Determine whether Laplace's equation in two dimensions a²u a?u + дх2 ду? Is satisfied by the functions 1 а) и (x-a)²+(y-b)² b) и %3 In[(x — а)? + (у — b)"] a, b: constant.

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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Determine whether Laplace's equation in two dimensions
a?u a?u
+
əx² ' əy2
Is satisfied by the functions
1
a) и
V(x-a)2+(y-b)2
b) и — In[(x — а)? + (у — b)?]
a, b: constant.
Transcribed Image Text:Determine whether Laplace's equation in two dimensions a?u a?u + əx² ' əy2 Is satisfied by the functions 1 a) и V(x-a)2+(y-b)2 b) и — In[(x — а)? + (у — b)?] a, b: constant.
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