cannot display image file to index page, using the edit/update method

when i pass data to my update method, every other input shows, except the image file...pls help me fix this... see the update PostsController

namespace App\Http\Controllers;

use Illuminate\Http\Request;
use App\Post;
use App\Http\Requests\CreatePostRequest;

class PostsController extends Controller
{
    /**
     * Display a listing of the resource.
     *
     * @return \Illuminate\Http\Response
     */
    public function index()
    {
        //
        $posts = Post::orderBy('created_at', 'desc')->paginate(12);
    
        return view('posts.index', compact('posts'));
        
    }

    /**
     * Show the form for creating a new resource.
     *
     * @return \Illuminate\Http\Response
     */
    public function create()
    {
        //renderd the URI(posts/create) for tis mtd
        return view('posts.create');
    }

    /**
     * Store a newly created resource in storage.
     *
     * @param  \Illuminate\Http\Request  $request
     * @return \Illuminate\Http\Response
     */
    public function store(CreatePostRequest $request)
    {
        //1. saving everytin frm the $request obj frm the form
        $input = $request->all();

        //2. storing the filename in the object, into $file variable, that is if the user actually choose a file
        if($file=$request->file('cover_image')){

            //3. storing the name of the file
            $filenameWithExt = $file->getClientOriginalName();

            //get just filename using php
            $filename = pathinfo($filenameWithExt, PATHINFO_FILENAME);

             //get just extension
            $extension = $request->file('cover_image')->getClientOriginalExtension();

              //filename to store
            $fileNameToStore = $filename.'_'.time().'.'.$extension;

            //upload the image
            $path = $request->file('cover_image')->storeAs('public/cover_images', $fileNameToStore);
            
           /*  //4. moving file frm xampp/tmp to image folder, whc wil b found under public
            $file->move('image', $fileNameToStore); */

            //5. equal the path column in db, to equal the filename
            $input['cover_image'] = $fileNameToStore;
        } else {
            $fileNameToStore = 'noimage.jpg';//if no image is deliberately selectd, use this deafault image
        }

        //now create evrytin to the db
        Post::create($input);
        return redirect('/posts');
        
        
        /* //files
        //the $request object a mtd called file, so it takes the name of the form 'file' frm the create view
        $file = $request->file('file');

        echo '<br>';

        echo $file->getClientOriginalName();//image name

        echo '<br>';

        echo $file->getClientSize();//image size */


        /* $this->validate($request, [
            'title' => 'required',
            'content' => 'required'  
        ]); */

        //tis returns evrytin to the post.index pg
       // return $request->all();

       //to get a specific inputs
        //return $request->get('title'); //or $request->title;

        //PERSISTING data to db, u can use any of the following groups
        //1. storing all the inputs into the create mtd. note dat this mtd requires u do put fillables in ur Post Model
       /*  Post::create($request->all());
        return redirect('/posts'); */

        //2. storing all inputs into a variable called input. tis useful whn files are invloved to be received
       /*  $input = $request->all();
        $input['title'] = $request->title;
        $input['content'] = $request->content;
        Post::create($request->all());   */
      
        //3. instantiating the class u want to create
        /* $post = new Post;
        $post->title =  $request->title;
        $post->content =  $request->content;
        $post->save(); */

        //at last we get redirected to the posts pg
    }

    /**
     * Display the specified resource.
     *
     * @param  int  $id
     * @return \Illuminate\Http\Response
     */
    public function show($id)
    {
        //
        $post = Post::findOrFail($id);
        return view('posts.show', compact('post'));
    }

    /**
     * Show the form for editing the specified resource.
     *
     * @param  int  $id
     * @return \Illuminate\Http\Response
     */
    public function edit($id)
    {
        //
        $post = Post::findOrFail($id);
        return view('posts.edit', compact('post'));
    }

    /**
     * Update the specified resource in storage.
     *
     * @param  \Illuminate\Http\Request  $request
     * @param  int  $id
     * @return \Illuminate\Http\Response
     */
    public function update(Request $request, $id)
    {
        
        //1. saving everytin frm the $request obj frm the form
        $input = $request->all();

        //2. storing the filename in the object, into $file variable, that is if the user actually choose a file
        if($file=$request->file('cover_image')){

            //3. storing the name of the file
            $filenameWithExt = $file->getClientOriginalName();

            //get just filename using php
            $filename = pathinfo($filenameWithExt, PATHINFO_FILENAME);

             //get just extension
            $extension = $request->file('cover_image')->getClientOriginalExtension();

              //filename to store
            $fileNameToStore = $filename.'_'.time().'.'.$extension;

            //upload the image
            $path = $request->file('cover_image')->storeAs('public/cover_images', $fileNameToStore);
            
           /*  //4. moving file frm xampp/tmp to image folder, whc wil b found under public
            $file->move('image', $fileNameToStore); */

            //5. equal the path column in db, to equal the filename
           /*  $input['cover_image'] = $fileNameToStore; */

            
        } /* else {
            $fileNameToStore = 'noimage.jpg';//if no image is deliberately selectd, use this deafault image
        } */

        //find the post->id sent frm the edit form
        $post = Post::findOrFail($id);

        if($request->hasFile('cover_image')){
            $input['cover_image'] = $fileNameToStore;
        }

        //update the object, by passing all values into it
        $post->update($input);
    
        return redirect('/posts');

        
    }

    /**
     * Remove the specified resource from storage.
     *
     * @param  int  $id
     * @return \Illuminate\Http\Response
     */
    public function destroy($id)
    {
        //
        //find the post->id sent frm the edit form
        $post = Post::findOrFail($id);

        
        if($post->cover_image !== 'noimage.jpg'){
            //Delete Image
            Storage::delete('public/cover_images/'.$post->cover_image);
        }

        //delete the object, with a particular id
        $post->delete($id);
        return redirect('/posts');
    }
}

see my index view:

@section('content')
    <h1>All Posts Page</h1>
    <ul>
        @foreach($posts as $post)
            <li class="list-group-item">
                <div class="img-style">
                    <img class="img-responsive" width="30%" src="/storage/cover_images/{{$post->cover_image}}" alt="">
                </div>
                <a href="{{route('posts.show', $post->id)}}">{{$post->title}}</a> <br>
                    {{$post->content}}
            </li><br><br>
        @endforeach
    </ul>
@endsection ```

see my route:
```<?php

/*
|--------------------------------------------------------------------------
| Web Routes
|--------------------------------------------------------------------------
|
| Here is where you can register web routes for your application. These
| routes are loaded by the RouteServiceProvider within a group which
| contains the "web" middleware group. Now create something great!
|
*/

Route::get('/', function () {
    return view('welcome');
});

/*
|--------------------------------------------------------------------------
| UGOBLOG ROUTES
|--------------------------------------------------------------------------
|
| Here is where you can register web routes for your application. These
| routes are loaded by the RouteServiceProvider within a group which
| contains the "web" middleware group. Now create something great!
|
*/
/* to activate the $error msg truout our appln */
Route::group(['middleware'=>'web'], function(){
    Route::resource('/posts', 'PostsController');
});