{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

math39100spring2005

math39100spring2005 - Department of Mathematics Math 391...

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

View Full Document Right Arrow Icon
Department of Mathematics Math 391 Final Examination Date: May, 2005 Part I. Answer ALL questions. Total 64 points. 1 . [13 Points] Solve the initial value problem: y 00 - 4 y 0 + 4 y = x 2 + 12 e 2 x , y (0) = 1 , y 0 (0) = 0 . 2 . [8 Points] Solve y cos( xy ) + y 2 x dx + x cos( xy ) + 1 2 ln( x ) + 1 e y dy = 0 . 3 . [9 Points] Find the general solution to y 00 - 2 y 0 + y = e x x . 4 . [7 Points] Solve xy 0 - 2 y = xy + xe x . 5 . [13 Points] For the equation 2 xy 00 - y 0 + y = 0, (a) Show x = 0 is a regular singular point. (b) Find the indicial equation and the recurrence relation corresponding to the larger root. (c) Find the first four terms of the series solution valid near x > 0 correcponding to the larger root. 6 . [4 Points] Use separation of variables to replace the partial differential equation: xtu xx + u xt + tu x = 0 , where u is a function of x and t , by two ordinary differential equations. 7 . [10 Points] Use the Laplace Transform method to solve: y 00 + 4 y = 2 , y (0) = 1 , y 0 (0) = 3 . Note that: L{ e at } = 1 s - a , L{ sin at } = a s 2 + a 2 L{ cos at } = s s 2 + a 2 . Part II begins on the back.
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
Part II. Answer any THREE (3) COMPLETE questions. Total: 36 points. 8 . [12 Points] Find the Fourier series for f ( x ) = ( x + 2 if - 2 < x 0; 2 - x if 0 < x 2, where f ( x + 4) = f ( x ) for all
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