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Differential Equations Lecture Work Solutions 123

Differential Equations Lecture Work Solutions 123 - µ Z...

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4. u xx + u yy + u zz = 0 u x (0 , y, z ) = 0 , u x ( L, y, z ) = 0 u y ( x, 0 , z ) = 0 , u y ( x, L, z ) = 0 u ( x, y, W ) = 0 X X + Y Y + Z Z = 0 u ( x, y, 0) = 4 cos 3 π L x cos 4 π L y X X = Y Y Z Z = λ X + λ X = 0 BC : X (0) = X ( L ) = 0 λ n = L 2 X n = cos L x n = 0 , 1 , 2 · · · Y + µ Y = 0 BC : Y (0) = Y ( L ) = 0 µ m = L 2 Y m = cos
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Unformatted text preview: ( λ + µ ) Z = 0 Z ( W ) = 0 Z − ± ( nπ L ) 2 + ( mπ L ) 2 Z = 0 Z nm = cosh s nπ L ² 2 + mπ L ² 2 ( z − W ) 123...
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