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1. $$3$$

2. $$2$$

3. $$1$$

4. $$2$$

13. $$y=-\frac{x^{2}}{2}+c$$

14. $$y=x\cos x-\sin x+c$$

15. $$y=\frac{x^{2}}{2}\ln x-\frac{x^{2}}{4}+c$$

16. $$y=-x\cos x+2\sin x+c_{1}+c_{2}x$$

17. $$y=(2x-4)e^{x}+c_{1}+c_{2}x$$

18. $$y=\frac{x^{3}}{3}-\sin x+e^{x}+c_{1}+c_{2}x$$

19. $$y=\sin x+c_{1}+c_{2}x+c_{3}x^{2}$$

20. $$y=-\frac{x^{5}}{60}+e^{x}+c_{1}+c_{2}x+c_{3}x^{2}$$

21. $$y=\frac{7}{64}e^{4x}+c_{1}+c_{2}x+c_{3}x^{2}$$

22. $$y=-(x-1)e^{x}$$

23. $$y=1-\frac{1}{2}\cos x^{2}$$

24. $$y=3-\ln (\sqrt{2}\cos x)$$

25. $$y=-\frac{47}{15}-\frac{37}{5}(x-2)+\frac{x^{5}}{30}$$

26. $$y=\frac{1}{4}xe^{2x}-\frac{1}{4}e^{2x}+\frac{29}{4}$$

27. $$y=x\sin x+2\cos x-3x-1$$

28. $$y=(x^{2}-6x+12)e^{x}+\frac{x^{2}}{2}-8x-11$$

29. $$y=\frac{x^{3}}{3}+\frac{\cos 2x}{6}+\frac{7}{4}x^{2}-6x+\frac{7}{8}$$

30. $$y=\frac{x^{4}}{12}+\frac{x^{3}}{6}+\frac{1}{2}(x-2)^{2}-\frac{26}{3}(x-2)-\frac{5}{3}$$

40.

1. $$576$$ ft
2. $$10$$ s

41.

b. $$y=0$$

43.

a. $$(-2c-2,\infty )\: (-\infty ,\infty )$$