Value at a given point from a differential equation

Question

Given $$y\dfrac{dy}{dx}=x+y$$. What is the substitution for $y$ which can yield a solution?

Answer 1

With $$y(x)=xv(x)$$ we get the equation $$\frac{dv(x)}{dx}=\frac{-v(x)^2+v(x)+1}{xv(x)}$$