Error: Data source name not found and no default driver specified

When working with ODBC connections in Ax, you may come across this error message:

[Microsoft][ODBC Driver Manager] Data source name not found and no default driver specified

Or the complete error message:

ODBC operation failed.

Unable to logon to the database.

[Microsoft][ODBC Driver Manager] Data source name not found and no default driver specified

Object 'OdbcConnection' could not be created

Then you check the control panel - Administrative tools - ODBC connections.
And you see your datasource is there. You check the name, and it's spelled ok. So what could be wrong? (Always check the most probable cause of your error message first, a typing error.)

As you might know, the Ax client is a 32 bit application. And nowadays, you might have a 64 bit operating system. Datasources created the default way in a 64 bit operating system cannot be used by Ax. So you need to create a 32 bit datasource.
There is an alternative panel applet to create a 32 bit datasource, fe in Windows Server 2008. You'll find this applet in the C:\Windows\SysWOW64 folder, called odbcad32.exe. (Now watch out, a file by the same name might be available in the C:\Windows\System32 folder. This is NOT the version needed.)

Start the executable C:\Windows\SysWOW64\odbcad32.exe and create your 32 bit datasource. Afterwards, re-execute your code. Did that help make the error go away?
(Some Microsoft info about the issue.)