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

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Solution:

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

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

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

$Rightarrow$ $y=fracc1pm cos x$

Posted by

Deependra Verma

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