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Q.

The solution of the differential yxy+2x2y2dx+xxy−x2y2dy=0 is given by

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a

2logx-logy-1xy=c

b

2logy-logx-1xy=c

c

2logx+logy+1xy=c

d

2logy+logx+1xy=c

answer is A.

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Detailed Solution

xy(ydx+xdy)+x2y2(2ydx-xdy)=0÷by x3y3⇒∫d(xy)x2y2+∫2xdx−1ydy=∫0⇒−1xy+2log⁡|x|−log⁡|y|=c

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