I want to remove the default text from search form widget which comes with the WordPress. The code for default search form widget is in the wp-include/default-widgets.php. We can’t modify the core file of WordPress for this.

Here is the better solution so even if you upgrade the WordPress then also you custom code will not be over written with new WordPress files.

To change the default search widget form in WordPress here is the code which you have to put it in functions.php file of your theme :

function override_search_widget(){
<form id="searchform" method="get" action="<?php bloginfo('home'); ?>">
<input type="text" name="s" id="s" size="15" />
<input type="submit" id="searchsubmit" value="<?php echo attribute_escape(__('Search')); ?>" />
if ( function_exists('register_sidebar_widget') )
register_sidebar_widget(__('Search'), 'override_search_widget');