# APPENDIX 2

# Answers toOdd-Numbered Problems

**Problem Set 1.1,** page 8

**1.****3.***y*=*ce*^{x}**5.***y*= 2*e*^{−x}(sin*x*− cos*x*+*c***7.****9.***y*= 1.65*e*^{−2x}+ 0.35**11.****13.***y*= 1/(1 + 3*e*^{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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