If you only have one mail account in your Eudora, click on the Tools menu and select Options...

In the options screen, click on the Sending Mail icon and select the check box labeled Allow authentication.  Click Ok and you are done.

If you are running multiple accounts, click on the Tools menu, then the Personalities option.  In the Personalities window, select your MainTree account and select Properties.

In the Generic Properties, select the Authentication Allowed check box then click Ok and you are done.