Laravel multi select options ajax request

I'm trying to add multiple courses for a user using ajax. When I click on submit button, everything else updated but the courses. I don't know what I did wrong. Please help me...

This is my blade:

                            <input type="hidden" name="user_id" id="user_id" value="{{$user_details->id}}">
                            @csrf
                            <div class="form-group">
                                <label for="name">Name</label>
                                <input type="text" class="form-control"  id="name"  name="name" value="{{$user_details->name}}">
                            </div>
                            <div class="form-group">
                                <label for="email">Email</label>
                                <input type="text" class="form-control"  id="email"  name="email" value="{{$user_details->email}}">
                            </div>
                            <div class="form-group">
                                <label for="courses_id">Courses</label>
                                @php
                                    $all_courses = $user_details->courses_id;
                                @endphp
                                <select name="courses_id[]" multiple id="course" class="form-control nice-select wide">
                                @foreach($courses as $data)
                                @if($all_courses)
                                    <option @if(in_array($data->id,$all_courses)) selected @endif value="{{$data->id}}">{{$data->title}}</option>
                                @else
                                    <option value="{{$data->id}}">{{$data->title}}</option>
                                @endif
                                @endforeach
                                </select>
                            </div>
                            <button type="submit" class="btn btn-primary mt-4 pr-4 pl-4">{{__('Update User')}}</button>
                        </form>

    <script>
        $(document).ready(function() {

            if($('.nice-select').length > 0){
                $('.nice-select').niceSelect();
            }

            $(document).on('change','select[name="courses_id[]"]',function (e) {
                e.preventDefault();
                var selectedId = $(this).val();
                $.ajax({
                    url : "{{route('admin.user.course.by.slug')}}",
                    type: "POST",
                    data: {
                        _token : "{{csrf_token()}}",
                        id: selectedId
                    },
                    success:function (data) {
                        $('#course').html('');
                        $.each(data,function (index,value) {
                            $('#course').append('<option '+selected+' value="'+value.id+'">'+value.title+'</option>');
                            $('.nice-select').niceSelect('update');
                        });
                    }
                });
            });
        } );
    </script>

My controller:

namespace App\Http\Controllers;

use App\Courses;
use App\User;
use Illuminate\Http\Request;
use Illuminate\Support\Facades\Hash;

class UserController extends Controller
{


    public function edit($id)
    {
        $user_details = User::find($id);
        $courses = Courses::where(['status'=> 'publish'])->get();

        return view('backend.user.edit-user')->with([ 'user_details' => $user_details, 'courses' => $courses]);
    }

    public function user_update(Request $request)
    {

        $this->validate($request, [
            'name' => 'required|string|max:191',
            'email' => 'required|string|max:191',
            'courses_id' => 'nullable',
        ],[
            'name.required' => __('Name is required'),
            'email.required' => __('Email is required'),
        ]);

        User::find($request->user_id)->update([
            'name' => $request->name,
            'email' => $request->email,
            'courses_id' => serialize($request->courses_id),
        ]);

        return redirect()->back()->with(['msg' => __('User Profile Updated Successfully..'), 'type' => 'success']);
    }

    public function course_by_slug(Request $request){
        $all_courses = Courses::where(['status' => 'publish'])->get();
        return response()->json($all_courses);
    }

}

My route: Route::prefix(user')->middleware(['adminPermissionCheck:Users Manage'])->group(function () { Route::get('/edit/{id}', 'UserController@edit')->name('admin.user.edit'); Route::post('/update', 'UserController@user_update')->name('admin.user.update'); Route::post('/course-by-slug', 'UserController@course_by_slug')->name('admin.user.course.by.slug');

});