JSFiddle - React, Tailwind, and code Playground

HTML

<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.4.1/jquery.js"></script>
<script src="http://ajax.googleapis.com/ajax/libs/jqueryui/1.7.2/jquery-ui.min.js"></script>
<link rel="stylesheet" href="http://ajax.googleapis.com/ajax/libs/jqueryui/1.7.2/themes/base/jquery-ui.css">
    <label for="startDate">Date :</label>
    <input name="startDate" id="startDate" class="date-picker" />

CSS

.ui-datepicker-calendar {
    display: none;
}

JavaScript

$(function() {
    $('#startDate').datepicker({
        dateFormat: "mm/yy"
    }) 
    .datepicker('setDate', new Date())
    .datepicker("option", "changeMonth", true)
    .datepicker("option", "changeYear", true)
    .datepicker("option", "showButtonPanel", true)
    .datepicker("option", "onClose", function(e){
         var month = $("#ui-datepicker-div .ui-datepicker-month :selected").val();
         var year = $("#ui-datepicker-div .ui-datepicker-year :selected").val();
         $(this).datepicker("setDate",new Date(year,month,1));
})
});