Differential Equations Lecture Work Solutions 149

Differential Equations Lecture Work Solutions 149 - 3. utt...

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3. u tt c 2 u xx = S ( xt ) u ( x, 0) = f ( x ) u t ( x, 0) = 0 a. u (0 ,t )= A ( t ) u ( L, t )= B ( t ) w = αx + β β = A ( t ) αL + β = B α = B β L w = B ( t ) A ( t ) L x + A ( t ) w xx =0 w tt = ¨ B ¨ A L x + ¨ A v = u w u = v + w v tt c 2 v xx = S ( x, t ) w tt ˆ S ( x, t ) v ( x, 0) = f ( x ) B (0) A (0) L x A (0) F ( x ) v t ( x, 0) = 0 w t ( x, 0) = 0 ˙ B (0) ˙ A (0) L x ˙ A (0) G ( x ) v (0 ,t )=0 v ( L, t )=0 Solve the homogeneous λ n = L 2 n =1 , 2 , ··· φ n =s in L x v ( x, t )= X n =1 v n ( t )s in L x ˆ S ( x, t
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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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