The above equation is of the form i.e. linear differential equation.

Here, P = cot x and Q = cosec x

Integrating factor = e^{∫ P dx}

Considering ∫ P

∵ e^{log x} = x

∴ I.F = sin x

Now, General solution is

⇒ y (I.F) = ∫ Q (I.F) dx + C

⇒ y sin x = ∫ cosec x sin x dx + C

⇒y sin x = x + C

=(D)