Only backup drive and differential backups Is it possible to restore the differential backup without a full backup, but having backup of the entire hard disk?

Example:


2017-01-01: DIFF backup
2017-01-02: entire hard disk backup (NO FULL backup)
2017-01-03: DIFF backup
2017-01-04: DIFF backup


Any suggestions?
No, differential backups cannot be applied on their own and cannot be applied to a database that has been fully brought online, which one from the entire disk backup would be.  You need to restore a full backup first, with norecovery, then the differential.  

You would also only apply one differential backup, not several, the last diff backup will contain all of the data changed since the last full backup.