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

Explanation

Given equation can be written as,


`frac{d y}{d x}-y tan x=-2 sin x` …..... (1)


Here `P=-tan x`


` Rightarrow int P d x=-int tan x d x=-log sec x=log cos x`


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,


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