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1 13 8546 2 3 i 5 a dv dt 2 rx 2 y 2 b z r 2 br 2 11

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𝜆 1 ≅ − 13 . 8546; 𝜆 2 , 𝜆 3 0 . 0939556 ± 10 . 1945 i 5. a. dV dt = − 2 𝜎 ( rx 2 + y 2 + b ( z r ) 2 br 2 ) 11. b. c = 0 . 5 : P 1 ( 2 4 , 2 , 2 ) ; 𝜆 = 0 , 0 . 05178 ± 1 . 5242 i c = 1 : P 1 = (0 . 8536 , 3 . 4142 , 3 . 4142); 𝜆 = 0 . 1612 , 0 . 02882 ± 2 . 0943 i P 2 (0 . 1464 , 0 . 5858 , 0 . 5858); 𝜆 = − 0 . 5303 , 0 . 03665 ± 1 . 1542 i 12. a. P 1 (1 . 1954 , 4 . 7817 , 4 . 7817); 𝜆 = 0 . 1893 , 0 . 02191 ± 2 . 4007 i P 2 (0 . 1046 , 0 . 4183 , 0 . 4183); 𝜆 = − 0 . 9614 , 0 . 007964 ± 1 . 0652 i d. T 1 5 . 9 13. a., b., c. c 1 1 . 243 14. a. P 1 (2 . 9577 , 11 . 8310 , 11 . 8310); 𝜆 = 0 . 2273 , 0 . 009796 ± 3 . 5812 i P 2 (0 . 04226 , 0 . 1690 , 0 . 1690); 𝜆 = − 2 . 9053 , 0 . 09877 ± 0 . 9969 i c. T 2 11 . 8 15. a. P 1 (3 . 7668 , 15 . 0673 , 15 . 0673); 𝜆 = 0 . 2324 , 0 . 007814 ± 4 . 0078 i P 2 (0 . 03318 , 0 . 1327 , 0 . 1327); 𝜆 = − 3 . 7335 , 0 . 1083 ± 0 . 9941 i b. T 4 23 . 6 Chapter 10 Section 10.1, page 468 1. y = − sin ( x ) 2. y = ( cot ( 2 𝜋 ) cos ( 2 x ) + sin ( 2 x )) 2 3. y = 0 for all L ; y = c 2 sin ( x ) if sin ( L ) = 0 4. y = − tan ( L ) cos ( x ) + sin ( x ) if cos ( L ) 0; no solution if cos ( L ) = 0 5. No solution
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Boyce 9131 BMAnswersToProblems 2 March 11, 2017 15:55 598 598 Answers to Problems 6. y = ( 𝜋 sin ( 2 x ) + x sin ( 2 𝜋 )) 2 sin ( 2 𝜋 ) 7. No solution 8. y = c 2 sin (2 x ) + 1 3 sin x 9. y = c 1 cos (2 x ) + 1 3 cos x 10. y = 1 2 cos x 11. y = − 5 2 x + 3 2 x 2 12. y = − 1 9 x 1 + 1 9 (1 e 3 ) x 1 ln x + 1 9 x 2 13. No solution 14. 𝜆 n = ( 2 n 1 2 ) 2 , y n ( x ) = sin ( 2 n 1 2 x ) ; n = 1 , 2 , 3 , 15. 𝜆 n = ( 2 n 1 2 ) 2 , y n ( x ) = cos ( 2 n 1 2 x ) ; n = 1 , 2 , 3 , 16. 𝜆 0 = 0 , y 0 ( x ) = 1; 𝜆 n = n 2 , y n ( x ) = cos nx ; n = 1 , 2 , 3 , 17. 𝜆 n = ( (2 n 1) 𝜋 2 L ) 2 , y n ( x ) = cos ( (2 n 1) 𝜋 x 2 L ) ; n = 1 , 2 , 3 , 18. 𝜆 0 = 0 , y 0 ( x ) = 1; 𝜆 n = ( n 𝜋 L ) 2 , y n ( x ) = cos ( n 𝜋 x L ); n = 1 , 2 , 3 , 19. 𝜆 n = − ( (2 n 1) 𝜋 2 L ) 2 , y n ( x ) = sin ( (2 n 1) 𝜋 x 2 L ) ; n = 1 , 2 , 3 , 20. 𝜆 n = 1 + ( n 𝜋 ∕ ln L ) 2 , y n ( x ) = x sin ( n 𝜋 ln x ∕ ln L ); n = 1 , 2 , 3 , 21. a. w ( r ) = G ( R 2 r 2 ) (4 𝜇 ) c. Q is reduced to 0.3164 of its original value. 22. a. y = k ( x 4 2 Lx 3 + L 3 x ) 24 b. y = k ( x 4 2 Lx 3 + L 2 x 2 ) 24 c. y = k ( x 4 4 Lx 3 + 6 L 2 x 2 ) 24 Section 10.2, page 476 1. T = 2 𝜋 5 2. T = 1 3. Not periodic 4. T = 2 L 5. T = 1 6. Not periodic 7. T = 2 8. T = 4 9. f ( x ) = 2 L x in L < x < 2 L ; f ( x ) = − 2 L x in 3 L < x < 2 L 10. f ( x ) = x 1 in 1 < x < 2; f ( x ) = x 8 in 8 < x < 9 11. f ( x ) = − L x in L < x < 0 13. b. f ( x ) = 2 L 𝜋 n = 1 ( 1) n n sin ( n 𝜋 x L ) 14. b. f ( x ) = 1 2 2 𝜋 n = 1 sin ((2 n 1) 𝜋 x L ) 2 n 1 15. b. f ( x ) = − 𝜋 4 + n = 1 ( 2 cos ((2 n 1) x ) 𝜋 (2 n 1) 2 + ( 1) n + 1 sin ( nx ) n ) 16. b. f ( x ) = 1 2 + 4 𝜋 2 n = 1 cos ((2 n 1) 𝜋 x ) (2 n 1) 2 17. b. f ( x ) = 3 L 4 + n = 1 ( 2 L cos ((2 n 1) 𝜋 x L ) (2 n 1) 2 𝜋 2 + ( 1) n + 1 L sin ( n 𝜋 x L ) n 𝜋 ) 18. b. f ( x ) = n = 1 ( 2 n 𝜋 cos ( n 𝜋 2 ) + ( 2 n 𝜋 ) 2 sin ( n 𝜋 2 ) ) × sin ( n 𝜋 x 2 ) 19. b. f ( x ) = 4 𝜋 n = 1 sin ((2 n 1) 𝜋 x 2) 2 n 1 20. b. f ( x ) = 2 𝜋 n = 1 ( 1) n + 1 n sin ( n 𝜋 x ) 21. b. f ( x ) = 2 3 + 8 𝜋 2 n = 1 ( 1) n n 2 cos ( n 𝜋 x 2 ) 22. b. f ( x ) = 1 2 + 12 𝜋 2 n = 1 cos ((2 n 1) 𝜋 x 2) (2 n 1) 2 + 2 𝜋 n = 1 ( 1) n n sin ( n 𝜋 x 2 ) 23. b.
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