The cause of this error is that a login is being attempted to a database with the "ApplicationPoolIdentity" account. In a development environment, you would prefer using your credentials to log into a SQL Express database. This can be fixed by doing the following:
- Go to IIS Manager
- Click on Application Pools
- Click on the offending application pool
- Click on the "Advanced Settings ..." link on the right-hand-side
- Find the "Identity" property and change it from "ApplicationPoolIdentity" to "LocalSystem"