For my datetime field I used jQuery date/timepicker.
http://trentrichardson.com/examples/timepicker/
This worked fine.
But on the update form, when I try to output date from database on this date/timepicker input field, it does not work. When I inspect the element the date value is there (in correct ui date/timepicker format) as shown in the image below:

How can I make date value from PHP appear on datepicker field ?
Instead of setting the value of the generated input field, pass in a defaultValue argument when you’re creating the picker. See the Options tab, other options, i.e.
This looks like it may only work when selected (e.g. it says “on focus”).
Alternatively, while I’m not familiar with timepicker, you should be able to use the setDate() method to set the date/time, with something like this in a
$(document).readyor similiar: