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Question

Find the solution of (2x−y+1)dx+(2y−x−1)dy=0.

A
x2+y2xy+(xy)=c.
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B
x2y2xy+(xy)=c.
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C
x2+y2+xy+(xy)=c.
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D
x2y2+xy+(xy)=c.
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Solution

The correct option is A x2+y2xy+(xy)=c.
Given (2xy+1)dx+(2yx1)dy=0

(2x+1)(dx)+(2y1)dy(ydx+xdy)=0

Integrating we get,

(2x+1)(dx)+(2y1)dydxy=0

x2+x+y2yxy=c

x2+y2xy+(xy)=c.

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