math39100fall2005

math39100fall2005 - Department of Mathematics Math 391...

Info iconThis 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 Fall 2005 Part I. Answer ALL questions. Total 70 points. 1 . [6 Points] Find the general solution to y (4) - 4 y 00 + 4 y = 0. 2 . [10 Points] Solve ˆ e y 2 - 5 y sin( xy ) + 1 x ! dx + ˆ 2 xye y 2 - 5 x sin( xy ) - 1 y ! dy = 0. 3 . [5 Points] Suppose u ( x,t ) satisfies the partial differential equation: tu xx + 2 xu xt + xtu x = 0 . Use the separation of variables method to replace the partial differential equation by two ordinary differential equations. 4. (a) [5 Points] Using only the definition, find the Laplace Transform Y ( s ) of y ( t ) = e at where a is a constant. For what values of s does the Laplace Transform Y ( s ) exist? (b) [10 Points] Solve, using Laplace Transforms, the initial value problem: y 00 - 4 y 0 + 4 y = 3 , y (0) = 0 , y 0 (0) = 1 . (See table at end of exam.) 5 . [6 Points] Find two linearly independent solutions of 2 x 2 y 00 + 3 xy 0 - y = 0 for x > 0 and compute their Wronskian. 6
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

math39100fall2005 - Department of Mathematics Math 391...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online