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?
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