Try this:
$("#colapse_div").collapsible();
But it will probably fail, cause jQM has a problem while styling a dynqamically created collapsible set.
Best bet is to use good old:
$('[data-role="content]').trigger('create');
This line will restyle all new content added to the div content. You can go even further and use:
$('[data-role="content]').trigger('pagecreate');
This line will restyle all new page content, including footer and header.
Read my other article/answer to find out more about enhancing markup of dynamically added content: jQuery Mobile: Markup Enhancement of dynamically added content
Working jsFiddle example: http://jsfiddle.net/Gajotres/ck6uK/