It looks like the differential equation is
[tex]y'-\dfrac y{x+1}=2[/tex]
Multiply both sides by 1/(x + 1) :
[tex]\dfrac{y'}{x+1}-\dfrac y{(x+1)^2} = \dfrac2{x+1}[/tex]
The left side is now a derivative of a product,
[tex]\left(\dfrac y{x+1}\right)' = \dfrac2{x+1}[/tex]
Integrate both sides with respect to x :
[tex]\dfrac y{x+1} = 2\ln|x+1|+C[/tex]
Solve for y :
[tex]y = 2(x+1)\ln|x+1| + C(x+1)[/tex]
