Elementary Differential Equations and Boundary Value Problems - W. Boyce, R. DiPrima 8th edition (Wiley, 2004)Solution- 课后习题参考答案.pdf
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—————————————————————————— CHAPTER 1. ——
Chapter One
Section 1.1
1.
For CÞ , the slopes are negative, and hence the solutions decrease. For CÞ , the
slopes are positive , and hence the solutions increase. The equilibrium solution appears to
be CabœÞ , to which all other solutions converge.
3.
For C Þ , the slopes are :9=3tive, and hence the solutions increase. For C Þ
, the slopes are negative , and hence the solutions decrease. All solutions appear to
diverge away from the equilibrium solution Cabœ Þ .
5.
For C Î# , the slopes are :9=3tive, and hence the solutions increase. For
C Î#, the slopes are negative , and hence the solutions decrease. All solutions
diverge away from
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page 1
—————————————————————————— CHAPTER 1. ——
the equilibrium solution Cabœ Î# .
6.
For C # , the slopes are :9=3tive, and hence the solutions increase. For C # ,
the slopes are negative , and hence the solutions decrease. All solutions diverge away
from
the equilibrium solution Cabœ # .
8. For all solutions to approach the equilibrium solution Cabœ#Î$ , we must have
C ! C#Î$w C ! C#Î$w
for , and for . The required rates are satisfied by the
w
differential equation C œ#$C .
9. For solutions other than Cabœ#to diverge from Cœ# , Cabmust be an increasing
function for C# , and a decreasing function for C# . The simplest differential
equation
w
whose solutions satisfy these criteria is C œC# .
10. For solutions other than CabœÎ$ to diverge from CœÎ$ , we must have C !w
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