MATH 256 Study Guide - Midterm Guide: Phase Plane, Fourier Series
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Be sure that this examination has 13 pages including this cover. 2 11 two sided cheat sheets are permitted. You are encouraged to explain all steps in your solutions. The plea of accident or forgetfulness shall not be received: candidates must not destroy or mutilate any examination material; must hand in all examination papers; and must not take any examination material from the. 15 examination room without permission of the invigilator. Page 3 of 13 pages (c) find a particular solution to t2y + 6ty + 4y = 28t3, and hence nd the solution to this inhomogeneous problem that satis es initial conditions y(1) = 1, y (1) = 0. Find the general solution of the homogeneous system: (i) for = 2; (ii) for = 3. x = ax. Page 5 of 13 pages (c) sketch the phase plane close to x = 0 for the two above cases: (i) = 2; (ii) = 3.
