Generally it is not recommended to perform edits from the back end in the system tables, however please make sure you have a full current backup of the database before performing the below queries:
1) Check if any of the below system tables have entries for city_2 feature class using SQL server management studio.
select * from dbo.GDB_ITEMS where Name = 'Featureclassname'
Select * from SDE_table_registry where table_Name = 'Featureclassname';
Select * from SDE_column_registry where table_Name = 'Featureclassname';
Select * from SDE_geometry_columns where f_table_name = 'Featureclassname';
Select * from SDE_layers where table_name = 'Featureclassname';
2) If you are able to find entries in some of the tables, you could try removing them using the following:
delete from dbo.GDB_ITEMS where Name = 'Featureclassname';
delete from SDE_table_registry where table_Name = 'Featureclassname';
delete from SDE_column_registry where table_Name = 'Featureclassname';
delete from SDE_geometry_columns where f_table_name = 'Featureclassname';
delete from SDE_layers where table_name = 'Featureclassname';