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APPM 2360 Midterm: appm2360summer2014exam3_sol

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turquoisegnu128

31 Jan 2019

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On the front of your bluebook write: (1) your name, (2) your student id number, (3) your instructor"s name, and (4) a grading table. Text books, class notes, and calculators are not permitted. Problem 1: (25 points) consider the ode t2y + ty 4y = f (t). (a) let f (t) = 0. Explain your response. (c) find a particular solution to the ode for f (t) = 4t 4. (d) find the general solution to the ode for f (t) = 4t 4. The ode yields the equation tr(r(r 1) + r 4) = 0. So we solve r2 4 = 0 to get r = 2 . (b) s = {t2, t 2} forms the basis for the solution space of this ode . Note that this vector space must have dimension two because the ode is second order. We claim that s is a linearly independent set via the wronskian: t2.

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