Substituting u(r) with r as in Prob. 9 into u xx + u yy + u zz

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Substituting u(r) with r as in Prob. 9 into u_xx + u_yy + u_zz = 0, verify that u" + 2u'/r = 0, in agreement with (7).

Data from Prob. 9

Show that the only solution of Laplace’s equation depending only on r = √x² + y² + z² is u = c/r + k with constant c and k.

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Advanced Engineering Mathematics

ISBN: 978-0470458365

10th edition

Authors: Erwin Kreyszig

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Question Posted: Sep 30, 2022 06:10 AM

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Substituting u(r) with r as in Prob. 9 into u xx + u yy + u zz

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If a 0 then r ax2 y2 z2 r2 cr212 and the unique solution is u cr ...View the full answer

Advanced Engineering Mathematics

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