MATH 3D Study Guide - Midterm Guide: Phase Diagram
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April 25, 2017: find an explicit solution to the following di erential equation: (cid:18) (cid:19) xy(cid:48) + x + 3 y = e 2xy 2: find the solution to the following di erential equation (implicit okay): (ey + 1)2 e y +(cid:2)(ex + 1)3e x(cid:3) dy. = 0, y(0) = 0 dx: find the solution to the following di erential equation: y(cid:48)(cid:48) 4y(cid:48) + 13y = 0, y(0) = 11, y(cid:48)(0) = 19. 4. (a) find the general solution to the following di erential equation: y(cid:48)(cid:48)(cid:48) + 12y(cid:48)(cid:48) + 36y(cid:48) = 0 (b) use your work in part (b) to solve the following di erential equation: y(cid:48)(cid:48)(cid:48) + 12y(cid:48)(cid:48) + 36y(cid:48) = 108x2. = (y 7)2(y 3)(y + 1) dy dt: determine whether the following sets of functions are linearly independent: (a) {sin x, cos x, x sin x} (b) (cid:8)xex, x2ex, e2x(cid:9) (c) (cid:8)cos2 x, sin2 x, 1(cid:9)
