find a differential equation whose solution is the given n-parameter family of solutions. r = tan(+c) where c is a constant.

find a differential equation whose solution is the given n-parameter family of solutions.1. r = Θtan(Θ+c) where c is a constant.i tried to differentiate this and then substitute a value for c but the answer given is Θr'=Θ^2+r^2+r and that is not what I got.