Section 5.2

1. $15 \cdot (2 x) - 16 \cdot (3 x^{2}) - 6 \cdot (5 x - 8 x^{2}) \equiv 0$ $15 \cdot (2 x) - 16 \cdot (3 x^{2}) - 6 \cdot (5 x - 8 x^{2}) \equiv 0$
2. $(- 4) (5) + (5) (2 - 3 x^{2}) + (1) (10 + 15 x^{2}) \equiv 0$ $(- 4) (5) + (5) (2 - 3 x^{2}) + (1) (10 + 15 x^{2}) \equiv 0$
3. $1 \cdot 0 + 0 \cdot \sin x + 0 \cdot e^{x} \equiv 0$ $1 \cdot 0 + 0 \cdot \sin x + 0 \cdot e^{x} \equiv 0$
4. $(6) (17) + (- 51) (2 \sin^{2} x) + (- 34) (3 \cos^{2} x) \equiv 0$ $(6) (17) + (- 51) (2 \sin^{2} x) + (- 34) (3 \cos^{2} x) \equiv 0$
5. $1 \cdot 17 - 34 \cdot \cos^{2} x + 17 \cdot \cos 2 x \equiv 0$ $1 \cdot 17 - 34 \cdot \cos^{2} x + 17 \cdot \cos 2 x \equiv 0$
6. $(- 1) (e^{x}) + (1) (\cosh x) + (1) (\sinh x) \equiv 0$ $(- 1) (e^{x}) + (1) (\cosh x) + (1) (\sinh x) \equiv 0$
13. $y (x) = \frac{4}{3} e^{x} - \frac{1}{3} e^{- 2 x}$ $y (x) = \frac{4}{3} e^{x} - \frac{1}{3} e^{- 2 x}$
14. $y (x) = \frac{1}{2} (3 e^{x} - 6 e^{2 x} + 3 e^{3 x})$ $y (x) = \frac{1}{2} (3 e^{x} - 6 e^{2 x} + 3 e^{3 x})$
15. $y (x) = (2 - 2 x + x^{2}) e^{x}$ $y (x) = (2 - 2 x + x^{2}) e^{x}$
16. $y (x) = - 12 e^{x} + 13 e^{2 x} - 10 {x e}^{2 x}$ $y (x) = - 12 e^{x} + 13 e^{2 x} - 10 {x e}^{2 x}$
17. $y (x) = \frac{1}{9} (29 - 2 \cos 3 x - 3 \sin 3 x)$ $y (x) = \frac{1}{9} (29 - 2 \cos 3 x - 3 \sin 3 x)$
18. $y (x) = e^{x} (2 - \cos x - \sin x)$ $y (x) = e^{x} (2 - \cos x - \sin x)$
19. $y (x) = x + 2 x^{2} + 3 x^{3}$ $y (x) = x + 2 x^{2} + 3 x^{3}$
20. $y (x) = 2 x - x^{- 2} + x^{- 2} \ln x$ $y (x) = 2 x - x^{- 2} + x^{- 2} \ln x$
21. $y (x) = 2 \cos x - 5 \sin x + 3 x$ $y (x) = 2 \cos x - 5 \sin x + 3 x$
22. $y (x) = 4 e^{2 x} - e^{- 2 x} - 3$ $y (x) = 4 e^{2 x} - e^{- 2 x} - 3$
23. $y (x) = e^{- x} + 4 e^{3 x} - 2$ $y (x) = e^{- x} + 4 e^{3 x} - 2$
24. $y (x) = e^{x} (3 \cos x + 4 \sin x) + x + 1$ $y (x) = e^{x} (3 \cos x + 4 \sin x) + x + 1$
38. $y_{2} (x) = \frac{1}{x^{3}}$ $y_{2} (x) = \frac{1}{x^{3}}$
39. $y_{2} (x) = x e^{x / 2}$ $y_{2} (x) = x e^{x / 2}$
40. $y_{2} (x) = x e^{x}$ $y_{2} (x) = x e^{x}$
41. $y_{2} (x) = x + 2$ $y_{2} (x) = x + 2$
42. $y_{2} (x) = 1 + x^{2}$ $y_{2} (x) = 1 + x^{2}$

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Table of Contents for Section 5.2

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Table of Contents for
Section 5.2