Thermodynamics Question(Euler's Form)

[derrickb]

Homework Statement

A system obeys the equations:

P=-(NU)/(NV-2AVU)

and

T=2CU^1/2V^1/2e^AU/N/(N-2AU)

Find the fundamental equation
Hint: to integrate let s=Duⁿv^me^-Au

Where D, n, m are constants to be determined.

Homework Equations

Aside from the given ones,
V=Nv
U=Nu
du/ds=T
du/dv=-P

The Attempt at a Solution

I attached a picture of my work. I must have made a small mistake somewhere because I feel like I am very close to the answer.

 

[derrickb]

Here is the picture rotated.