guerra_exam2

guerra_exam2 - Second Midterm February 19, 2009 NAME...

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Second Midterm February 19, 2009 NAME (Please print) Question Score 1 2 3 4 5 Total (Max Possible: 100) Instructions: 1. All questions are worth 20 points. 2. No calculators, computers, notes, books are permitted. 3. Do all computations on the examination paper. You may use the backs of the pages if necessary. Make your work readable. 4. Put answers inside the boxes (when applicable). 5. Please signify your adherence to the honor code: I, , have neither given nor received aid in completion of this examination. 1
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QUESTION 1 Score Solve the initial value problem: y 00 + 4 y 0 + 4 = 0 y (0) = 1 y 0 (0) = - 1 2
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Score The differential equation: y (5) - 9 y (4) - 33 y (3) - 61 y (2) + 56 y 0 - 20 y = 0 has characteristic polynomial: ( λ - 1)( λ - 2) 2 ( λ - 2 - i )( λ - 2 + i ) Write the general solution of the nonhomogeneous equation: y (5) - 9 y (4) - 33 y (3) - 61 y (2) + 56 y 0 - 20 y = 5 xe 2 x + 6 e - 2 x cosx You are not asked to find the numerical values of the constants involved in the partic- ular solution. 3
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guerra_exam2 - Second Midterm February 19, 2009 NAME...

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