dr + (2r cot θ + sin 2θ) dθ = 0
\(\therefore\) \(\cfrac{dr}{d\theta}\) + (2r cot θ + sin 2θ) = 0
\(\therefore\) \(\cfrac{dr}{d\theta}\) + (2 cot θ)r = -sin 2θ ……(1)
This is the linear differential equation of the form dr
\(\cfrac{dr}{d\theta}\) + P . r = Q, where P = 2 cot θ and Q = -sin 2θ
\(\therefore\) the solution of (1) is given by
This is the general solution.