1. The problem statement, all variables and given/known data
See attached picture of the problem.
2. Relevant equations
See attached picture of the pair of diff equations.
3. The attempt at a solution
I was able to solve the problem up to the point the picture gets to. However, the author says he obtained this by integrating. I couldn't figure out how to do this by direct integration, so I modified the pair of equations into two 2nd order ODE's, each of one function, and solved them.
Is there a way to directly integrate these equations? I have a feeling I'm going to feel dumb when I hear the answer. Please let me know if you need any more info.
Thanks for your help,