Elementary Differential Equations 8th edition by Boyce ch01

# Elementary Differential Equations, with ODE Architect CD

This preview shows pages 1–4. Sign up to view the full content.

—————————————————————————— —— CHAPTER 1. ________________________________________________________________________ page 1 Chapter One Section 1.1 1. For , the slopes are C  "Þ& negative , and hence the solutions decrease. For , the C  "Þ& slopes are , and hence the solutions increase. The equilibrium solution appears to positive be , to which all other solutions converge. C > œ "Þ& a b 3. For , the slopes are C   "Þ& :9=3 tive , and hence the solutions increase. For C   "Þ& , the slopes are , and hence the solutions decrease. All solutions appear to negative diverge away from the equilibrium solution . C > œ  "Þ& a b 5. For , the slopes are C   "Î# :9=3 tive , and hence the solutions increase. For C   "Î# , the slopes are , and hence the solutions decrease. All solutions negative diverge away from

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
—————————————————————————— —— CHAPTER 1. ________________________________________________________________________ page 2 the equilibrium solution . C > œ  "Î# a b 6. For , the slopes are C   # :9=3 tive , and hence the solutions increase. For , C   # the slopes are , and hence the solutions decrease. All solutions diverge away negative from the equilibrium solution . C > œ  # a b 8. For solutions to approach the equilibrium solution , we must have all C > œ #Î\$ a b C  ! C  #Î\$ C  ! C  #Î\$ w w for , and for . The required rates are satisfied by the differential equation . C œ #  \$C w 9. For solutions than to diverge from , must be an other increasing C > œ # C œ # C > a b a b function for , and a function for . The simplest differential C  # C  # decreasing equation whose solutions satisfy these criteria is . C œ C  # w 10. For solutions than to diverge from , we must have other C > œ "Î\$ C œ "Î\$ C  ! a b w for , and for . The required rates are satisfied by the differential C  "Î\$ C  ! C  "Î\$ w equation . C œ \$C  " w 12. Note that for and . The two equilibrium solutions are and C œ ! C œ ! C œ & C > œ ! w a b C > œ & C  ! C  & a b . Based on the direction field, for ; thus solutions with initial w values than diverge from the solution . For , the slopes are greater & C > œ & !  C  & a b negative between , and hence solutions with initial values and all decrease toward the ! &
—————————————————————————— —— CHAPTER 1. ________________________________________________________________________ page 3 solution . For , the slopes are all ; thus solutions with initial C > œ ! C  ! a b positive values less than approach the solution . ! C > œ ! a b 14. Observe that for and . The two equilibrium solutions are C œ ! C œ ! C œ # C > œ ! w a b and . Based on the direction field, for ; thus solutions with initial C > œ # C  ! C  # a b w values than diverge from . For , the slopes are also greater # C > œ # !  C  # a b positive between , and hence solutions with initial values and all increase toward the ! # solution C > œ # C  ! a b . For , the slopes are all ; thus solutions with initial negative values than diverge from the solution . less ! C > œ ! a b 16. Let be the total amount of the drug in the patient's body at a b a b a b + Q > in milligrams any given time . The drug is administered into the body at a rate of > 2<= &!! a b constant 71Î2<Þ

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern