Exception has occurred. PlatformException (PlatformException(-3, Permission denied, )) - database

Question

I tried to build an application, which should write data in a real time database. I tried an example I found in the internet, but now I get an error. The error I get is:
Exception has occurred.
PlatformException (PlatformException(-3, Permission denied, ))
This is the code I tried:
import 'package:flutter/material.dart';
import 'package:firebase_database/firebase_database.dart';
void main() => runApp(MyApp());
class MyApp extends StatelessWidget {
//final DBRef = FirebaseDatabase.instance.reference();
#override
Widget build(BuildContext context) {
return MaterialApp(
title: "Test",
home: Scaffold(
appBar: AppBar(
title: Text("Testo"),
),
body: Column(
children: <Widget>[
RaisedButton(
child: Text("Write Data"),
onPressed: () {
writeData();
},
),
],
),
),
);
}
void writeData() {
print("pressed");
FirebaseDatabase.instance
.reference()
.child("1")
.set({"id": "ID1", "data": "This is a test"});
}
}
I found in the internet, that my rule in the database could be wrong, that could be the mistake, but I didn't find a solution. This are my rules(I haven´t changed them):
rules_version = '2';
service cloud.firestore {
match /databases/{database}/documents {
match /{document=**} {
allow read, write: if request.time < timestamp.date(2020, 7, 29);
}
}
}
I don´t know why I get this error, hopefully someone can help me.