Find the general solution of the differential equations: `x(dx)/(dy)+y-x+x ycotx=0(x!=0)`

Explanation

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`x frac{d y}{d x}+y-x+x y cot x=0,(x neq 0)`

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or `x frac{d y}{d x}+y(1+x cot x)=x`

or `frac{d y}{d x}+(frac{1}{x}+cot x) y=1`

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

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`P=frac{1}{x}+cot x`

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