<?php if(is_home()): ?>

<div>Your div.</div>

<?php endif; ?>

<?php if(is_home()): ?>

<div>Your div.</div>

<?php endif; ?>

<?php if(is_front_page()): ?>

<div>Your div.</div>

<?php endif; ?>

<?php if( $_SERVER['REQUEST_URI'] == '/' ) { ?>
<div id="home_only">Content goes here..</div>
<?php } ?>

#your-div{
display: none;
}

.body-class-page-id #your-div {
display: block;
}

<?php if( $_SERVER['REQUEST_URI'] == '/' ) { ?>
<div id="home_only">Content goes here..</div>
<?php } ?>