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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.