# P9-24 - Hint for Problem 9.24 May 9, 2011 The problem is...

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Hint for Problem 9.24 May 9, 2011 The problem is T xx + T yy = sin( ωx ) T ( x = 0) = T ( x = l ) = T ( y = 0) = 0 , T ( y → ∞ ) bounded . The PDE can be reduced to a homogenous one by the substitution U = T + A sin( ωx ) U xx = T xx - 2 sin( ωx ) U yy = T yy . Substitute into the PDE to determine the value of A for it to be homogenous: U xx + 2 sin( ωx ) + U yy = sin( ωx ) A = ω - 2 . Now the problem becomes U xx + U yy = 0 U ( x = 0) = ω - 2 sin( ω 0) = 0 U ( x = l ) = ω - 2 sin( ωl ) U ( y = 0) = ω - 2 sin( ωx ) U ( y → ∞

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## This note was uploaded on 08/30/2011 for the course CGN 2200 taught by Professor Glagola during the Spring '11 term at University of Florida.

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P9-24 - Hint for Problem 9.24 May 9, 2011 The problem is...

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