11.18: A.2.1- Section 2.1 Answers
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1. y=e−ax
2. y=ce−x3
3. y=ce−(lnx)2/2
4. y=cx3
5. y=ce1/x
6. y=e−(x−1)x
7. y=exlnx
8. y=πxsinx
9. y=2(1+x2)
10. y=3x−k
11. y=2(coskx)1/k
12. y=13+ce−3x
13. y=2x+cxex
14. y=e−x2(x22+c)
15. y=−e−x+c1+x2
16. 7ln|x|x+32x+cx
17. y=(x−1)−4(ln|x−1|−cosx+c)
18. y=e−x2(x34+cx)
19. y=2ln|x|x2+12+cx2
20. y=(x+c)cosx
21. y=c−cosx(1+x)2
22. y=−12(x−2)3(x−1)+c(x−2)5(x−1)
23. y=(x+c)e−sin2x
24. y=exx2−exx3+cx2
25. y=e3x−e−7x10
26. y=2x+1(1+x2)2
27. y=1x3ln(1+x22)
28. y=12(sinx+cscx)
29. y=2ln|x|x+x2−12x
30. y=(x−1)−3[ln(1−x)−cosx]
31. y=2x2+1x2(0,∞)
32. y=x2(1−lnx)
33. y=12+52e−x2
34. y=ln|x−1|+tanx+1(x−1)3
35. y=ln|x|+x2+1(x+2)4
36. y=(x2−1)(12ln|x2−1|−4)
37. y=−(x2−5)(7+ln|x2−5|)
38. y=e−x2(3+∫x0t2et2dt)
39. y=1x(2+∫x1sinttdt)
40. y=e−x∫x1tanttdt
41. y=11+x2(1+∫x0et1+t2dt)
42. y=1x(2e−(x−1)+e−x∫x1etet2dt)
43. G=rλ+(G0−rλ)e−λtlimt→∞G(t)=rλ
45. y=y0e−a(x−x0)+e−ax∫xx0eatf(t)dt
48.