How do we solve the following differential equation?

Question

dr/[ (m/(r^2)) + vcos(theta) ] = r*d(theta)/(-vsin(theta)

The answer is given as vr^2*sin^2(theta) - 2mcos(theta) = k , k is a constant

But I'm really confused how to do this one, since there are several variables involved

Answer 1

only r and θ are the variables involved.
It could just as easily be written as
dr/(m/r^2 + n) = r/k dθ
or,
r/(m+nr^2) dr= 1/k dθ
But that integrates as a log, so sumpn's up.