A) \[{{x}^{2}}-xy+{{y}^{2}}+x+y=c\]
B) \[{{x}^{2}}-xy-{{y}^{2}}+x+y=c\]
C) \[{{x}^{2}}-xy+{{y}^{2}}+x-y=c\]
D) \[{{x}^{2}}+xy+{{y}^{2}}+x+y=c\]
E) \[{{x}^{2}}-xy-{{y}^{2}}-x-y=c\]
Correct Answer: A
Solution :
\[(2x-y+1)dx+(2y-x+1)dy=0\] \[\Rightarrow \]\[2xdx+dx-ydx+2y\text{ }dy+dy-x\text{ }dy=0\] \[\Rightarrow \]\[2x\text{ }dx+dx-d(xy)+2y\text{ }dy+dy=0\] On integrating both sides \[\Rightarrow \] \[2.\frac{{{x}^{2}}}{2}+x-xy+\frac{2.{{y}^{2}}}{2}+y=0\] \[\Rightarrow \] \[{{x}^{2}}+x-xy+{{y}^{2}}+y=c\]
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