Derive Equations 6.71 and 6.72,

\[ \begin{aligned} x_{1}(t) & =B_{1}^{\prime} e^{-a_{1} t} \cos \left(\omega_{d 1} t-\phi_{d 1}^{\prime}\right) \\ & +B_{2}^{\prime} e^{-a_{2} t} \cos \left(\omega_{d 2} t-\phi_{d 2}^{\prime}\right) \\ x_{2}(t) & =B_{1} e^{-a_{1} t} \cos \left(\omega_{d 1} t-\phi_{d 1}\right) \\ & +B_{2} e^{-a_{2} t} \cos \left(\omega_{d 2} t-\phi_{d 2}\right) \end{aligned} \]