SYSDATE is an Oracle only function.
The ANSI standard defines current_date or current_timestamp which is supported by Postgres and documented in the manual:
http://www.postgresql.org/docs/current/static/functions-datetime.html#FUNCTIONS-DATETIME-CURRENT
(Btw: Oracle supports CURRENT_TIMESTAMP as well)
You should pay attention to the difference between current_timestamp, statement_timestamp() and clock_timestamp() (which is explained in the manual, see the above link)
The part where up_time like sysdate does not make any sense at all. Neither in Oracle nor in Postgres. If you want to get rows from “today”, you need something like:
select up_time
from exam
where up_time = current_date
Note that in Oracle you would probably want trunc(up_time) = trunc(sysdate) to get rid of the time part that is always included in Oracle.