The solution of Laplace's equation Urx + Uyry 0 < r < 3, 0 < y< 4, subject to the boundary conditions u(x, 0) = 3x – x², u(x, 4) = 0, u(0, y) = 0, u(3, y) = 0. has the form u(x, y) O within the rectangular region - NT(3–x) 2 sin() L an sinh n=1 O b) ∞ E an sinh () sin() NTY 3 п-1 c) None of these nT(4-y) sin (") NAX sinh n=1 Oe ax + By + yry+ d
The solution of Laplace's equation Urx + Uyry 0 < r < 3, 0 < y< 4, subject to the boundary conditions u(x, 0) = 3x – x², u(x, 4) = 0, u(0, y) = 0, u(3, y) = 0. has the form u(x, y) O within the rectangular region - NT(3–x) 2 sin() L an sinh n=1 O b) ∞ E an sinh () sin() NTY 3 п-1 c) None of these nT(4-y) sin (") NAX sinh n=1 Oe ax + By + yry+ d
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 33E
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Transcribed Image Text:The solution of Laplace's equation Uæx + Uyy
0 < x < 3, 0 < y < 4, subject to the boundary conditions
u(z, 0) = 3x – x², u(x, 4) = 0, u(0, y) = 0, u(3, y) = 0, has
the form u(x, y)
O within the rectangular region
-
%3D
NT(3–x)
2 sin()
E an
sinh
4
n=1
E an sinh(") sin()
пту
3
3
n=1
O) None of these
NT(4-y)
) an
a, sinh 2 sin()
3
O e) ax
+By+yry+8
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