nagle_differential_equations_ISM_Part40

# nagle_differential_equations_ISM_Part40 - Figures 25 K100...

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Figures Figure 5–J : Problem 34, Section 5.4 Figure 5–K : Problem 14, Section 5.8 191

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Chapter 5 Figure 5–L : Problem 12, Review Problems Figure 5–M : Problem 16, Review Problems 192
CHAPTER 6: Theory of Higher-Order Linear Differential Equations EXERCISES 6.1: Basic Theory of Linear Differential Equations 2. (0 , ) 4. ( - 1 , 0) 6. (0 , 1) 8. Linearly dependent; 0 10. Linearly independent; - 2 tan 3 x - sin x cos x - sin 2 x tan x - 2 tan x 12. Linearly dependent; 0 14. Linearly independent; ( x + 2) e x 16. c 1 e x + c 2 cos 2 x + c 3 sin 2 x 18. c 1 e x + c 2 e - x + c 3 cos x + c 4 sin x 20. (a) c 1 + c 2 x + c 3 x 3 + x 2 (b) 2 - x 3 + x 2 22. (a) c 1 e x cos x + c 2 e x sin x + c 3 e - x cos x + c 4 e - x sin x + cos x (b) e x cos x + cos x 24. (a) 7 cos 2 x + 1 (b) - 6 cos 2 x - (11 / 3) 26. y ( x ) = n +1 j =1 γ j - 1 y j ( x ) 34. The coefficient is the Wronskian W [ f 1 , f 2 , f 3 ] ( x ) 193

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Chapter 6 EXERCISES 6.2: Homogeneous Linear Equations with Constant Coefficients 2. c 1 e x + c 2 e - x + c 3 e 3 x 4. c 1 e - x + c 2 e - 5 x + c 3 e 4 x 6. c 1 e - x + c 2 e x cos x + c 3 e x sin x 8. c 1 e x + c 2 xe x + c 3 e - 7 x 10. c 1 e - x + c 2 e ( - 1+ 7 ) x + c 3 e ( - 1 -
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