Differential Equations Lecture Work Solutions 99

Differential Equations Lecture Work Solutions 99 - b. X (0)...

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b. X (0) = X ( L )=0 Y (0) = Y ( H )=0 X n =s in L n = L 2 n =1 , 2 , ··· Y nm =s in H nm = L 2 + H 2 m =1 , 2 , ··· u ( x, y, t )= X n =1 X m =1 ± a nm cos c ² λ nm t + b nm sin c ² λ nm t ³ sin L x sin H y f ( x, y )= X n =1 X m =1 a nm sin L x sin H y g ( x, y )= X n =1 X m =1 c ² λ nm b nm sin L x sin H y a nm ,b nm in a similar fashion to part a. a nm = R H 0 R L 0 f ( x, y )s in
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