(Two-dimensional potential problems) Show that the functions x 2 - )'2. XY. xl(x2 + y2)
Chapter 12, Problem 12.1.188(choose chapter or problem)
(Two-dimensional potential problems) Show that the functions \(x^{2}-y^{2} \cdot x y \cdot x /\left(x^{2}+y^{2}\right), e^{x} \cos y, e^{x} \sin y, \cos x \cosh y \ln \left(x^{2}+y^{2}\right)\), and arctan (y/x) satisfy Laplace's equation \(u_{x x}+u_{y y}=0\). (Two-dimensional potential problems are best solved by complex analysis, as we shall see in Chap. 18.)
Text Transcription:
x^2-y^2, xy, x/(x^2+y^2), e^x cos y, e^x sin y, cos x, cosh y, ln(x^2+y^2)
u_xx+u_yy=0
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