I would like to know if i can put a mobile home in my backyard?

I think this is a question you need to ask your landlord, as well as the city or town in which you live. Most likely, there are zoning ordinances which regulate whether or not you can permanently park a mobile home on a residential lot.

Just to add to this answer... Even if the zoning ordinance permits what you're trying to do, if the house is part of a homeowner's association, there many also be certain restrictive covenants in the community's bylaws which prohibits the storing of mobile homes. You're better to do your homework now, rather than find yourself being cited for any number of potential violations later.