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
    }
  });
}