounded solution of Laplace's equation Upr +Ur + uge = 3 which satisfies the boundary condition O outside the circle r u(3,0) = 3+ 2 sin(40) – 3 cos(20) is r-" [an cos(no) + bn sin(n0)], where ao u(r, 0) = + E 2 n=1 O a) None of these - 2 O otherwise b) ao = 6, a2 3, b4 = 1, an = bn c) ao = 6, a2 = -27, b4 = 162, an 162, ат = bn = 0 otherwise d) ao = 6, a2 = -3, b4 = 2, an = bn = 0 otherwise = -3, 64 2, ат Br e) ao = 3, a2 = -27, b4 = 162, a, = bn 162, ап — O otherwise
Transcribed Image Text:The bounded solution of Laplace's equation Upr +Ur + uge = 3 which satisfies the boundary condition O outside the circle r u(3,0) = 3+ 2 sin(40) – 3 cos(20) is r-" [an cos(no) + bn sin(n0)], where ao u(r, 0) = + E 2 n=1 O a) None of these - 2 O otherwise b) ao = 6, a2 3, b4 = 1, an = bn c) ao = 6, a2 = -27, b4 = 162, an 162, ат = bn = 0 otherwise d) ao = 6, a2 = -3, b4 = 2, an = bn = 0 otherwise = -3, 64 2, ат Br e) ao = 3, a2 = -27, b4 = 162, a, = bn 162, ап — O otherwise
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