09FDC9DCd01 - , y (0) = 7 (a) What is the longest interval...

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M427K EXAM 2B Your name: SPRING, 2010 Dr. Schurle 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) Find the general solution of y 00 - 3 y 0 + 2 y = 8 t + 20 cos 2 t.
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YOUR SCORE: /100 2. (15 points) The linear differential operatior L is given by L = ( D - 5) 3 ( D 4 + 16) . Find the general solution of L [ y ] = 0. 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. y 00 - 12 y 0 + 36 y = 7 t 2 e 6 t + 2 t 3 - 4 te - 6 t sin(3 t )
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4. (10 points) Consider the following initial value problem. ( x 2 + x - 6)( x - 7) y 00 + 4 xy 0 - 3 y = t 2 , y (0) = 1
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Unformatted text preview: , y (0) = 7 (a) What is the longest interval in which you are sure that a solution exists? (b) Could the power series solution centered at x = 0 be used to get a good approx-imation for y (1 . 5)? Why or why not? 5. (15 points) Find the general solution of ( x-7) 2 y 00-5( x-7) y + 13 y = 0 on x < 7. 6. (15 points) Find the general solution of x 2 y 00-3 xy + 4 y = 2 x 2 ln x on x > 0. 7. (15 points) Find the recurrence relation and the rst four nonzero terms of the power series solution centered at x = 0 for the initial value problem (1-x ) y 00 + 2 xy + 3 y = 0 , y (0) = 6 , y (0) = 1 ....
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09FDC9DCd01 - , y (0) = 7 (a) What is the longest interval...

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