Design pattern for database manager class

I implemented a class Database Manager that manages operations on two database engines. The class has a private variable databaseEngine which is set before using class methods (drop database, create database, run script, compare, disconnect, etc.) and based on this variable the class recognizes how to behave.

However, and I know it's wrong, Database Manager's methods are full of switch cases like this one:

public void CreateNewDatabase(String databaseName){

switch (databaseEngine){
  case "mysql":
      //Executes a prepared statement for dropping mysql database (databaseName
  break;
  case "postgres":
      //Executes a prepared statement for dropping postgres database (databaseName
  break;
...
    }
}

I require a good advice about this. I want to load everything from configuration and resources folders, I mean, the prepared statement for creating and dropping, etc. If a new database engine needs to be supported, it won't be a headache as It would just require to save sql sripts in a resources file and any other data in a configuration file. Please, suggest me any design pattern useful for this case.