要在ViewModel中观察数据库的更改，可以使用Android Jetpack组件中的LiveData和Room来实现。以下是一个示例解决方案的代码示例：

1. 创建一个包含数据库操作的Repository类，例如MyRepository：

public class MyRepository {
    private MyDao myDao;
    private LiveData> myEntities;

    public MyRepository(Application application) {
        MyDatabase db = MyDatabase.getInstance(application);
        myDao = db.myDao();
        myEntities = myDao.getAllMyEntities();
    }

    public LiveData> getAllMyEntities() {
        return myEntities;
    }

    public void insertMyEntity(MyEntity myEntity) {
        new InsertAsyncTask(myDao).execute(myEntity);
    }

    private static class InsertAsyncTask extends AsyncTask {
        private MyDao asyncTaskDao;

        InsertAsyncTask(MyDao dao) {
            asyncTaskDao = dao;
        }

        @Override
        protected Void doInBackground(final MyEntity... params) {
            asyncTaskDao.insert(params[0]);
            return null;
        }
    }
}

2. 在ViewModel中观察数据库的更改，例如MyViewModel：

public class MyViewModel extends AndroidViewModel {
    private MyRepository repository;
    private LiveData> myEntities;

    public MyViewModel(@NonNull Application application) {
        super(application);
        repository = new MyRepository(application);
        myEntities = repository.getAllMyEntities();
    }

    public LiveData> getAllMyEntities() {
        return myEntities;
    }

    public void insertMyEntity(MyEntity myEntity) {
        repository.insertMyEntity(myEntity);
    }
}

3. 在Activity或Fragment中使用ViewModel来观察数据库的更改，例如MyActivity：

public class MyActivity extends AppCompatActivity {
    private MyViewModel myViewModel;
    private MyAdapter myAdapter;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_my);

        myViewModel = ViewModelProvider.AndroidViewModelFactory.getInstance(getApplication()).create(MyViewModel.class);
        myAdapter = new MyAdapter();

        RecyclerView recyclerView = findViewById(R.id.recyclerView);
        recyclerView.setLayoutManager(new LinearLayoutManager(this));
        recyclerView.setAdapter(myAdapter);

        myViewModel.getAllMyEntities().observe(this, new Observer>() {
            @Override
            public void onChanged(List myEntities) {
                myAdapter.setMyEntities(myEntities);
            }
        });

        // 插入一个新的实体
        MyEntity newEntity = new MyEntity("Example");
        myViewModel.insertMyEntity(newEntity);
    }
}

这个示例中，MyRepository负责与数据库进行交互，MyViewModel用于将数据提供给Activity或Fragment，并观察数据库更改。当数据库中的数据发生变化时，MyViewModel会通知观察者（在这里是Activity或Fragment），然后更新UI。