My DE course uses an online homework service to distribute and collect homework. One of the problems in this set is to furnish an autonomous DE consistent with the phase portrait below:
I came up with $y' = (y-1)^2(y-3)^2(y-5)^2$, which the program rejected. Have I made a mistake, or has the program?
Edit: Another problem was to find an autonomous DE consistent with the phase portrait
For this, I came up with $(y-1)(y-3)^2(y-5)$. I expanded this into $y^4 - 12y^3 + 50y^2 - 84y + 45$ and got marked correct. When I expanded $(y-1)^2(y-3)^2(y-5)^2$ into $225-690 y +799 y^2 - 444 y^3+127$ $ y^4 -18 y^5 +y^6$ using Walpha, I got marked wrong.
Is there some error I'm making? (And do problems like this actually arise in "real life"?!)