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Question

The solution of (1x1(xy)2)dx+(1(xy)21y)dy=0.

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Solution

Given the difference equation is {1x1(xy)2}dx+{1(xy)21y}dy=0
on, dydxdyy+dydx(xy)2=0
on, dxxdyy+d(yx)(yx)2=0
Now, integrating both sides we have,
log|x|log|y|+(1yx)=c
on, log|x|log|y|=1(yx)+c
where c is integrating constant.


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