Entity simple example and base class. Base class comes from @vkhorikov (https://github.com/vkhorikov/DddInAction/tree/master/DddInPractice.Logic/Common).

Appointment.cs

using System;

class Appointment : Entity
{
    public string Title { get; set; }
    public int PatientId { get; set; }
    public int RoomId { get; private set; }
    public int? DoctorId { get; set; }
    public bool IsConfirmed { get; private set; }
    // Value object
    public DateTimeRange TimeRange { get; private set; }
    
    public Appointment()
    {
        IsConfirmed = false;
    }

    public void UpdateRoom(int newRoomId)
    {
        RoomId = newRoomId;
        // Additional logic here
    }

    public void UpdateTime(DateTimeRange newStartEnd)
    {
        TimeRange = newStartEnd;
        // Additional logic here
    }
}

Entity.cs

public abstract class Entity
{
    public virtual long Id { get; protected set; }

    public override bool Equals(object obj)
    {
        var other = obj as Entity;
        if (ReferenceEquals(other, null))
            return false;
        if (ReferenceEquals(this, other))
            return true;
        if (GetType() != other.GetType())
            return false;
        if (Id == 0 || other.Id == 0)
            return false;

        return Id == other.Id;
    }

    public static bool operator ==(Entity a, Entity b)
    {
        if (ReferenceEquals(a, null) && ReferenceEquals(b, null))
            return true;
        if (ReferenceEquals(a, null) || ReferenceEquals(b, null))
            return false;
        return a.Equals(b);
    }

    public static bool operator !=(Entity a, Entity b)
    {
        return !(a == b);
    }

    public override int GetHashCode()
    {
        return (GetType().ToString() + Id).GetHashCode();
    }
}