2930Prelim 2 Fall 2009_noSolution.pdf

2930Prelim 2 Fall 2009_noSolution.pdf - Mathematics 2930...

Info icon This preview shows pages 1–2. Sign up to view the full content.

Mathematics 2930. Fall 2009 Prelim I I Thursday, November 19, 2009 7.30 PM - 9 PM Instructions: Write your name, your TA’s name and section number on your exam booklet No calculators, other electronic devices, or notes are allowed in this exam. Give reasons for your answers and show all work There are 5 problems, each worth 20 points. Good luck ! 1. (a) (10 points) Find a general solution of: y - y - 2 y + 2 y = 0 (1) Here, y is a function of x for all real x and denotes a derivative with respect to x . Make sure that the correct number of arbitrary constants appear in your solution. Hint : The fourth degree polynomial equation: r 4 - r 2 - 2 r + 2 = 0 (2) has two roots r 1 = r 2 = 1. First find the other two roots r 3 and r 4 . (b) (10 points) Now consider the equation: y - y - 2 y + 2 y = e x (3) Find a particular solution of (3). 2. (20 points) Determine the unique solution x ( t ) of the following problem. ¨ x + 4 x = sin( t ) cos( t ) , x (0) = ˙ x (0) = 0 (4) where ˙ x dx/dt .
Image of page 1

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

Image of page 2
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