set input date in datetimepicker code example
Example 1: set datetimepicker javascript
// when start datetimepicker change -> will effect end datetimepicker change too
$('#membership_start').on('dp.change', function(e){
$('#membership_end').data("DateTimePicker").date(e.date);
});
Example 2: datepicker select date programmatically bootstrap
$("#datepicker").datepicker("setDate", new Date);