Find the general solution of the differential equations: `(1+x^2)dy+2x y dx=cotx dx""""(x!=0)`

Explanation

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`(1+x^{2}) d y+2 x y d x=cot x d x`


`frac{d y}{d x}+(frac{2 x}{1+x^{2}}) y=frac{cot x}{1+x^{2}} `


Integrating Factor is ` e ^ {qquad int frac{2 x d x}{1+x^{2}}}=1+x^{2}`


`rightarrow y(1+x^{2})=int cot x d x=log sin x+C`


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The solution of the equation is `y(1+x^{2})=log sin x+C`