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Get Full Access to Elementary Differential Equations And Boundary Value Problems - 11 Edition - Chapter 10.8 - Problem 1
Get Full Access to Elementary Differential Equations And Boundary Value Problems - 11 Edition - Chapter 10.8 - Problem 1

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# Answer: a. Find the solution u( x, y) of Laplaces equation in the rectangle 0 < x < a, 0 ISBN: 9781119256007 392

## Solution for problem 1 Chapter 10.8

Elementary Differential Equations and Boundary Value Problems | 11th Edition

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Problem 1

a. Find the solution u( x, y) of Laplaces equation in the rectangle 0 < x < a, 0 < y < b, that satisfies the boundary conditions u(0, y) = 0, u(a, y) = 0, 0 < y < b, u( x, 0) = 0, u( x, b) = g( x), 0 < x < a. b. Find the solution if g( x) = x, 0 x a/2, a x, a/2 x a. G c. For a = 3 and b = 1, plot u versus x for several values of y and also plot u versus y for several values of x. (Use enough terms in the Fourier series to accurately approximate the nonhomogeneous boundary condition.) G d. Plot u versus both x and y in three dimensions. Also draw a contour plot showing several level curves of u( x, y) in the xyplane.

Step-by-Step Solution:
Step 1 of 3

L1 - 3 2 1 2 3 2 − 2 2x(1 − x ) 3+ 3x (1 − x ) 3 ex. a) Simplify: 2 2 (1 − x ) 3 2 1/3 2 3 2 −2/3 2x(1 − x ) + 3x (1 − x ) b) Solve for x: 2 2/3 =0 (1 − x )

Step 2 of 3

Step 3 of 3