get_header();

use names, and call the homepage header using it’s name :
get_header( $name );
read about it in codex
i tried to apply it but unfortunately my theme does not support custom headers ..

It sounds like you already created a child theme? If so, just copy the header.php from the parent theme’s folder to your child theme’s folder.

Find this code in the header.php file:

<div class="header-image">
	<?php $header_image = get_header_image();
		if ( ! empty( $header_image ) ) { ?>
			<a href="<?php echo esc_url( home_url( '/' ) ); ?>" title="<?php echo esc_attr( get_bloginfo( 'name', 'display' ) ); ?>" rel="home">
				<img src="<?php header_image(); ?>" width="<?php echo get_custom_header()->width; ?>" height="<?php echo get_custom_header()->height; ?>" alt="" />
			</a>
		<?php } // if ( ! empty( $header_image ) ) ?>
	</div>

and replace it with:

<div class="header-image">
	<?php
		if (is_front_page()) {
			$header_image = get_header_image();
			if ( ! empty( $header_image ) ) {
			?>
				<a href="<?php echo esc_url( home_url( '/' ) ); ?>" title="<?php echo esc_attr( get_bloginfo( 'name', 'display' ) ); ?>" rel="home">
					<img src="<?php header_image(); ?>" width="<?php echo get_custom_header()->width; ?>" height="<?php echo get_custom_header()->height; ?>" alt="" />
				</a>
			<?php
			}
		}
	?>
	</div>

You don’t need to worry about the get_header() function. It’s not involved with the header image.

thanks linux that should indeed do the trick