Curl get url ID from database

I'm trying to make a car service script. I have did the curl script to get the information which I need (Mark,Model etc..) from a different url, but it works only when I have set the whole url + id in the variable. ex: https://ovi.rdw.nl/default.aspx?kenteken=81-DT-HD where 81-DT-HD must be the platenumber of the car. I'm trying to get the ID from the url like: kenteken.php?id=81-DT-HD but its not working.This is the script so far:

<?php 
$id = $_GET['id'];

$url = 'https://ovi.rdw.nl/default.aspx?kenteken=$id';
$content = file_get_contents($url);
$first_step = explode( '<div class="ui-block-d border ovigrid" id="Merk">' , $content );
$first1_step = explode("</div>" , $first_step[1] ); ?>

When I try to visit the site (www.site.com/kenteken.php?id=81-DT-HD its nothing to display. When I have set the whole url in $url + the id it works but when I try to get the id from somewhere else its not working.