The solution of the differential equation (x+1) (d y)/(d x)=1+y is

$(x+1) \frac{d y}{d x}=1+y \Rightarrow \int \frac{1}{1+y} d y=\int \frac{1}{1+x} d x$

$\Rightarrow \log |1+y|=\log |1+x|+\log |c|$

taking logarithmic constant

for convenience

so  $\log |1+y|=\log |c(1+x)|$

$\Rightarrow \frac{1+y}{1+x}=c$  or  $\frac{1+x}{1+y}=c$

Option: 3