Users are under no obligation to accept answers at all. Users also vary in their preferences regarding when to accept an answer; some people may accept an answer months later, for example. Per the help center:
Accepting an answer is not meant to be a definitive and final statement indicating that the question has now been answered perfectly. ...
This has been discussed before on SE meta (links at the end).
The consensus there seems to be: if it seems that a new user does not know about accepting answers, it's appropriate to post a polite comment on the question saying something like:
Welcome to Academia.SE. If one of the answers below fixes your issue, you should accept it (click the check mark ...
What to do in such cases? Could we just report to a mod to accept a correct answer for such posts?
No, even moderators cannot accept an answer to questions other than their own.
The possibility of having answers accepted by the community or moderators was brought up several times on the main Meta (e.g., here) and declined. Briefly: There is no need for it, ...
From the help center:
As the author of the question, you have an additional option:
accepting an answer that you believe is the best solution to your
To accept an answer:
Choose one answer that you believe is the best solution to your
To mark an answer as accepted, click on the check mark beside
the answer to ...
In this case (I saw 34 votes!), I think you could spare 50 reputation units (I'm not sure if points is the right word) to offer a bounty. Then you could write your own answer acknowledging the two contributions, accept your answer, and split the bounty to the two best contributors.
To quote from the site's Tour page:
The person who asked can mark one answer as "accepted".
Accepting doesn't mean it's the best answer, it just means that it worked for the person who asked.
I don't think there's any moral compunction to choose an answer. Accepting just
lets other people know which choice you've made, amongst the answers (...