Differential Equations Lecture Work Solutions 93

Differential Equations Lecture Work Solutions 93 - 1b. X...

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1b. X 0 (0) = X ( L )=0 Y 0 (0) = Y 0 ( H )=0 X n =co s n 1 2 π L n = n 1 2 π L 2 n =1 , 2 , ··· Y nm =c o s H nm = n 1 2 π L 2 + H ± 2 n =1 , 2 , ··· m = 0 , 1 , 2 , ··· u ( x, y, t )= X n =1 1 2 a n 0 e n 0 t cos n 1 2 π L x + X m =1 X n =1 a nm e nm t cos n 1 2 π L x cos H y a nm = R H 0 R L 0 f ( x, y )cos n
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