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)⇒logxy=xy+c
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