public AuthenticationMode AuthenticationMode {get; set;}

public async Task OpenEnterpriseGeodatabase()
{
    await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
    {
        // Opening a Non-Versioned SQL Server instance.
        DatabaseConnectionProperties connectionProperties = new DatabaseConnectionProperties(EnterpriseDatabaseType.SQLServer)
        {
            AuthenticationMode = AuthenticationMode.DBMS,

            // Where testMachine is the machine where the instance is running and testInstance is the name of the SqlServer instance.
            Instance = @"testMachine\testInstance",

            // Provided that a database called LocalGovernment has been created on the testInstance and geodatabase has been enabled on the database.
            Database = "LocalGovernment",

            // Provided that a login called gdb has been created and corresponding schema has been created with the required permissions.
            User = "gdb",
            Password = "password",
            Version = "dbo.DEFAULT"
        };

        using (Geodatabase geodatabase = new Geodatabase(connectionProperties))
        {
            // Use the geodatabase
        }
    });
}

public async Task DefaultQueryDescription()
{
    await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
    {
        DatabaseConnectionProperties databaseConnectionProperties = new DatabaseConnectionProperties(EnterpriseDatabaseType.SQLServer)
        {
            AuthenticationMode = AuthenticationMode.DBMS,
            Instance = "instance",
            Database = "database",
            User = "user",
            Password = "password"
        };

        using (Database database = new Database(databaseConnectionProperties))
        {
            QueryDescription queryDescription = database.GetQueryDescription("CUSTOMERS");

            using (Table table = database.OpenTable(queryDescription))
            {
                //use table
            }
        }
    });
}