Use the following code with any HTML/Javascript widget to display search bar in the widgets area. I used Enhanced Text WordPress plugin to implement this code. Enhanced Text WordPress plugin is a plugin which is used in embed HTML, JavaScript or CSS in the widgets area.
Search Bar HTML Code(for Widgets) in WordPress:
OUTPUT:
You can change the width of the search bar widget using the CSS option width. E.g. width:195px;. Replace the text in the form with your URL in the form action tag.