For the most part the von Kaman-Pohlhausen integral method results in simply ODEs that can be readily solved analytically. The algebra leading to those ODEs can be tedious though. But I don't think it warants using Mathematica to do the algebra. Faster to do it by hand. I have attached some notes on how this can be done for a thermal boundary layer over a flat plate. I have other heat transfer examples that make use of Mathematica at the following sites: https://sites.google.com/site/ekayasolutionsteaching/home

https://sites.google.com/site/chemengwithmathematica/home

Enjoy!

Thanks dear