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Unformatted text preview: MAT 212  Midterm Exam
February 23, 2010.
Name: Student Id: 1. • (15) If a, b and c are > 0, show that every solution y (t) of ay + by + cy = 0 is such that limt→+∞ y (t) = 0 • (5) Give one example of a linear second order equation for which y (t) = 0 (constant zero function) is the only solution such that limt→+∞ y (t) = 0. 1 2. (20) Solve y (3) + 6y + y − 34y = 0. (Hint: e−4t . cos t is a solution). 3. (25) Solve y (4) − 8y = 0. 4. • (30) Using the variation of parameters, solve y − 4y + 4y = (t + 1).e2t • (5) Rewrite the equation as a system of two ﬁrst order equations. ...
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This document was uploaded on 04/01/2011.
 Spring '09

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