The circuit is given in the figure.

Solution:

$ \begin{gathered} \\ I_1(s)=a+b \\\\ \frac{V_1(s)-V_x(s)}{1}=\frac{V_x(s)}{2}+\frac{V_x(s)-V_2(s)}{2} \\\\ 2 V_1(s)-2 V_x(s)=2 V_x(s)-V_2(s) \\\\ 4 V_x(s)=2 V_1(s)+V_2(s) \\\\ V_x(s)=\frac{1}{2} V_1(s)+\frac{1}{4} V_2(s)....(1) \\\\ \text { KCL } at \text { node }(2) \\\\ I_2(s)+b=C \\\\ \therefore I_2(s)=c-b \\\\ I_2(s)=\frac{V_2(s)}{4}-\left[\frac{V_x(s)-V_2(s)}{2}\right] \\\\ =\frac{1}{4} V_2(s)+\frac{1}{2} V_2(s)-\frac{1}{2} V_x(s) \\\\ =\frac{3}{4} V_2(s)-\frac{1}{2} V_x(s)....(2) \\ \end{gathered} \\ $ …