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Question

Solution of (xy2+x)dx+(yx2+y)dy=0

A
(x2+1)(y2+1)=c
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B
(xy+1)(xy1)=c
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C
(x3+1)(y3+1)=c
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D
(1x2)(1y2)=c
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Solution

The correct option is A (x2+1)(y2+1)=c
x(y2+1)dx+y(x2+1)dy=0
(2xx2+1)dx+(2yy2+1)dy=0
let t=x2+1>k=y2+1dt=2xdxdk=2ydy
dtt+dkk=log c
kt=c
(x2+1)(y2+1)=c

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