The solution of the differential equation (d y/d x)+y cot x= sin x is y sin x=k(2 x- sin 2 x)+c then k is

Question

The solution of the differential equation (d y/d x)+y cot x= sin x is y sin x=k(2 x- sin 2 x)+c then k is (A) 1 / 2 (B) 1 / 3 (C) 1 / 4 (D) 1 / 5

Tardigrade Admin · Accepted Answer

I.F. =e∫ cot x d x=ei n sin x= sin x solution is, y sin x=∫ sin 2 x d x+c y sin x=(1/2) ∫(1- cos 2 x) d x+c y sin x=(1/4)(2 x- sin 2 x)+c

Q. The solution of the differential equation $\frac{d y}{d x} + y cot x = sin x$ is $y sin x = k (2 x - sin 2 x) + c$ then $k$ is