Use the separation of variables, u(x, y) = x (x)Y (y), to solve the following partial diffe equation J²u ər² J²u Əy² in a domain with 0

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 25E
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Use the separation of variables, u(x, y) = X(x)Y(y), to solve the following partial differential
equation
V²u =
+
dy?
(4)
%3D
in a domain with 0 < x <1 and 0 < y < 1. The boundary conditions are
u(0, y) = 0,
u(x, 0) = 0,
u(1, y) = 0
(5)
u(x, 1) = 1
(6)
Transcribed Image Text:Use the separation of variables, u(x, y) = X(x)Y(y), to solve the following partial differential equation V²u = + dy? (4) %3D in a domain with 0 < x <1 and 0 < y < 1. The boundary conditions are u(0, y) = 0, u(x, 0) = 0, u(1, y) = 0 (5) u(x, 1) = 1 (6)
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