Live Demo: Bootstrap Navbar with Search Box in Dropdown

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
<title>Bootstrap Navbar with Search Box in Dropdown</title>
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Varela+Round">
<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/bootstrap/4.5.0/css/bootstrap.min.css">
<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">
<script src="https://code.jquery.com/jquery-3.5.1.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/popper.js@1.16.0/dist/umd/popper.min.js"></script>
<script src="https://stackpath.bootstrapcdn.com/bootstrap/4.5.0/js/bootstrap.min.js"></script>
<style>
body {
	font-family: 'Varela Round', sans-serif;
}
.form-control {
	box-shadow: none;
	border-radius: 4px;
}
.navbar {
	background: #fff;
	padding-left: 16px;
	padding-right: 16px;
	border-bottom: 1px solid #dfe3e8;
	border-radius: 0;
}
.navbar .navbar-brand {
	padding-left: 0;
	font-size: 20px;
	padding-right: 50px;
}
.navbar .navbar-brand b {
	font-weight: bold;
	color: #eb5844;		
}
.navbar .navbar-nav > a {
	margin: 0 0.25rem;
}
.navbar a, .navbar a:active {
	color: #888;
	font-size: 15px;
	background: transparent;
}
.navbar a:hover, .navbar a:focus {
	color: #f08373;
}
.navbar .navbar-nav.show > a, .navbar .navbar-nav > a.active {
    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;
}
.input-group-append .btn, .input-group-append .btn:active {
	border-color: #eb5844;
	background: #eb5844 !important;
}
.navbar .nav-item i {
	font-size: 18px;
	line-height: 16px;
}
.navbar .search-dropdown .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 a {
	padding: 6px 20px;
}
.navbar .search-dropdown .dropdown-menu {
	width: 400px;
	padding: 20px;
	left: auto;
	right: 0;
	font-size: 14px;
}
@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 = $(".search-dropdown");
	var toogleBtn = $(".search-dropdown .dropdown-toggle");
	
	// Toggle search and close icon for search dropdown
	dropdown.on("show.bs.dropdown", function(e){
		toogleBtn.toggleClass("d-none");
	});
	dropdown.on("hide.bs.dropdown", function(e){
		toogleBtn.addClass("d-none");
		toogleBtn.first().removeClass("d-none");
	});
});
</script>
</head> 
<body>
<nav class="navbar navbar-expand-lg">
	<a href="#" class="navbar-brand">Brand<b>Name</b></a>  		
	<button type="button" class="navbar-toggler" data-toggle="collapse" data-target="#navbarCollapse">
		<span class="navbar-toggler-icon"></span>
	</button>
	
	<div id="navbarCollapse" class="collapse navbar-collapse justify-content-start">
		<div class="navbar-nav">
			<a href="#" class="nav-item nav-link">Home</a>
			<a href="#" class="nav-item nav-link">About</a>			
			<div class="nav-item dropdown">
				<a href="#" data-toggle="dropdown" class="nav-item nav-link dropdown-toggle">Services</a>
				<div class="dropdown-menu">					
					<a href="#" class="dropdown-item">Web Design</a>
					<a href="#" class="dropdown-item">Web Development</a>
					<a href="#" class="dropdown-item">Graphic Design</a>
					<a href="#" class="dropdown-item">Digital Marketing</a>
                </div>
            </div>
			<a href="#" class="nav-item nav-link active">Pricing</a>
			<a href="#" class="nav-item nav-link">Blog</a>
			<a href="#" class="nav-item nav-link">Contact</a>
        </div>		
		<div class="navbar-nav ml-auto">			
			<div class="nav-item dropdown search-dropdown">
				<a data-toggle="dropdown" class="nav-item nav-link dropdown-toggle" href="#"><i class="fa fa-search"></i></a>
				<a data-toggle="dropdown" class="nav-item nav-link dropdown-toggle d-none" href="#"><i class="fa fa-close"></i></a>
				<div class="dropdown-menu">
					<div>
                        <form>
                            <div class="input-group search-box">								
                                <input type="text" id="search" class="form-control" placeholder="Search here...">
								<div class="input-group-append">
									<button type="button" class="btn btn-primary"><i class="fa fa-search"></i></button>
								</div>
                            </div>
                        </form>                        
                    </div>
                </div>
            </div>
			<a href="#" class="nav-item nav-link"><i class="fa fa-facebook"></i></a>
			<a href="#" class="nav-item nav-link"><i class="fa fa-twitter"></i></a>
			<a href="#" class="nav-item nav-link"><i class="fa fa-google-plus"></i></a>
			<a href="#" class="nav-item nav-link"><i class="fa fa-pinterest-p"></i></a>
        </div>
	</div>
</nav>
</body>
</html>