Differential Equations Lecture Work Solutions 51

Differential Equations Lecture Work Solutions 51 - 1 a. ut...

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1a. u t = ku xx u (0 ,t )=0 u ( L, t )=0 u ( x, 0) = 6 sin 9 πx L u ( x, t )= X n =1 B n sin nπx L e k ( L ) 2 t u ( x, 0) = X n =1 B n sin nπx L 6s in 9 πx L the only term from the sum that can survive is for n =9 w ith B 9 =6 B n =0 for n 6 =9 u ( x, t )=6s in 9 πx L e k ( 9 π L ) 2 t b. u ( x, 0) = 2 cos 3 πx L u ( x, t )= X n =1 B n
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