I Solving the Brachistochrone problem with friction

This Wolfram Alpha Page contains a derivation of the parametric form of the brachistochrone curve that result from either assuming friction or its absence.

I am asking for help understanding how the solution to the differential equation obtained from applying the Euler-Lagrange equation to the integrand of the the integral representing the total time of descent is obtained. This differential equation can be found on step (30) of the page. I am asking for help in understanding the next step, how setting dy / dx = cot(theta/2) results in the given parametric forms for x and y (in terms of theta), as given in steps (32) and (33).
 
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Is that step simply choosing an integrating factor that fits the differential equation you're trying to solve?
 
Is that step simply choosing an integrating factor that fits the differential equation you're trying to solve?
I don't believe the differential equation is linear, or resolvable into linear form, so I don't think that that would help me get to a solution. I hope you can help me find another way, though.
 
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