How can I only backup the operating system

You need to include the windows namespace folders.

Basically these:
Documents and Settings
Boot
PerfLogs
Program Files
Program Files (x86)
ProgramData
Users
Windows
bootmgr


and also bootmgr and boot folder if you have that on your os partition

Move the contents of your Windows personal user folders (Documents, Desktop,Pictures, etc). Note move just the contents, the folders must remain to maintain the integrity of the Win 10 setup structure.

My example ...
- periodically run Robocopy to move user folder contents to another partition/drive (use the MOV command line option, MOVE command line option will delete the empty folder. You don't want that.

- separately backup this partition/drive - I use SynchbackFree; backups files in native format)

- then use Macrium Reflect (freeware) to create an image of the OS and program files (i.e. without user created files, although there might be the odd one here-and-there. Meh!)

Can be done manually, as/when required or scheduled using Task Scheduler.

In most cases, there are minimal user created files to move - most programs allow re-direction of default Save/Save as/Open user folder, away from the Windows default C:\Users\{username}\Documents, etc

Macrium Reflect (and others I suppose) can be set to automatically manage the number of image files kept on your backup disk so only the most recent 1,2,5.. whatever you wish.. are kept. Good choices mean you are unlikely to run out of backup space with an appropriately sized external disk, for example.

You are prompted to configure this when creating your first image.

The first image is the largest- subsequent differential images (difference between first and 'now') are smaller e.g. under half the size of the first.

1Tb external disks are around £40- maybe less. 2Tb a bit more.

How much is a secure backup worth to you? How much time would it cost you if you didn't have an adequate one? That's what you need to decide, I suggest.

You need to back up all partitions comprising the O/S - typically 4 for UEFI. The other 3 besides the Windows partition are small.

The answer to your question somewhat depends on whether your data is on the C drive or in a separate partition.

To me, the best solution is to keep data on a separate drive (if only one drive, a separate partition).

Then you can use the excellent Macrium Reflect Free to backup all partitions (except partition/drive containing your data).

One way to do this if you are using a single drive is to create a separate partition for your user files. You can easily move your large user folders containing documents, photos, videos and other stuff to that partition.

Your C: partition will then contain only the Windows OS and any programs you have chosen to install there. Then use a respected backup program like Macrium Reflect Free to backup (image) your C: drive and the other hidden partitions required to boot Windows to another location of your choice.

I use this method on a laptop having only one drive to do a scheduled backup of the OS to the second partition I mentioned. This is high risk if the drive fails so I also have other external backups.

Steve C said:

One way to do this if you are using a single drive is to create a separate partition for your user files. You can easily move your large user folders containing documents, photos, videos and other stuff to that partition.

Your C: partition will then contain only the Windows OS and any programs you have chosen to install there. Then use a respected backup program like Macrium Reflect Free to backup (image) your C: drive and the other hidden partitions required to boot Windows to another location of your choice.

I use this method on a laptop having only one drive to do a scheduled backup of the OS to the second partition I mentioned. This is high risk if the drive fails so I also have other external backups.

As I said in previous post .