The solution of $$x+ydy/dxy$$−$$xdy/dx=xsin2$$⁡$$x2+y2y3$$ is given by

Correct option is 1−cotx2+y2=xy2+c

Questions

$The solution of \frac{x + y d y / d x}{y - x d y / d x} = \frac{x \sin^{2} (x^{2} + y^{2})}{y^{3}} is given by$

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−cotx2+y2=xy2+c

tanx2+y2=x2y2+c

cotx2+y2=xy+c

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detailed solution

Correct option is A

x+ydydxy−xdydx=xsin2x2+y2y3 xdx+ydyydx−xdy=xsin2⁡x2+y2y3xdx+ydysin2⁡x2+y2=x(ydx−xdy)y3⇒d−cot⁡x2+y22=xydx−x2dyy3=xyydx−xdyy2⇒d−cot⁡x2+y2=2xydyx−xdyy2⇒d−cot⁡x2+y2=dxy2⇒−cot⁡x2+y2=xy2+c

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The solution of x+ydy/dxy−xdy/dx=xsin2⁡x2+y2y3 is given by

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$The solution of \frac{x + y d y / d x}{y - x d y / d x} = \frac{x \sin^{2} (x^{2} + y^{2})}{y^{3}} is given by$