{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

apm255finalexam2 - APM255 Fall 2007 Final Exam Instructor W...

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

View Full Document Right Arrow Icon
1 APM255 Fall 2007 Final Exam Instructor: W. Zhang Student’s Name: Mark: Instruction: Close books and notes. Show your work and justify your answers. Calculators permitted. 1. (10 pts.) Identify if the following ordinary differential equations (ODEs) to be linear or nonlinear, separable (or non-separable), and autonomous or non-autonomous. . (a) 0 cos 3 ln = + x yx x y y e x (b) 0 1 2 / 1 = + y y (c) x y y y cos ) 1 ( 4 3 = 2. (10 pts.) A tank initially contains 50 gal of pure water. Brine containing 2 lb of salt per gallon enters the tank at the rate of 5 gal/min., and the well-mixed solution leaves the tank at the rate of 3 gal/min. Set-up (do not solve) the ODE initial value problem that describe the amount of salt, x(t) , the tank contains at time t.
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
2 3. (30 pts.) Solve the general and singular solutions (if there are) of the following ODEs. (a) x y y y cos ) 1 ( 4 3 =
Image of page 2
3 (b) 0 3 3 = + x y y x
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
4 4. (15 pts.) Show by direct computation that ) )( )( ( 1 1 1 det 2 2 2 a c c b b a c b a c b a = .
Image of page 4
5 5. (15 pts.) Find a basis and the dimension of the solution space of
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