8.3.8 Systems of ordinary differential equations
Problem:
Find the solution of the inhomogeneous system of differential equations:
\[
\left\{\begin{array}{c}
\dot{\bar{x}}=\left(\begin{array}{ll}
0 & 3 \\
3 & 0
\end{array}\right) \bar{x}+\left(\begin{array}{c}
-1 \\
t
\end{array}\right) \\
\bar{x}=\left(\begin{array}{l}
0 \\
1
\end{array}\right)
\end{array}\right.
\]