Bootstrap Carousel with dynamic items does not slide

as in http://bootply.com/83370 with your carousel having class .carousel

$('.carousel').carousel({interval:false});
$('.carousel-inner').append('<div class="item"><img data-src="holder.js/900x500/auto/#555:#5555" src="data:image/png;base64,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" alt="900x500"><div class="carousel-caption"><h3>Third slide label</h3><p>Praesent commodo cursus magna, vel scelerisque nisl consectetur.</p></div></div>');
$('.carousel-indicators li').removeClass('active');
$('.carousel-indicators').append('<li data-target="#carousel-example-captions" data-slide-to="1" class="active"></li>');
$('.carousel').carousel('next');

Removing the carousel data and then triggering it again does the job!

$("#main-navigation-carousel").carousel("pause").removeData();
$("#main-navigation-carousel").carousel(target_slide_index);

Since the carousel should not auto slide it is important to use .carousel("pause").removeData().

Try this :

<!-- Carousel -->
<div id="myCarousel" class="carousel slide" data-ride="carousel">
    <!-- Indicators -->
    <ol class="carousel-indicators" id="car_id"></ol>
    <div class="carousel-inner" id="car_inner"></div>
    <a class="left carousel-control" href="#myCarousel" role="button" data-slide="prev"><span class="glyphicon glyphicon-chevron-left"></span></a>
    <a class="right carousel-control" href="#myCarousel" role="button" data-slide="next"><span class="glyphicon glyphicon-chevron-right"></span></a>
</div><!-- /.carousel -->

//json data result = [{"id_img": 17,"img_filename": "ca0d8455-2702-4560-a444847429e36670.jpg"},{"id_img": 18,"img_filename": "eb0c6c77-fbd7-4f2c-bf22-10c874eefbf6.jpeg"},{"id_img": 19,"img_filename": "e7568c87-babb-4049-aed6-27b97866a817.png"}]
    var x = $.getJSON('../Json/GetImage', function (data) {
      $("#myCarousel").carousel("pause").removeData();
      var content_indi = "";
      var content_inner = "";
      $.each(data, function (i, obj) {
        content_indi += '<li data-target="#myCarousel" data-slide-to="' + i + '"></li>';
        content_inner += '<div class="item" style="background:url(&#39/images/' + obj.img_filename + '&#39) no-repeat center center;background-size: cover"></div>';
      });
      $('#car_id').html(content_indi);
      $('#car_inner').html(content_inner);
      $('#car_inner .item').first().addClass('active');
      $('#car_indi > li').first().addClass('active');
      $('#myCarousel').carousel();
    });