Replacing connection string with a method in factory pattern

Question

I am planning to replace the factory created connection string which is from web.config with a function generated connection string. I am confused where to make this change?

Connection String in Web config as below:

<connectionStrings>
      <add name="ConnectionStringToDB" connectionString="Data Source=GTD,2431;Network Library=DBMSSOCN;Initial Catalog=WorkflowExecutionDB;User ID=Dev_FID;Password=****" providerName="System.Data.SqlClient" />  
  </connectionStrings>

Currently following code will call this above connection string:

  DatabaseProviderFactory factory;            /* enterprise data library*/
  Database ConnectionStringToDB;             /* database schema*/
  factory = new DatabaseProviderFactory();
  // Create a Database object from the factory using the connection string name.
  ConnectionStringToDB = factory.Create("ConnectionStringToDB");
  DbCommand dbCmd = ConnectionStringToDB.GetStoredProcCommand("SP_Name");

Suppose i need to change the connection string which is coming from web-config to function method result as like below, where i need to put the GetConnectionString() in the code? :

 public static string GetConnectionString()
    {
      return "Data Source=GTD,2431;Network Library=DBMSSOCN;Initial Catalog=WorkflowExecutionDB;User ID=Dev_FID;Password=****" providerName="System.Data.SqlClient"     
     }

Following might be wrong:

ConnectionStringToDB = factory.Create(GetConnectionString());

What the is the right way?