Exam2B - y 00-8 y + 16 y = 43 te 4 t + 5 t 2 cos(9 t ) 4....

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
M427K EXAM 2B FALL, 2009 Dr. Schurle Your name: Your UTEID: Show all your work on these pages. Be organized and neat. Your work should be your own; there should be no talking, reading notes, checking laptops, using cellphones, . . . . 1. (15 points) Given that the general solution of y 00 - y 0 - 2 y = 0 is y = c 1 e - t + c 2 e 2 t , find the general solution of y 00 - y 0 - 2 y = 12 e 3 t + 30 sin t.
Background image of page 1

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

View Full DocumentRight Arrow Icon
YOUR SCORE: /100 2. (15 points) Find the general solution of 27 y (8) + 243 y (7) + 513 y (6) + 4987 y (5) + 48528 y (4) + 114598 y 000 - 1480 y 00 - 14400 y 0 - 34000 y = 0 . HINT: 27 r 8 + 243 r 7 + 513 r 6 + 4987 r 5 + 48528 r 4 + 114598 r 3 - 1480 r 2 - 14400 r - 34000 factors as ( r + 5) 3 ( r 2 - 6 r + 34)(27 r 3 - 8). 3. (15 points) Write the simplest form of a particular solution y p of the following dif- ferential equation. DO NOT EVALUATE THE CONSTANTS that appear in your answer.
Background image of page 2
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y 00-8 y + 16 y = 43 te 4 t + 5 t 2 cos(9 t ) 4. (10 points) Determine the longest interval in which you are sure that a solution of the following intial value problem exists. ( x 2-16)( x + 2) y 00 + 3 xy-4 y = 0 , y (0) = 27 , y (0) = 2 5. (15 points) Given that x and x 4 form a fundamental set of solutions of the associated homogeneous dierential equation, nd the general solution of y 00-4 x y + 4 x 2 y = 9 x + 3 x 5 . 6. (15 points) Find the general solution of x 2 y 00-7 xy + 16 y = 0 on x > 0. 7. (15 points) Find a polynomial solution of the following dierential equation. (1-x 2 ) y 00-2 xy + 30 y = 0...
View Full Document

This note was uploaded on 01/27/2012 for the course MATH 427 k taught by Professor Goddard during the Fall '10 term at University of Texas at Austin.

Page1 / 4

Exam2B - y 00-8 y + 16 y = 43 te 4 t + 5 t 2 cos(9 t ) 4....

This preview shows document pages 1 - 4. Sign up to view the full document.

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