Working example: http://jsfiddle.net/Gajotres/vmZyn/
$(document).on('pageshow', '#index', function(){
$('.ui-collapsible').children().next().hide();
$('.ui-collapsible').children().next().slideDown(1500);
});
You want to use a pageshow event. At that point page you can animate sliding.
In case you want to do it only one (like document ready) use this syntax instead:
$(document).on('pageinit', '#index', function(){
$('.ui-collapsible').children().next().hide();
$('.ui-collapsible').children().next().slideDown(1500);
});
Unlike pageshow, pageinit will trigger only once.