How can I execute jQuery within a *Basic page* content type node?
I am not sure, but You can try to change filter to Full HTML, or the second method, create template file for that content type like node--NAMEOFNODETYPE.tpl.php and clear cache and put your javascript code inside it.

example:

&lt;div&gt;
     // Here YOUR JAVASCRIPT CODE
     &lt;?php print render($content['body']); ?&gt;
&lt;/div&gt;


Or another method, in template_preprocces_page you can check: for all nodes by one type - just check:

$node = menu_get_object();
if($node-&gt;type == "your type") {
  drupal_add_js('YOUR CODE', 'inline');
}


for only one node by nid:

$node = menu_get_object();
if($node-&gt;nid == YOUR NID) {
  drupal_add_js('YOUR CODE', 'inline');
}