这个问题在这里已经有答案了：

php中单引号字符串和双引号字符串的区别是什么(12个答案）
两年前关门了。
更新代码以反映双引号与单引号。
我没有用mysql表中的date\u requested值填充，而是得到以下结果。

Date  <input type="text" id="datepicker" name="date_requested" value="$date_requested"> <br/><br/>

此行将在文本框中放置$date\u requested。
我也试过了

Date  <input type="text" id="datepicker" name="date_requested" value="<?php echo "$date_requested" ?>"/> <br/><br/>

这一行将php echo放在文本框中。
任何方向都是值得赞赏的。下面是代码的周围部分：

if($_SERVER['REQUEST_METHOD'] == "POST")
{
    mysql_connect("localhost", "root","") or die(mysql_error()); //Connect to server
    mysql_select_db("first_db") or die("Cannot connect to database"); //Connect to database
    $query = mysql_query("Select * from time_off_requests Where time_off_key='$time_off_key'"); // SQL Query
    $date_requested = $_POST["date_requested"];
    $time_off_begin = $_POST["time_off_begin"];
    $time_off_end = $_POST["time_off_end"];//date
    $use_pto = $_POST["use_pto"];
    $user = $_SESSION["user"];
    $time_off_key = $_SESSION["time_off_key"];
    mysql_query("UPDATE time_off_requests SET date_requested='$date_requested', time_off_begin='$time_off_begin', time_off_end='$time_off_end', use_pto='$use_pto' WHERE time_off_key='$time_off_key'") ;
    header("location: home.php");
}
if($tok_exists)
    {
    Print '
    <form action="edit.php" method="POST">
        Date  <input type="text" id="datepicker" name="date_requested" value="<?php echo "$date_requested" ?>"/> <br/><br/>
        All Day  <input type="checkbox" name="all_day[]" value="no" /> <br/>
        Start Time  <input type="time"  id="timepicker" name="time_off_begin" /> <br/>
        End Time  <input type="time" id="timepicker2" name="time_off_end" /> <br/> <br/>
        Use PTO <Select name="use_pto">
        <option value="">Select</option>
        <option value="Yes">Yes</option>
        <option value="No">No</option>
        </select> <br/><br/>
       <input type ="submit" value="Edit Request">  
    </form>
    ';
    }
    else
    {
        Print '<h2 align="center">There is no data to be edited.</h2>';
    }
?>