Relaxation time approximation and ideal hydrodynamics

[IWantToLearn]

Homework Statement

please check attachment

Homework Equations

please check attachment

The Attempt at a Solution

since the deviation from f_0 to f is linear
then we can write f=f_0 + C where C is some constant
this should be enough to prove the first question (i think so)
for the second part i used the ideal gas equation to drive the partial derivatives with respect to time for density, velocity and temperature
but i couldn't able to get the answer[/B]

 

[IWantToLearn]

unfortunetly there is nothing more