Find week days date from range of the two dates

<?php
$start    = new DateTime('2013-05-01');
$end      = new DateTime('2013-08-30');
$interval = DateInterval::createFromDateString('1 day');
$period   = new DatePeriod($start, $interval, $end);

foreach ($period as $dt) {
    if ($dt->format("N") == 2 || $dt->format("N") == 4) {
        echo $dt->format("l Y-m-d") . "<br>\n";
    }
}

See it in action

What this code does:

1. Creates a starting date object using DateTime.
2. Creates a starting date object using DateTime.
3. Creates a DateInterval object to represent our interval of time to iterate through. In this case 1 day.
4. Creates a DatePeriod object to manage these objects.
5. Using DatePeriod, it iterates through the date starting with the starting date and ending at the end date. We use DateTime::format() with the N parameter to get the day number of the week. If the day number of the week is 2 (Tuesday) or 4 (Thursday) echo out it's value.

Some PHP-Fu

$start_date = '2013-05-01';
$last_date = '2013-08-30';

$dates = range(strtotime($start_date), strtotime($last_date),86400);
$days = array('tuesday' => array(), 'thursday' => array());

array_map(function($v)use(&$days){
        if(date('D', $v) == 'Tue'){
            $days['tuesday'][] = date('Y-m-d', $v);
        }elseif(date('D', $v) == 'Thu'){
            $days['thursday'][] = date('Y-m-d', $v);
        }
    }, $dates); // Requires PHP 5.3+

print_r($days);

Output

Array
(
    [tuesday] => Array
        (
            [0] => 2013-05-07
            [1] => 2013-05-14
            [2] => 2013-05-21
            [3] => 2013-05-28
            [4] => 2013-06-04
            [5] => 2013-06-11
            [6] => 2013-06-18
            [7] => 2013-06-25
            [8] => 2013-07-02
            [9] => 2013-07-09
            [10] => 2013-07-16
            [11] => 2013-07-23
            [12] => 2013-07-30
            [13] => 2013-08-06
            [14] => 2013-08-13
            [15] => 2013-08-20
            [16] => 2013-08-27
        )

    [thursday] => Array
        (
            [0] => 2013-05-02
            [1] => 2013-05-09
            [2] => 2013-05-16
            [3] => 2013-05-23
            [4] => 2013-05-30
            [5] => 2013-06-06
            [6] => 2013-06-13
            [7] => 2013-06-20
            [8] => 2013-06-27
            [9] => 2013-07-04
            [10] => 2013-07-11
            [11] => 2013-07-18
            [12] => 2013-07-25
            [13] => 2013-08-01
            [14] => 2013-08-08
            [15] => 2013-08-15
            [16] => 2013-08-22
            [17] => 2013-08-29
        )

)

Online demo

$start_date = strtotime("2013-05-01");
$last_date = strtotime("2013-08-30");
while ($start_date <= $last_date) {
    $start_date = strtotime('+1 day', $start_date);
    if (date('N',$start_date) == 2 || date('N',$start_date) == 4){
        echo date('Y-m-d', $start_date).PHP_EOL;
    }
}