Question 5 Consider the Laplace's equation on the quarter disk contained in the first quadrant, with a mixed boundary condition: Ихх + Иуу %3D 0, х> 0, у > 0, х? + у? < а?, u(x,0) = 0, 0 < x < a, иx (0, у) %3D 0, 0 <уха. (а) Find the general solution to this problem (as an infinite series). (b) Find the solution corresponding to the condition u(a cos 0, a sin 0) = sin(0) + 2 sin(30) on the boundary x² + y² = a², x, y > 0.
Question 5 Consider the Laplace's equation on the quarter disk contained in the first quadrant, with a mixed boundary condition: Ихх + Иуу %3D 0, х> 0, у > 0, х? + у? < а?, u(x,0) = 0, 0 < x < a, иx (0, у) %3D 0, 0 <уха. (а) Find the general solution to this problem (as an infinite series). (b) Find the solution corresponding to the condition u(a cos 0, a sin 0) = sin(0) + 2 sin(30) on the boundary x² + y² = a², x, y > 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer a and b in detail.
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Transcribed Image Text:Question 5
Consider the Laplace's equation on the quarter disk contained in the first
quadrant, with a mixed boundary condition:
И хх + Иуу — 0, х> 0, у > 0, x2 + у? < а?,
и (х, 0) 3 0, О <x<а,
иx (0, у) %3D 0, 0 <у<а.
(a)
Find the general solution to this problem (as an infinite series).
(b)
Find the solution corresponding to the condition u(a cos 0, a sin 0)
sin(0) +
2 sin(30) on the boundary x² + y² = a², x, y > 0.
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