public DatabaseConnectionProperties( 
   EnterpriseDatabaseType databaseManagementSystemType
)

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
        }
    });
}