如何从不同日期的mysql数据库中获取数据?

I have table called reservations.And I have following values.

res_id hotel_id room_type start      end        qty
  1048        1 standard  2015-05-18 2015-05-20   1

I have a hotel search option. And if user enter start date as 2015-05-16 and end date as 2015-05-19 and search my bookedrooms.php display zero value for standard room type. My sql query is;

$sql1 = mysql_query("select * from reservations where start >= '".$start."' 

and

end <= '".$end."'   and  room_type = 'standard' ");

if there any error in my checking dates,

start >= '".$start."' and end <= '".$end."' 

Are start and end actual dates? If so you should probably cast them.

"select * from reservations where start >= date('".$start."') and end <= date('".$end."') and room_type = 'standard' "