The solution of the differential equation (y+xxy(x+y))dx+(yxy(x+y)−$$x)dy=0$$ is

Correct option is 3x2+y22+2tan−1xy=c

Questions

$The solution of the differential equation (y + x \sqrt{x y} (x + y)) d x + (y \sqrt{x y} (x + y) - x) d y = 0 is$

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x2y22+tan−1xy=c

x2+y22+tan−1yx2=c

x2+y22+2tan−1xy=c

x2+y2+tan−1x2y=c

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detailed solution

Correct option is C

ydx−xdy+xxy(x+y)dx+yxy(x+y)dy=0ydx−xdy+(x+y)xy(xdx+ydx)=0ydx−xdyy2+xy+1xydx2+y22=0dx2+y22+dxyxy+1xy=0⇒x2+y22+2tan−1⁡xy=c

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The solution of the differential equation (y+xxy(x+y))dx+(yxy(x+y)−x)dy=0 is

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$The solution of the differential equation (y + x \sqrt{x y} (x + y)) d x + (y \sqrt{x y} (x + y) - x) d y = 0 is$