Chapter 9 - Systems of Differential Equations - 9.6 Variation-of-Parameters for Linear Systems - True-False Review - Page 624: e

False

From Theorem 9.6.1 we have: $$x_p(t)=X(t)\int^t_0 X^{-1}(S)b(s) ds$$ then integration constants will add to this. Hence there are many particular solutions $x_p$ that satisfy the nonhomogeneous vector differential equation $x′ = Ax + b$. Hence, the statement is not true.