The dynamics of a multi input and multi output system with inputs \(x_{1}(t)\) and \(x_{2}(t)\) and outputs \(y_{1}(t)\) and \(y_{2}(t)\) is described by following set of differential equations.
\[
\begin{aligned}
\ddot{y}_{1}(t)+2 \dot{y}_{1}(t)+3 y_{2}(t) & =x_{1}(t)+x_{2}(t) \\
\ddot{y}_{2}(t)+3 \dot{y}_{1}(t)+y_{1}(t)-y_{2}(t) & =x_{2}(t)+\dot{x}_{1}(t)
\end{aligned}
\]
Find transfer functions:
(a) \(\left.\frac{\mathrm{Y}_{1}(s)}{\mathrm{X}_{1}(s)} \right|_{X_{2}=0}\)
(b) \(\left.\frac{\mathrm{Y}_{2}(s)}{\mathrm{X}_{1}(s)} \right|_{X_{2}=0}\)
(c) \(\left.\frac{\mathrm{Y}_{1}(s)}{\mathrm{X}_{2}(s)} \right|_{X_{1}=0}\)
(d) \(\left.\frac{\mathrm{Y}_{2}(s)}{\mathrm{X}_{2}(s)} \right|_{X_{1}=0}\)