Solve the initial value problem: `dy=cos x\ (2-y\ cosec x)dx`

Explanation

We have,


``
`d y=cos x(2-y {cosec} x) d x `


`Rightarrow quad frac{d y}{d x}=2 cos x-y {cosec} x cdot cos x`


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


``
This is a linear differential equation.


On comparing it with `frac{d y}{d x}+P y=Q`, we get


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