Calculating Homothetic Vector Fields

[axlsaml1]

can anyone please give me an example of how to calculate the homothetic vector field of
say

a Bianchi Type I exact solution of the Einstein field equation

(refer to dynamical systems in cosmology by Wainwright and Ellis chapter 9)


note : I know already how to calculate the killing vector field of a homogeneous, isotropic line element

 

[smallphi]

Don't you have to take the given metric, write explicitly the defining differential equations for a homotetic vector field and try to solve these? Is there another way?