Differential Equations Lecture Work Solutions 104

Differential Equations Lecture Work Solutions 104 - y= 0...

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1/4 1 φ = 0 φ x = 0 φ = 0 φ y = 0 Figure 33: Domain fro problem 1 of 7.4 1. ϕ ( x, y )= XY X 0 Y + XY 0 + λXY =0 X 0 X = λ Y 0 Y = µ X 0 + µX =0 Y 0 +( λ µ ) Y =0 X (0) = X 0 (1) = 0 Y (0) = Y 0 (1 / 4) = 0 ⇓⇓ X n =s in ( n 1 2 ) πx Y nm =s in( m 1 2 )4 πy µ n = h ( n 1 2 ) π i 2 λ nm = h ( n 1 2 ) π i 2 +[ (4 m 2) π ] 2 n =1 , 2 , ··· m =1 , 2 , ··· ϕ nm =s in( n 1 2 ) πx sin (4 m 2) πy λ nm =[ ( n
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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