How do I find P as a function of r for a Vanderwaals gas?

[haras]

So, I've been given that archimedes principal for an atmospheric layer of gas on a planet is
dP/dr = -rho*g
where g is constant.

For a vanderwaals gas,
P = rhot*R*T - a*rho^2

I used the quadratic formula & solved for rho and put that into the dP/dr equation. getting...

dP = [((-RT +/- ((RT)^2 - 4aP)^.5) / 2a ] dr

now i need to separate the variables and integrate, to get P as a function of r, but how do i get P out of the right side of the equation?

Thanks!

 

[StatusX]

Don't you need an equation for T?