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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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Question

H3.

5)
Find a function u(x, y) which satisfies the Laplace equation
1
1
Au = Urr + ur +2400 = 0
in the disc x² + y² <6, and which satisfies the data u(x, y) = y + y² on the disc's
boundary. Express your answer in terms of Cartesian coordinates.
Hint: transform the boundary data, and solve the Laplacian, in terms of polar coordi-
nates. Once the particular solution is found, transform back to Cartesian coordinates.
The identity 2 sin² 0 = 1- cos(20) may be useful.

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