You just need to use the correct methods instead of calling the constructors. Use parseto create local dates and local time objects, then pass two objects to the method of LocalDateTime:
LocalDate datePart = LocalDate.parse("2013-01-02");
LocalTime timePart = LocalTime.parse("04:05:06");
LocalDateTime dt = LocalDateTime.of(datePart, timePart);
EDIT
-, Date 2 . , , SimpleDateFormat. , .
String startingDate = new SimpleDateFormat("yyyy-MM-dd").format(startDate);
String startingTime = new SimpleDateFormat("hh:mm:ss").format(startTime);