The solution of D.E is $$x+ydydxy$$−$$xdydx=xcos2$$⁡$$x2+y2y3$$ is

Correct option is 1tanx2+y2=x2y2+C

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$The solution of D.E is \frac{x + y \frac{d y}{d x}}{y - x \frac{d y}{d x}} = \frac{x \cos^{2} (x^{2} + y^{2})}{y^{3}} is$

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tanx2+y2=x2y2+C

cotx2+y2=x2y2+C

tanx2+y2=y2/x2

cotx2+y2=y2/x2+C

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detailed solution

Correct option is A

x+ydydxy−xdydx=xy2 ycos2⁡x2+y2x+ydydxcos2⁡x2+y2=xyy−xdydxy2122x+2ydydxcos2⁡x2+y2=xyy−xdydxy2→12∫sec2⁡x2+y2dx2+y2=∫xyd(x/y)→12tanx2+y2=x2y22+Ctanx2+y2=x2y2+C

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The solution of D.E is x+ydydxy−xdydx=xcos2⁡x2+y2y3 is

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$The solution of D.E is \frac{x + y \frac{d y}{d x}}{y - x \frac{d y}{d x}} = \frac{x \cos^{2} (x^{2} + y^{2})}{y^{3}} is$