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The general solution of the differential equation \[(2x-y+1)dx+(2y-x+1)dy=0\] is    [Karnataka CET 2005]

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.                 \[{{x}^{2}}-{{y}^{2}}-2xy+x-y=c\]
Answer» C.                 \[{{x}^{2}}-{{y}^{2}}+2xy-x+y=c\]


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