Solve the following differential equations: `(dy)/(dx)=ytanx-2sinx`

Explanation

Given,` frac{dy}{dx}-y tan x=-2 sin x....(1)`
`
Here P=-tanx Rightarrow int P d x=-int tan x d x=-log sec x=log cos x`
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therefore I.F. =e^{log cos {x}}=cos {x}`

Multiplying (1) by I.F ., we get
`
cos x frac{d y}{d x}-y sin x=-2 sin x cos x`

Integrating both sides we get
`
y cos x=-int sin 2 x+c=frac{1}{2} cos 2 x+c`
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