A) \[2(x-y)+\log (x-y)=x+c\]
B) \[2(x-y)-\log (x-y+2)=x+c\]
C) \[2(x-y)+\log (x-y+2)=x+c\]
D) None of these
Correct Answer: C
Solution :
Let \[x-y=v\]and \[\frac{dy}{dx}=1-\frac{dv}{dx},\]thus the equation reduces to \[\frac{dv}{dx}=\frac{v+2}{2v+5}\]Þ\[\int_{{}}^{{}}{\frac{2v+5}{v+2}}dv=\int_{{}}^{{}}{dx}\] Þ \[\int_{{}}^{{}}{\left[ 2+\frac{1}{(v+2)} \right]}dv=\int_{{}}^{{}}{dx}\] Þ \[2v+\log (v+2)=x+c\] or \[2(x-y)+\log (x-y+2)=x+c\].
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