Dickfore

Yes, this is what I got too. Just rewriting it for further reference:

[tex]
\frac{dp}{du} - \frac{p}{2 u} - \frac{u^{\frac{1}{2}}}{a} - \frac{n u^{2} \, (u - c)}{a \, b \, p} = 0
[/tex]