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2. Show that u₁ = x³ 3xy² and u₂ = log(x² + y²) are solutions to Laplace's equation Uxx + Uyy = 0. Where are they defined?

2. Show that u₁ = x³ 3xy² and u₂ = log(x² + y²) are solutions to Laplace's equation Uxx + Uyy = 0. Where are they defined?

Advanced Engineering Mathematics
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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x³ 3xy² and u2 = = 0. Where are they defined? 2. Show that u₁ Uxx + Uyy = = log(x² + y²) are solutions to Laplace's equation
Transcribed Image Text:x³ 3xy² and u2 = = 0. Where are they defined? 2. Show that u₁ Uxx + Uyy = = log(x² + y²) are solutions to Laplace's equation
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