nagle_differential_equations_ISM_Part55

nagle_differential_equations_ISM_Part55 - Chapter 7 2 4 6 8...

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Unformatted text preview: Chapter 7 2 4 6 8 1 0 1 2 K 2 K 1 1 2 Figure 7K : The graph of y ( t ) in Problem 32. 1 2 3 4 5 6 7 1 Figure 7L : The graph of g ( t ) in Problem 42. 2 . 5 5 . 0 7 . 5 K 1 1 2 Figure 7M : The graph of y ( t ) in Problem 22. 2 4 6 8 1 0 1 2 K 1 . 0 K 0 . 5 0 . 5 1 . 0 Figure 7N : The graph of y ( t ) in Problem 24. 266 CHAPTER 8: Series Solutions of Differential Equations EXERCISES 8.1: Introduction: The Taylor Polynomial Approximation 2. 2 + 4 x + 8 x 2 + 4. 1 2 x 2 + 1 6 x 3- 1 20 x 5 + 6. x- 1 6 x 3 + 1 120 x 5 + 8. 1- sin 1 2 x 2 + (cos 1)(sin 1) 24 x 4 + 10. (a) p 3 ( x ) = 1 2 + x 4 + x 2 8 + x 3 16 (b) 3 = 1 4! 24 (2- ) 5 1 2 4 1 (3 / 2) 5 1 2 4 = 2 3 5 . 00823 (c) 2 3- p 3 1 2 = 1 384 . 00260 (d) See Fig. 8A on page 276 12. The differential equation implies that the functions y ( x ), y ( x ), and y 00 ( x ) exist and continuous. Furthermore, y 000 ( x ) can be obtained by differentiating the other terms: y 000 =- py 00...
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nagle_differential_equations_ISM_Part55 - Chapter 7 2 4 6 8...

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