data don't update in laravel 5.4

Controller:

 public function update(Request $request, $id)
{
    $students = StudentModel::find($id);
    $students->student_name = $request->input('student_name');
    $students->roll_number  = $request->input('roll_number');
    print_r($students);
    $students->save();
    if ($save) {
       return redirect()->back()->with('success', 'Save Successfully !!');
    }
    
}

view :

@extends('layouts/mainlayout')

@section('content')

        <a href="{{ URL::to('add-student') }}" class="btn btn-success">Add Student</a>
        <a href="{{ URL::to('add-course') }}" class="btn btn-success">Add Course</a>
        <a href="{{ URL::to('/') }}" class="pull-right btn btn-info">View all Student</a>
        
    <div class="col-xs-offset-3 col-xs-6">
        <h3 class="text-center">Add Student</h3>
        @if (session()->has('success'))
                <h1 class="text-center text-success">{{ session('success') }}</h1>
            @endif
        <form class="form-horizontal" method="PUT" action="{{ action('HomeController@update',$students['id'])}}"  accept-charset="UTF-8">
                <input type="hidden" name="_token" value="<?php echo csrf_token(); ?>">
            
            <div class="form-group">
                <label class="control-label col-xs-3" for="student_name">Student Name</label>
                <div class="col-xs-9">
                    <input type="text" name="student_name" id="student_name" class="form-control" value="{{$students->student_name}}">
                </div>
            </div>
            <div class="form-group">
                <label class="control-label col-xs-3" for="roll_number">Student Roll</label>
                <div class="col-xs-9">
                    <input type="number" name="roll_number" id="" class="form-control" value="{{ $students->roll_number}}">
                </div>
            </div>
            <div class="form-group">
                <label class="control-label col-xs-3"></label>
                <div class="col-xs-9">
                    <input type="submit" class="btn btn-success" name="submit" value="Submit">
                </div>
            </div>
        </form>
    </div>
</div>

@stop