Command started a process using PID

You could use the -o switch to specify your output format:

$ ps -eo args

From the man page:

    Command with all its arguments as a string. Modifications to the arguments may be shown. [...]

You may also use the -p switch to select a specific PID:

$ ps -p [PID] -o args

pidof may also be used to switch from process name to PID, hence allowing the use of -p with a name:

$ ps -p $(pidof dhcpcd) -o args

Of course, you may also use grep for this (in which case, you must add the -e switch):

$ ps -eo args | grep dhcpcd | head -n -1

GNU ps will also allow you to remove the headers (of course, this is unnecessary when using grep):

$ ps -p $(pidof dhcpcd) -o args --no-headers

On other systems, you may pipe to AWK or sed:

$ ps -p $(pidof dhcpcd) -o args | awk 'NR > 1'
$ ps -p $(pidof dhcpcd) -o args | sed 1d

Edit: if you want to catch this line into a variable, just use $(...) as usual:

$ CMDLINE=$(ps -p $(pidof dhcpcd) -o args --no-headers)

or, with grep :

$ CMDLINE=$(ps -eo args | grep dhcpcd | head -n -1)