@ecterrab , Here I am trying to see how to do the general case. I am not in the right direction though. I am using the definition available in the maple for Ricci tensor. Is that how it is to be done? Then I proceed as you have done. However got stuck in the middle. perturbed_metric_(general_case)2.mw

@ecterrab 
Thankyou for your reply, I'll soon upload the maple file with the result I am getting.
within a couple of days I'll upload

@ecterrab Thankyou again, I was looking for this solution. However, as I want to calculate this in frw background. Can you also explain the general case. I tried following your direction by uncommenting the new definition of metric, however, I couldn't find the remaining steps.

Thanking you in advance
Jose

How can I define delta as a function of coordinates? Also, I want the result only up to the first order only. 
 

Also, it would be a great help if someone can tell me how to get linearized Einsteins equations using maple