Answer
False
Work Step by Step
If $x_p$ is a particular solution to the vector differential equation $x′ = Ax+b$,
then $(c.x_p)'=c.x_p'=c.(Ax_p+b)$
Since $A(c.x_p)+b=c.(Ax_p)+b$, the statement is not true.
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: d
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