# exam2F09 - MATH 216 SECOND MIDTERM EXAM Please write your...

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MATH 216 SECOND MIDTERM EXAM November 16, 2009 Please write your name: Section: The test contains 8 problems worth 100 points total. To get the full credit you have to show your work . 12 Problem Points Score 12 1 2 14 3 12 4 12 5 12 14 6 7 12 Total 100 8 Typeset by A M S -T E X 1

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Name: ( 12 points ) 1. Problem. Find the solution of the di±erential equation y ± - 2 y ± +2 y =s in x that satis²es the initial conditions y (0) = 0, y ± (0) = 0. 2
Name: ( 14 points ) 2. Problem. Find all solutions of the di±erential equation y ± + y = e - x . 3

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Name: ( 12 points ) 3. Problem. Consider the diferential equation y ± + y = x sin x + e x . IF you use the method oF undetermined coe±cients, in what Formw i l lyoulookFor apart icu larso lut ion y ( x )o Ftheequat ion? You do not have to solve the equation. 4
Name: ( 12 points ) 4. Problem. Using the method of variation of parameters, Fnd all solutions of the di±erential equation y ± + y = 1 sin 2 x . You may use any of the following integrals ± dx sin x =ln ² ² ² ² 1 - cos x sin x ² ² ² ² + C, ± dx sin 2 x = - cos x sin x + C ± cos x

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exam2F09 - MATH 216 SECOND MIDTERM EXAM Please write your...

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