A) \[{{x}^{2}}+{{y}^{2}}+xy-x+y=c\]
B) \[{{x}^{2}}+{{y}^{2}}-xy+x+y=c\]
C) \[{{x}^{2}}-{{y}^{2}}+2xy-x+y=c\]
D) \[{{x}^{2}}-{{y}^{2}}-2xy+x-y=c\]
Correct Answer: B
Solution :
Given differential equation is \[(2x-y+1)\,dx+(2y-x+1)\,dy=0\] \[\Rightarrow \,\,2x\,dx+2y\,dy-(y\,dx+x\,dy)\] \[+\,dx+dy=0\] \[\Rightarrow \,\,\,(2x\,dx+2y\,dy)-d\,\,(xy)+dx+dy=0\] On integrating both sides, we get \[{{x}^{2}}+{{y}^{2}}-xy+x+y=c\]
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