Use mouseenter and leave instead of hover.
<script type="text/javascript">
$('#first').mouseenter(function(){
$('.div1').show();
});
$('#first').mouseleave(function(){
$('.div1').hide();
});
$('#second').mouseenter(function(){
$('.div2').show();
});
$('#second').mouseleave(function(){
$('.div2').hide();
});
</script>
An also find my fiddle for above solution:
fiddle[
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