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MA 2327 Assignment 5 Due 23 November 2015 Id: 2327-f2015-5.m4,v 1.1 2015/11/16 14:52:59 john Exp john 1. Solve the initial value problem x′′′ (t) − x′′ (t) − x′ (t) + x(t) = 0, x(0) = 1, x′ (0) = 2, x′′ (0) = 3 by the method of undetermined cooefficients. 2. For the initial value problem for linear constant coefficient homogeneous equations, the method of undetermined coefficients always leads to a system of linear equations with a unique solution. For boundary value problems this may or may not be true, depending on the coefficients and the boundary conditions. Consider the boundary value problem x′′ (t) + ω 2 x(t) = 0, x(−1) = p, x(1) = q for real ω, p and q. When does this have a solution? When is that solution unique? 1