Differential Equations Lecture Work Solutions 138

# Differential Equations Lecture Work Solutions 138 - R L [ x...

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1b. u (0 ,t )= u x ( L, t )=1 w = x +1 v t = kv xx + x v (0 ,t )=0 v x ( L, t )=1 v ( x, 0) = x ( L x ) ( x +1 ) eigenvalues: h n 1 2 π L i 2 n =1 , 2 , ··· eigenfunctions: sin n 1 2 π L xn =1 , 2 , ··· v = X n =1 v n ( t )s in n 1 2 ± π L x x = X n =1 s n sin n 1 2 ± π L xs n = R L 0 x sin n 1 2 π L xdx R L 0 sin 2 n 1 2 π L xdx ˙ v n + k h n 1 2 π L i 2 v n = s n v n ( t )= v n (0) e [ ( n 1 2 ) π L ] 2 kt + s n 1 e [ ( n 1 2 ) π L ] 2 t [ ( n 1 2 ) π L ] 2 v n (0) =
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Unformatted text preview: R L [ x ( L x ) ( x + 1)] sin n 1 2 L x dx R L sin 2 n 1 2 L x dx Coecients of expansion of initial condition for v u = v + w 138...
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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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