SharePoint 2010: Databases running in compatibility range, upgrade recommended

Problem
You find the following entry in the SharePoint 2010 Central Administration Review problems and solutions All Reports listing:

Title	Databases running in compatibility range, upgrade recommended
Severity	2 - Warning
Category	Configuration
Explanation	The following databases have versions that are older than the current SharePoint software, but are within the backwards compatible range: ...
Remedy	To achieve optimal results from these databases, use Upgrade-SPContentDatabase to upgrade Content databases, or psconfig.exe to upgrade other databases.  For more information about this rule, see "http://go.microsoft.com/fwlink/?LinkID=142697".
Failing Servers
Failing Services	SPTimerService (SPTimerV4)
Rule Settings	View

 
This problem can also occur for the BDC database.  Performing a Psconfig upgrade does not resolve it.  However, a simple solution is available.

Solution

• Content Database: In an elevated SharePoint 2010 management shell, execute the PowerShell command presented in the message.
• BDC Database: In an elevated SharePoint 2010 management shell, execute the following command: (Get-SPDatabase | ?{$_.type -eq "Microsoft.SharePoint.BusinessData.SharedService.BdcServiceDatabase"}).Provision(). 

References

• Upgrade-SPContentDatabase
• "Database is in compatibility range and upgrade is recommended" for BDCServiceDatabase after March 2013 Upgrade

Notes

• If this fails, verify that the SharePoint 2010 Timer service has been started.
• The above solutions also work for SharePoint 2013.
• Thanks to Markus Hintner for the solution to this problem when it occurs for the BDC database.