I am developing step by step the problem of the brachystochrone with friction described in Wolfram MathWorld but I don't understand how to go from step 29 to 30, i.e.,
how reduces this equation
$(1+y'^2)(1+\mu y')+2(y-\mu x)y''=0$
into
$\frac{1+y^{\prime 2}}{(1+\mu y^\prime)^2}=\frac{C}{y-\mu x}$