APPENDIX 2

Answers toOdd-Numbered Problems

image

Problem Set 1.1, page 8

  • 1. image
  • 3. y = cex
  • 5. y = 2ex(sin x − cos x + c
  • 7. image
  • 9. y = 1.65e−2x + 0.35
  • 11. image
  • 13. y = 1/(1 + 3ex)
  • 15. y = 0 and y = 1 because y′ = 0 for these y
  • 17. expimage, t = 1011(1n 2)/1.4 [sec]
  • 19. Integrate yg twice, y′(t) = gt + v0, y′(0) = v0 = 0 (start from rest), then image, where y(0) = y0 = 0

Problem Set 1.2, page 11

  • 11. Straight lines parallel to the x-axis
  • 13. y = x
  • 15. mv′ = mgbv2, v′ = 9.8 − v2, v(0) = 10, v′ = 0 gives the limit/9.8 = 3.1 [meter/sec]
  • 17. Errors of steps 1, 5, 10: 0.0052, 0.0382, 0.1245, approximately
  • 19. x5 = 0.0286(error 0.0093), x10 = 0.2196(error 0.0189)

Problem Set 1.3, page 18

  • 1. If you add a constant later, you may not get a solution. Example: y′ = y, In |y| = x + c, image but not ex + c (with c ≠ 0)
  • 3. cos ...

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