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APPENDIX 2
Answers toOdd-Numbered Problems

Problem Set 1.1, page 8
1.
3. y = ce ^{x}
5. y = 2e ^{−x} (sin x − cos x + c
7.
9. y = 1.65e ^{−2x} + 0.35
11.
13. y = 1/(1 + 3e ^{x} )
15. y = 0 and y = 1 because y ′ = 0 for these y
17. exp , t = 10^{11} (1n 2)/1.4 [sec]
19. Integrate y ″ g twice, y ′(t ) = gt + v _{0} , y ′(0) = v _{0} = 0 (start from rest), then , where y (0) = y _{0} = 0
Problem Set 1.2, page 11
11. Straight lines parallel to the x -axis
13. y = x
15. mv ′ = mg − bv ^{2} , v ′ = 9.8 − v ^{2} , 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. x _{5} = 0.0286(error 0.0093), x _{10} = 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 e ^{x} + c (with c ≠ 0)
3. cos ...
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