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# Exam2A - y 9 y = 4 te 3 t 6 t 2 sin(5 t 4(10 points...

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M427K EXAM 2A 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 = 8 e 3 t + 10 sin t.

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YOUR SCORE: /100 2. (15 points) Find the general solution of 8 y (8) + 40 y (7) + 160 y (6) + 1413 y (5) + 5265 y (4) + 5724 y 000 - 4860 y 00 - 18225 y 0 - 21141 y = 0 . HINT: 8 r 8 +40 r 7 +160 r 6 +1413 r 5 +5265 r 4 +5724 r 3 - 4860 r 2 - 18225 r - 21141 factors as ( r + 3) 3 ( r 2 - 4 r + 29)(8 r 3 - 27). 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.

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Unformatted text preview: y + 9 y = 4 te 3 t + 6 t 2 sin(5 t ) 4. (10 points) Determine the longest interval in which you are sure that a solution of the following intial value problem exists. ( x 2-9)( x + 1) 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 diﬀerential equation, ﬁnd the general solution of y 00-4 x y + 4 x 2 y = 3 x 2 + 9 x 4 . 6. (15 points) Find the general solution of x 2 y 00-9 xy + 25 y = 0 on x > 0. 7. (15 points) Find a polynomial solution of the following diﬀerential equation. (1-x 2 ) y 00-2 xy + 20 y = 0...
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