The solution of differential equation $$x+yy1y$$−$$xy1=x2+2y2+y4x2$$ is

Correct option is 21x2+y2=2yx+c

Questions

$The solution of differential equation \frac{x + y y^{1}}{y - x y^{1}} = x^{2} + 2 y^{2} + \frac{y^{4}}{x^{2}} is$

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1x2−y2=2xy+c

1x2+y2=2yx+c

lnx2+y2=2yx+c

lnx2+y2=2xy=c

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detailed solution

Correct option is B

xdx+ydyydx−dxy=x2+2y2+y4x2=x4+2x2y2+y4x2=x2+y22x2⇒xdx+ydyx2+y22=ydx−xdyx212∫2xdx+2ydyx2+y22=xdy−ydxx2 Integrations on both sides 12x2+y2=yx+c⇒1x2+y2=2yx+c

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The solution of differential equation x+yy1y−xy1=x2+2y2+y4x2 is

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$The solution of differential equation \frac{x + y y^{1}}{y - x y^{1}} = x^{2} + 2 y^{2} + \frac{y^{4}}{x^{2}} is$