Solve the following initial value problem: `(dy)/(dx)+ycotx=2cosx ,\ y\ (pi/2)=0`

Explanation

`frac{d y}{d x}+frac{y cos x}{sin x}=2 cos x `


`Rightarrow sin x frac{d y}{d x}+y cos x=sin 2 x`


`Rightarrow y sin x=frac{-cos 2 x}{2}+c quad quad[c+{ }^{1} / 2=c_{1}]`


`=>y sin x=-cos ^{2}+c_{1} quad`


`Rightarrow y sin x+cos ^{2} x=c_{1}`