I am assigning an economics problem to my undergrads, and I have reduced the problem to a differential equation which I do not know how to solve. I can leave the problem for them at the point where the have to find the diff-eq but I would like to present the solution to the equation to them when we go over the problem set. Can anyone help?

Here is the equation:

Find p(v):

(1-v)(v-2p)-(vp-p^2)/p'=0
p(0)=0

The origin of the problem is in 2 sided bargaining. 2 players with valuations drawn from a uniform distribution make Take it or leave it offers to a seller whose valuation is also uniform on zero one.

Any help would be much appreciated.