Solve the differential equation: `2cosx(dy)/(dx)+4y\ sin x=sin2x ,`given that` \ y=0\ w h e n\ x=pi/3` .

Explanation

It is given that,
`2 \cos x \frac{d y}{d x}+4 y \sin x=\sin 2 x `

`\frac{d y}{d x}+4 y \frac{\sin x}{2 \cos x}=\frac{2 \sin x \cos x}{2 \cos x} `

`\frac{d y}{d x}+2 y \tan x=\sin x`

Comparing with `frac{d y}{d x}+P` and `y=Q`, we get

`P=2 \tan x `

`Q=\sin x`


Now,

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