Laminar flow fixed parallel plates

[MotoPayton]

http://books.google.com/books?id=p7...wAw#v=onepage&q=6.132 fluid mechanics&f=false

Can someone please tell me how they arrived at the equation 6.132 and the equation written directly above it. I can't figure it out and it seems as if they pulled it out of thin air.
Thank you.

 

[Chestermiller]

This all goes back to eqns. 122 and 123, and how you go about solving partial differential equations like these for the pressure. Eqn. 123 can be integrated with respect to y to show that the pressure will be equal to ρgy plus a function of x, f(x) (analogous to the constant of integration in solving an ordinary differential equation). You then substitute that result into equation 122, and find that f(x) is equal to x times the partial derivative of p with respect to x, plus a constant.

 

[MotoPayton]

Ok, I get it now. I didn't see the step of bringing that equation back into the PDE's. I was also confused on how the dp/dx was treated as constant wrt x but on the following page it shows that dp/dx is in fact constant and related to the viscosity and spatial properties.
Thank you.