Maybe. But you probably went about it wrong.
An option would have been to first partition the external drive using Apple's Disk Utility with two partitions: one for the Mac and one for Windows/PC. Then you could the same drive for both platforms.
However, that might not be best option. It would be best to dedicate an external drive exclusively to Time Machine. This would mean you would have to backup incrementally unless you have available ports that you can dedicate to each drive (depending on the external drive being either firewire or USB.) If you can dedicate a drive to a port, the Time Machine drive will back up per its settings automatically. Not sure what you're using to backup the Windows side.
Since you mention you have a MacBook Air, its uncertain how you're connecting as the Air has no USB or Firewire ports..
An option would have been to first partition the external drive using Apple's Disk Utility with two partitions: one for the Mac and one for Windows/PC. Then you could the same drive for both platforms.
However, that might not be best option. It would be best to dedicate an external drive exclusively to Time Machine. This would mean you would have to backup incrementally unless you have available ports that you can dedicate to each drive (depending on the external drive being either firewire or USB.) If you can dedicate a drive to a port, the Time Machine drive will back up per its settings automatically. Not sure what you're using to backup the Windows side.
Since you mention you have a MacBook Air, its uncertain how you're connecting as the Air has no USB or Firewire ports..
How Do I Backup Macbook Air To External Hard Drive External
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Nov 05, 2019 Every week, I do a SuperDuper clone of my MacBook Pro's hard drive, just in case, and do incremental backups of my files with Time Machine onto a different drive. (Also, look into a cloud backup solution as well. If you don't have at least one off-site backup of your stuff, you don't really have a backup. I like Backblaze.). Every week, I do a SuperDuper clone of my MacBook Pro's hard drive, just in case, and do incremental backups of my files with Time Machine onto a different drive. (Also, look into a cloud backup solution as well. If you don't have at least one off-site backup of your stuff, you don't really have a backup. I like Backblaze.).