how to handle double affiliation in a research article?

I would like to know how to handle the following situation:

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  I was working previously as a part time lecturer, or lecturer paid by hours, in an X university. While working there I developed a lecturing system that helped the students to cope with a subject in computer programming.

  
  


• 
  

  I moved for working in another university Y, in which they employed me for performing lecturing and research tasks. Actually university X did not pay for research, but only for lecturing tasks.

  
  

I have made a research paper based on the lecturing system that I implemented and tested in university X, but the place that will be paying for its actual publication, if accepted; will be my current place of work. So the question that I have is how should I handle that situation?

Should I put a double affiliation like:

Author: Layla
University Y (the place that is actually paying for the research task)
University X (my former place of work where I developed that methodology in my free time)

or should I only put University Y as my main affiliation?

I was wondering if that is possible, because if I put only as my affiliation university X (in which I am not longer working) they would not pay for the research, leaving me with financial problems to publish the article.

Any help?

Thanks