General Relativity, form of scale factor

[deadringer]

We are given a form of Einstein's field equations:

3R'' = -pR
R''R + 2((R')^2) = p(R^2)

where p is a constant and R' = dR/dt

Assuimg that R and R' are both positive, we are asked to show that the general solution is R(t) = A*[(t-ti)^(2/3)]

I'm very confused about this. If we substitute the required expression into the given equations it doesn't solve them! This indicates to me that there might be a mistake, but it' an old Oxford exam paper from the Maths department, so it should be reliable. N.b if you solve the above equations simultaneously you should get an exponentially increasing function for R(t).
Either the quesion is wrong or there is something I'm not seeing.

 

[Dick]

Is p supposed to be an energy density? If so then they sort of resemble the Friedmann equations with no pressure if you adjust a coefficient or two. And if p is constant the solution is exponential alright. On the other hand the solution you've given is for matter driven expansion - which is pressureless alright. But energy density=p is not constant in that case p*R(t)^3 is. I'm confused too.

 

[Mentz114]

We are given a form of Einstein's field equations:

3R'' = -pR
R''R + 2((R')^2) = p(R^2)

where p is a constant and R' = dR/dt

If p is constant the equations are independent and may not have a simultaneous solution. I'm confused too.