Answered: Laplace equations Show that if w = ƒ(u,…

Laplace equations Show that if w = ƒ(u, y) satisfies the Laplace equation ƒuu + ƒyy = 0 and if u = (x2 - y2) /2 and y = xy, then w satisfies the Laplace equation wxx + wyy = 0.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 30E

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Laplace equations Show that if w = ƒ(u, y) satisfies the Laplace equation ƒuu + ƒyy = 0 and if u = (x2 - y2) /2 and y = xy, then w satisfies the Laplace equation wxx + wyy = 0.

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