html - PHP sql reload not changing page contents

one text

I am making a search function for a page that loads data from an sql db. The page loads all rows upon loading and I need it to update the rows loaded when a search is made. When I search "abyss" I expect abyss1.9.0 to be returned but instead nothing is returned.

<?php
 $currentPage = 'software';
   include("head.php");

 $collapseVal=1;
 $db = new SQLite3('softwareinfo2.db');
 $res = $db->query("SELECT * FROM software ORDER BY Name COLLATE NOCASE ASC");

 $previous = '';
 $count = '1';
 ?>

    <h3>Packages</h3>
     <form name="search_form" action="" method="POST">
         <input type = "text" name="_input" placeholder = "Search...">
         <input type="submit" value="Submit">
     </form>
   <div class = "panel-group" id="accordion">

<?php
    if($_SERVER["REQUEST_METHOD"] == "POST") {
        $res = $db->prepare("SELECT * FROM software WHERE Name LIKE :filter ORDER BY Name COLLATE NOCASE ASC");
        $filter = "%".trim($_POST["_input"])."%";
        $res-> bindValue(':filter', $filter, SQLITE3_TEXT);
        $res->execute();
    } else {
        $res = $db->query("SELECT * FROM software ORDER BY Name COLLATE NOCASE ASC");
    }
?>

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