Ruby Doc has two sections: Core and Standard. Core comes by default and standard has additional libraries/methods etc. Does it mean I have to require these stan
Yep, you got it right. Core functionality is everything you don't have to require to use.
DateTime seems to be not in the core (are you running your line inside of rails console, maybe?)
DateTime.now # =>
# ~> -:1:in `<main>': uninitialized constant DateTime (NameError)
But Time is
Time # => Time
Time.now # => 2013-08-29 12:32:54 +0400
Only a few methods of Time are in core, though. To get more functionality (like Time.parse) you have to
require 'time'