Differential Equations Lecture Work Solutions 62

Differential Equations Lecture Work Solutions 62 - 5. c....

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5. c. u (0 ,y )=0 X (0) = 0 u ( L, y )=0 X ( L )=0 u ( x, 0) u y ( x, 0) = 0 Y (0) Y 0 (0) = 0 X 0 + λX =0 Y 0 n L 2 Y n =0 X (0) = 0 Y n (0) Y 0 n (0) = 0 X ( L )=0 Y n = A n cosh L y + B n sinh L y λ n = L 2 n =1 , 2 ,... Y 0 n = L n A n sinh L y + B n cosh L y o X n =s in L x Substitute in the boundary condition. A n L B n cosh 0 | {z } 6 =0 + B n L A n sinh 0 | {z } =0 =0 A n = L B n Y n = B n ± L cosh L y +s inh L y u ( x, y )= X n =1 b n sin L x ± L cosh L y +s inh L y Use the boundary condition u ( x, H )= f ( x ) f ( x )= X n =1 b n sin
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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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