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448F9B72d01 - (4 = 1 y(4 = 8(a What is the longest interval...

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M427K EXAM 2A 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 = 4 t + 40 cos 2 t.
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YOUR SCORE: /100 2. (15 points) The linear differential operatior L is given by L = ( D - 2) 3 ( D 4 + 81) . 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 - 10 y 0 + 25 y = 8 te 5 t + 3 t 4 - 10 te - 2 t cos(9 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
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Unformatted text preview: (4) = 1 , y (4) = 8 (a) What is the longest interval in which you are sure that a solution exists? (b) Could the power series solution centered at x = 4 be used to get a good approx-imation for y (6 . 5)? Why or why not? 5. (15 points) Find the general solution of ( x-3) 2 y 00-3( x-3) y + 13 y = 0 on x < 3. 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 first 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) = 2 , y (0) = 1 ....
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448F9B72d01 - (4 = 1 y(4 = 8(a What is the longest interval...

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