Live Demo: Bootstrap Navbar with Search Box in Dropdown

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Bootstrap Navbar with Search Box in Dropdown</title>
<link href="https://fonts.googleapis.com/css?family=Varela+Round" rel="stylesheet">
<link rel="stylesheet" href="https://fonts.googleapis.com/icon?family=Material+Icons">
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/font-awesome/4.7.0/css/font-awesome.min.css">
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css">
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js"></script>
<style>
	body {
		font-family: 'Varela Round', sans-serif;
	}
	.form-control {
		box-shadow: none;
		border-radius: 4px;
	}
	.form-control:focus {
		border-color: #f08373;
		box-shadow: 0 0 8px rgba(0,0,0,0.1);
	}

.navbar {
		background: #fff;
		padding-left: 16px;
		padding-right: 16px;
		border-bottom: 1px solid #dfe3e8;
		border-radius: 0;
	}
	.navbar .navbar-brand, .navbar .navbar-brand:hover, .navbar .navbar-brand:focus {
		padding-left: 0;
		font-size: 20px;
		padding-right: 50px;
	}
	.navbar .navbar-brand b {
		font-weight: bold;
		color: #eb5844;		
	}
	.navbar ul.nav li a {
		color: #888;
	}
	.navbar ul.nav li a:hover, .navbar ul.nav li a:focus {
		color: #f08373 !important;
	}
	.navbar ul.nav li.active > a, .navbar ul.nav li.open > a {
		color: #eb5844 !important;
		background: transparent !important;
	}
	.search-box {
		width: 100%;
        position: relative;
    }	
    .search-box input {		
		border-color: #dfe3e8;        
		box-shadow: none
    }
	.search-box input, .search-box .btn {
		min-height: 38px;
		border-radius: 2px;
	}
	.search-box .input-group-btn .btn {
		border-color: #eb5844;
		background: #eb5844;
		outline: none;
	}
	.navbar ul li i {
		font-size: 18px;
		line-height: 16px;
	}
	.navbar .navbar-right .dropdown-toggle::after {
		display: none;
	}
	.navbar .dropdown-menu {
		border-radius: 1px;
		border-color: #e5e5e5;
		box-shadow: 0 2px 8px rgba(0,0,0,.05);
	}
	.navbar .dropdown-menu li a {
		padding: 6px 20px;
	}
	.navbar .navbar-right .dropdown-menu {
		width: 400px;
		padding: 20px;
		left: auto;
		right: 0;
        font-size: 14px;
	}
	.hide {
		display: none !important;
	}
	@media (max-width: 768px){
		.navbar .navbar-right .dropdown-menu {
			width: 100%;
			background: transparent;
			padding: 10px 20px;
		}
		.navbar .input-group {
			width: 100%;
		}
	}
</style>
<script>
	$(document).ready(function(){
		var dropdown = $(".navbar-right .dropdown");
		var toogleBtn = $(".navbar-right .dropdown-toggle");
		
		// Toggle search and close icon for search dropdown
		dropdown.on("show.bs.dropdown", function(e){
			toogleBtn.toggleClass("hide");
		});
		dropdown.on("hide.bs.dropdown", function(e){
			toogleBtn.addClass("hide");
			toogleBtn.first().removeClass("hide");
		});
	});
</script>
</head> 
<body>
<nav class="navbar navbar-default navbar-expand-lg navbar-light">
	<div class="navbar-header">
		<a class="navbar-brand" href="#">Brand<b>Name</b></a>  		
		<button type="button" data-target="#navbarCollapse" data-toggle="collapse" class="navbar-toggle">
			<span class="navbar-toggler-icon"></span>
			<span class="icon-bar"></span>
			<span class="icon-bar"></span>
			<span class="icon-bar"></span>
		</button>
	</div>
	
	<div id="navbarCollapse" class="collapse navbar-collapse">
		<ul class="nav navbar-nav">
			<li><a href="#">Home</a></li>
			<li><a href="#">About</a></li>			
			<li class="dropdown">
				<a data-toggle="dropdown" class="dropdown-toggle" href="#">Services <b class="caret"></b></a>
				<ul class="dropdown-menu">					
					<li><a href="#">Web Design</a></li>
					<li><a href="#">Web Development</a></li>
					<li><a href="#">Graphic Design</a></li>
					<li><a href="#">Digital Marketing</a></li>
				</ul>
			</li>
			<li class="active"><a href="#">Pricing</a></li>
			<li><a href="#">Blog</a></li>
			<li><a href="#">Contact</a></li>
		</ul>		
		<ul class="nav navbar-nav navbar-right">			
			<li class="dropdown">
				<a data-toggle="dropdown" class="dropdown-toggle" href="#"><i class="fa fa-search"></i></a>
				<a data-toggle="dropdown" class="nav-link dropdown-toggle hide" href="#"><i class="fa fa-close"></i></a>
				<ul class="dropdown-menu">
					<li>
                        <form>
                            <div class="input-group search-box">								
                                <input type="text" id="search" class="form-control" placeholder="Search here...">
								<span class="input-group-btn">
									<button type="button" class="btn btn-primary"><i class="fa fa-search"></i></button>
								</span>
                            </div>
                        </form>                        
					</li>
				</ul>
			</li>
			<li><a href="#"><i class="fa fa-facebook"></i></a></li>
			<li><a href="#"><i class="fa fa-twitter"></i></a></li>
			<li><a href="#"><i class="fa fa-google-plus"></i></a></li>
			<li><a href="#"><i class="fa fa-pinterest-p"></i></a></li>
		</ul>
	</div>
</nav>
</body>
</html>

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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Bootstrap Navbar with Search Box in Dropdown</title>
<link href="https://fonts.googleapis.com/css?family=Varela+Round" rel="stylesheet">
<link rel="stylesheet" href="https://fonts.googleapis.com/icon?family=Material+Icons">
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/font-awesome/4.7.0/css/font-awesome.min.css">
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css">
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js"></script>
<style>
    body {
        font-family: 'Varela Round', sans-serif;
    }
    .form-control {
        box-shadow: none;
        border-radius: 4px;
    }
    .form-control:focus {
        border-color: #f08373;
        box-shadow: 0 0 8px rgba(0,0,0,0.1);
    }