Find the state vector via the formal-solution approach.

\(\dot{\mathbf{x}}=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ -1 & -2 & -3\end{array}\right] \mathbf{x}+\left[\begin{array}{l}0 \\ 0 \\ \frac{1}{4}\end{array}\right] u, u=e^{-t / 3} \sin t, \quad \mathbf{x}(0)=\left\{\begin{array}{l}0 \\ 1 \\ 0\end{array}\right\}\)