Differential Equations Lecture Work Solutions 80

Differential Equations Lecture Work Solutions 80 - 13. ut =...

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13. u t =2 u xx u (0 ,t )=0 u x ( L, t u ( x, 0) = sin 3 2 π L x u = XT X ˙ T X 0 T ˙ T 2 T = X 0 X = λX 0 + =0 ˙ T +2 λT X (0) = 0 X 0 ( L X n =s in n + 1 2 ± π L xn , 1 , ··· λ n = ² n + 1 2 ± π L 2 u ( x, t )= X n =1 a n e 2 [( ( n + 1 2 ) π L ] 2 t sin n + 1 2 ± π L x At t u ( x, 0) = X n =1 a n sin n + 1 2 ± π L x But also u ( x, 0) = sin 3 2 π L x Therefore
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