I thought it was the other way around!
Anybody could have committed the murder. We don't know who did.
Everybody could have committed the murder. We don't know who did.
Anybody can do that. (Come to think of it. This one is definitely correct.)
Everybody can do that. (Is this one wrong?)
Which of these sentences is correct:
1-What he does for a living isn't difficult. Everybody can do that.
2-Everybody could have commited the murder.
Both are correct. Context is missing. If you mean to say that only one person can do it or could have done it, then use 'anybody'.
'everybody' means, all bodies, every person in the group.
'anybody' means, one body, one person in the group.
That's why I suggested 'anybody'- a crime, like the one on the Orient Express, could have [one of] many perpetrators, but I assumed that his job would be carried out by a single person rather than a group.