APPENDIX 2
Answers toOdd-Numbered Problems
Problem Set 1.1, page 8
- 1.
- 3. y = cex
- 5. y = 2e−x(sin x − cos x + c
- 7.
- 9. y = 1.65e−2x + 0.35
- 11.
- 13. y = 1/(1 + 3ex)
- 15. y = 0 and y = 1 because y′ = 0 for these y
- 17. exp
, t = 1011(1n 2)/1.4 [sec]
- 19. Integrate y″ g twice, y′(t) = gt + v0, y′(0) = v0 = 0 (start from rest), then
, where y(0) = y0 = 0
Problem Set 1.2, page 11
- 11. Straight lines parallel to the x-axis
- 13. y = x
- 15. mv′ = mg − bv2, 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,
but not ex + c (with c ≠ 0)
- 3. cos ...
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