A) \[y=x\log x-x+2\]
B) \[y=(x+1)\log |x+1|-x+3\]
C) \[y=(x+1)\log |x+1|+x+3\]
D) \[y=x\log x+x+3\]
E) \[y=-(x+1)\log |x+1|+x+3\]
Correct Answer: B
Solution :
Given differential equation is \[{{e}^{dy/dx}}=(x+1)\] \[\Rightarrow \] \[\frac{dy}{dx}=\log (x+1)\] \[\Rightarrow \] \[dy=\log (x+1)dx\] \[\Rightarrow \] \[\int{dy}=\int{\log (x+1)}dx\] \[\Rightarrow \] \[y=(x+1)\log |x+1-x+c\] \[\because \] \[x=0,\text{ }y=3\] \[\therefore \] \[c=3\] \[\therefore \] \[y=(x+1)\log |x+1|-x+3\]
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