Chapter 6.6, Problem 1P

Assuming that $\text{X}\left(t\right)$ is a fundamental matrix for $\text{x}\text{'}=\text{P}\left(t\right)\text{x}$, show directly that

${\text{x}}_p=\text{X}\left(t\right){\displaystyle \underset{t_1}{\overset{t}{\int }}{\text{X}}^{-1}\left(s\right)g\left(s\right)}ds$

is a particular solution of Eq. (1), $\text{x}\text{'}=\text{P}\left(t\right)\text{x+g}\left(t\right)$.