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Q.

The general solution of the differential equation y(1−xy)dx=x(1+xy)dy is

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a

lnxy=xy+c

b

lnxy=xy+c

c

lny/x=xy+c

d

logxy=x+y+c

answer is A.

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Detailed Solution

ydx-xy2dx=xdy+x2ydy ydx−xdy=xy(xdy+ydx)ydxxy-xdyxy=xdy+ydx⇒∫dxx−dyy=∫d(xy)⇒log⁡xy=xy+c
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The general solution of the differential equation y(1−xy)dx=x(1+xy)dy is