Explanation Given: u ( x , y ) = cos ( a x ) e b y is harmonic. Formula used: A function u ( x , y ) satisfying u x x + u y y = 0 is called harmonic. d ( cos ( a x ) ) d x = − a sin ( a x ) d ( e a t + b ) d t = e a t + b d ( a t + b ) d t Calculation: u ( x , y ) = cos ( a x ) e b y u x = − a sin ( a x ) e b y...

Loose-leaf Version for Calculus: Early Transcendentals Combo 3e & WebAssign for Calculus: Early Transcendentals 3e (Life of Edition)

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ISBN: 9781319019846

Author: Jon Rogawski, Colin Adams

Publisher: W. H. Freeman

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Chapter 14.3, Problem 82E

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To find: all constant $a, b$ such that $u (x, y) = \cos (a x) e^{b y}$ is harmonic.

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Chapter 14.3, Problem 81E

Chapter 14.3, Problem 83E

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Chapter 14 Solutions

Loose-leaf Version for Calculus: Early Transcendentals Combo 3e & WebAssign for Calculus: Early Transcendentals 3e (Life of Edition)

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

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all constant a , b such that u ( x , y ) = cos ( a x ) e b y is harmonic.

To find: all constant a,b such that u(x,y)=cos(ax)eby is harmonic.

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Chapter 14 Solutions

To find: all constant $a, b$ such that $u (x, y) = \cos (a x) e^{b y}$ is harmonic.