Answer
False
Work Step by Step
If X(t) is a fundamental matrix for $x′ = Ax$, then a particular solution to the nonhomogeneous vector differential equation $x′ = Ax + b$ is $x_p(t) \_ X(t)u'(t)$. Hence $u(t)$ is not an arbitrary vector function.
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 9 - Systems of Differential Equations - 9.6 Variation-of-Parameters for Linear Systems - True-False Review - Page 624: b
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