With only a door being open after knocking, I would also say not to enter.
Nothing wrong with putting someone on the back door and front door - then attempting to contact the homeowners. Try using phone numbers for prior calls for service or case reports.
Next, contact neighbors. If you get a hold of a neighbor and they say the people are on vacation and always lock their door - now you got something.
Or, if you look inside the windows of the home and see someone in need of help or signs of a residential burglary.
I just don't see any exigency to enter right away without at least taking a few steps to figure out what is going on first.