Differential Equations Lecture Work Solutions 79

Differential Equations Lecture Work Solutions 79 - 12. utt...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
12. u tt c 2 u xx =0 0 <x<L u (0 ,t )= u ( L, t )=0 u ( x, 0) = f ( x ) u t ( x, 0) = g ( x ) XT 0 c 2 X 0 T =0 T 0 c 2 T = X 0 X = λ X 0 + λX =0 T 0 + λc 2 T =0 X (0) = X ( L )=0 X n =s in L xT 0 n + L ± 2 c 2 T n =0 n =1 , 2 , ··· λ n = L ± 2 T n = α n cos nπc L t + β n sin nπc L t u ( x, t )= X n =1 ² α n cos nπc L t + β n sin nπc L t ³ sin L x u ( x, 0) = f ( x )= X n =1 α n sin L x u t ( x, 0) = g ( x )= X n =1 nπc L β n sin
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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.

Ask a homework question - tutors are online