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Question

The solution of the differential equation (x2yx2)dydx+y2+xy2=0 is

A
log(xy)=1x+1y+C
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B
log(yx)=1x+1y+C
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C
log(xy)=1x+1y+C
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D
log(xy)+1x+1y=C
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Solution

The correct option is A log(xy)=1x+1y+C
Given differential equation is
(x2yx2)dydx+y2+xy2=0
1yy2dy+1+xx2dx=0
(1y21y)dy+(1x2+1x)dx=0
On integrating both sides, we get the required solution
2ylogy2x+logx=C
log(xy)=1x+1y+C

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