X $(20$ points$)$ Consider the parallel RLC circuit below with zero initial conditions. Note that the input $x(t)$ is the current source and the output is the current through the inductor.

a$.$ Using KCL$,$ write the equation modeling the system. Note that in the process you need to define the common voltage $v(t)$

b$.$ From the above equation, find the transfer function $H(s).$

c$.$ Find the output $y(t)$ in time domain if $I_s=2A,R=\frac{6}{5},L=1H$ and $C=\frac{1}{6}F$

d$.$ With the parameters above, find the unit step response $s(t)$