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Question

Differential equation represents 2xydx+(y2x2)dy=0

A
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C
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D
None of these
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Solution

The correct option is C None of these
Given, 2xydx+(y2x2)dy=0
(y2x2)dydx+2xy=0
Put y=vxdydx=v+xdvdx
(x2+x2v2)(xdvdx+v)+2x2v=0

dvdx=v3vx(v21)(v21)(v3v)dvdx=1x
Integrating both sides

(v21)(v3v)dvdxdx=1xdx
log(v2+1)+logv=logx+c
log(v1+v2)=logx+logCy=C(x2+y2)

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