[Engineer in making]

Hi everyone,
 
I'm trying to solve a fluid problem for isothermal, steady, unidirectional laminar flow of an incompressible non-Newtonian. And was asked to solve the navier stokes equation ( Momentum equation) for it. Here's the diagram:
 
http://prntscr.com/5bwfli
 
Shear stress formula :
http://prntscr.com/5bwful
 
Mementum equation:
http://prntscr.com/5bwdbu
My solution:
http://prntscr.com/5bweal
 
I'm just wondering If my approach for the problem and my solution was right since I'm having doubts about my solution.

[mjc123]

That's not a solution. A solution would give you u_x as a function of y.