How to hide image-url if no attachment?

Assuming you’re following this tutorial:

http://wp.tutsplus.com/tutorials/automagic-post-thumbnails-image-management/

Replace the echo statement at the end of get_attachment_picture with a return, then change your image code.

Here is your new image code:

// get the URL of the image
$src = get_attachment_picture();

// if the url is not empty, display the image
if(!empty($src)){
    ?>
    <img src="https://wordpress.stackexchange.com/questions/48896/<?php echo $src; ?>" />
    <?php
} else {
    // the url was empty, do not display the image
}

Here’s the modified function:

function get_attachment_picture(){  
    global $post, $posts;  
    $related_thumbnail =  get_post_meta($post->ID, 'image', true);                          //read post meta for image url  

    if($related_thumbnail == ""):
        $attachments = get_children( array(  
                                    'post_parent'    => get_the_ID(),  
                                    'post_type'      => 'attachment',  
                                    'numberposts'    => 1,  
                                    'post_status'    => 'inherit',  
                                    'post_mime_type' => 'image',  
                                    'order'          => 'ASC',  
                                    'orderby'        => 'menu_order ASC'  
                                    ) );  
        if(!empty($attachments)):                                               //check if there an attachment or not  
            foreach ( $attachments as $attachment_id => $attachment ) {  
              if(wp_get_attachment_image($attachment_id) != ""):  
                  $related_thumbnail = wp_get_attachment_url( $attachment_id );  
              endif;  
            }  
        else:                                                           // if no attachment  
            $first_img = '';  

            $output = preg_match_all('/<img.+src=[\'"]([^\'"]+)[\'"].*>/i', $post->post_content, $matches);  
            $first_img = $matches [1] [0];  

            if(!empty($first_img)):  
                $related_thumbnail = $first_img;  
            else:  
                $related_thumbnail = "";
            endif; 
        endif; 
    endif;   

    return $related_thumbnail; 
}