Elementary Differential Equations 8th edition by Boyce ch02

Elementary Differential Equations, with ODE Architect CD

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
—————————————————————————— —— CHAPTER 2. ________________________________________________________________________ page 18 Chapter Two Section 2.1 1 a b + Þ a b , Þ Based on the direction field, all solutions seem to converge to a specific increasing function. a b a b a b - Þ > œ / C > œ >Î$  "Î*  /  - / Þ The integrating factor is , and hence . $> #> $> It follows that all solutions converge to the function C > œ >Î$  "Î* Þ " a b 2 a b + Þ a b , . All slopes eventually become positive, hence all solutions will increase without bound. a b a b a b - Þ > œ / C > œ > / Î$  - / Þ The integrating factor is , and hence It is . #> $ #> #> evident that all solutions increase at an exponential rate. 3 a b +
Image of page 1

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

View Full Document Right Arrow Icon
—————————————————————————— —— CHAPTER 2. ________________________________________________________________________ page 19 a b a b , C > œ " Þ . All solutions seem to converge to the function ! a b a b a b - Þ > œ / C > œ > / Î#  "  - / Þ The integrating factor is , and hence It is . #> # > > clear that all solutions converge to the specific solution . C > œ " ! a b 4 . a b + a b , . Based on the direction field, the solutions eventually become oscillatory. a b a b - Þ > œ > The integrating factor is , and hence the general solution is . C > œ =38 #>  $-9= #> $ - %> # > a b a b a b in which is an arbitrary constant. As becomes large, all solutions converge to the - > function C > œ $=38 #> Î# Þ " a b a b 5 . a b +
Image of page 2
—————————————————————————— —— CHAPTER 2. ________________________________________________________________________ page 20 a b , . All slopes eventually become positive, hence all solutions will increase without bound. a b a b a b ' - Þ > œ /B:  #.> œ / Þ The integrating factor is The differential equation . #> can be written as , that is, Integration of both / C  #/ C œ $/ / C œ $/ Þ #> w #> > #> > w a b sides of the equation results in the general solution It follows that C > œ  $/  - / Þ a b > #> all solutions will increase exponentially. 6 a b + a b a b , Þ C > œ ! Þ All solutions seem to converge to the function ! a b a b - Þ > œ > The integrating factor is , and hence the general solution is . # C > œ  -9= > =38 #> - > > > a b a b a b # # in which is an arbitrary constant. As becomes large, all solutions converge to the - > function C > œ ! Þ ! a b 7 . a b +
Image of page 3

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

View Full Document Right Arrow Icon
—————————————————————————— —— CHAPTER 2. ________________________________________________________________________ page 21 a b a b , Þ C > œ ! Þ All solutions seem to converge to the function ! a b a b a b a b - Þ > œ /B: > C > œ > /  - / Þ The integrating factor is , and hence It is . # # > > # # clear that all solutions converge to the function . C > œ ! ! a b 8 a b + a b a b , Þ C > œ ! Þ All solutions seem to converge to the function ! a b a b a b c d a b - Þ > œ C > œ >+8 >  G Î Þ Since , the general solution is . a b a b "  > "  > # # # # " It follows that all solutions converge to the function . C > œ ! ! a b 9 a b + Þ
Image of page 4
—————————————————————————— —— CHAPTER 2.
Image of page 5

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

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern