Homework 12 - M341 H12(S Zhang 5.2-3 1 Solve the system by...

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Unformatted text preview: M341 H12 (S. Zhang) 5.2-3. 1. Solve the system by eigenfunctions: x 1 = 2 x 1 + 3 x 2 , x 2 = 2 x 1 + x 2 • ans: (5.2:2) det( A- λI ) = 0 , λ =- 1 , 4 For λ =- 1 3 3 | 2 2 | → x = C 1- 1 For λ = 4- 2 3 | 2- 3 | → x = C 3 2 x = x 1 x 2 = C 1 e- t 1- 1 + C 2 e 4 t 3 2 2. Solve the system by eigenfunctions: x 1 = 9 x 1 + 5 x 2 , x 2 =- 6 x 1 + 2 x 2 x 1 (0) = 1 , x 2 (0) = 0 • ans: (5.2:6) det( A- λI ) = 0 , λ = 3 , 4 For λ = 3 6 5 |- 6- 5 | → x = C 5- 6 For λ = 4 5 5 |- 6- 6 | → x = C 1- 1 x = x 1 x 2 = C 1 e 3 t 5- 6 + C 2 e 4 t 1- 1 By the initial conditions, C 1 =- 1 , C 2 = 6 So x 1 =- 5 e 3 t + 6 e 4 t , x 2 = 6 e 3 t- 6 e 4 t 3. Solve the system by eigenfunctions: x 1 = x 1- 5 x 2 , x 2 = x 1- x 2 • ans: (5.2:8) det( A- λI ) = 0 , λ = ± 2 i For λ = 2 i 1- 2 i- 5 | 1- 1- 2 i | → x = C 5 1- 2 i x = x 1 x 2 = C 1 cos 2 t 5 1- sin 2 t- 2 + C 2 cos 2 t- 2 + sin 2 t 5 1 4. Solve the system by eigenfunctions: x 1 = 5 x 1- 9 x 2 , x 2 = 2 x 1- x 2 • ans: (5.2:13)(5....
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This homework help was uploaded on 04/07/2008 for the course MATH 341 taught by Professor Zhang during the Fall '08 term at University of Delaware.

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Homework 12 - M341 H12(S Zhang 5.2-3 1 Solve the system by...

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