How to Add Image to WordPress RSS-Feed with no Plug-in?

Here is a great example. How to display featured post thumbnails in WordPress feeds

paste this code snippet in your theme functions.php file

// display featured post thumbnails in WordPress feeds
function wcs_post_thumbnails_in_feeds( $content ) {
    global $post;
    if( has_post_thumbnail( $post->ID ) ) {
        $content="<p>" . get_the_post_thumbnail( $post->ID ) . '</p>' . $content;
    }
    return $content;
}
add_filter( 'the_excerpt_rss', 'wcs_post_thumbnails_in_feeds' );
add_filter( 'the_content_feed', 'wcs_post_thumbnails_in_feeds' );