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=-Ux. 2. Given two functions u(x, y) and v(x, y) satisfying: u = vy and uy a) Show that u(x, y) and v(x, y) are harmonic functions, that is: Urr + Uyy = 0, VII + Uyy = 0. b) If u(x, y) = x² - y² - x + y, then find v(x, y).

=-Ux. 2. Given two functions u(x, y) and v(x, y) satisfying: u = vy and uy a) Show that u(x, y) and v(x, y) are harmonic functions, that is: Urr + Uyy = 0, VII + Uyy = 0. b) If u(x, y) = x² - y² - x + y, then find v(x, y).

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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2. Given two functions u(x, y) and v(x, y) satisfying: u = vy and uy = −Ur. a) Show that u(x, y) and v(x, y) are harmonic functions, that is: Urr + Uyy = 0, - Var + Vyy = 0. b) If u(x, y) = x² - y² − x + y, then find v(x, y).
Transcribed Image Text:2. Given two functions u(x, y) and v(x, y) satisfying: u = vy and uy = −Ur. a) Show that u(x, y) and v(x, y) are harmonic functions, that is: Urr + Uyy = 0, - Var + Vyy = 0. b) If u(x, y) = x² - y² − x + y, then find v(x, y).
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