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(dy/dx)^2 + 2y cot x dy/dx=y^2 has the solution

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Solution:      

                (fracmathrmd ymathrmd x)^2+2ycot x fracmathrmd ymathrmd x-y^2=0

         Rightarrow       fracmathrmd ymathrmd x=frac-2ycot xpm sqrt4y^2cot^2x+4y^22

        Rightarrow          fracmathrmd ymathrmd x= -y(cot xpm csc x )Rightarrow fracdyy=(-cot xpm csc x)dx

        Rightarrow                        y=fracc1pm cos x

 

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Deependra Verma

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