determine equation of state from entropy

A_B

1. The problem statement, all variables and given/known data
The entropy is given as
[tex]S=a \left(VNU \right)^{\frac{1}{3}} [/tex]
Find the equation of state.

2. The attempt at a solution
I've tried writing [itex]dS[/itex] in terms of [itex]dP[/itex] and [itex]dT[/itex] then using the fact that [itex]dS[/itex] is a perfect differential equate the partial derivatives of the terms. This got me nowhere. I also tried using Maxwell relations.
[tex]\left( \frac{\partial S}{\partial V} \right) _T = \left( \frac{\partial P}{\partial T} \right) _V[/tex]

Thanks
Alex

A_B

How about I use the definition of temperature?
[tex] \frac{1}{T} = \left( \frac{\partial S}{\partial U} \right) = \frac{a}{3} \left( \frac{VT}{U^2} \right)^{1/3} [/tex]