The solution of $e^{d y / d x}=x+1, y(0)=3$ is

The family of curves whose $x$ and $y$ intercepts of a tangent at any point are respectively double the $x$ and $y$ coordinates of that point is

If a curve passes through the point $$(1,1)$$ and at any point $$(x, y)$$ on the curve, the product of the slope of its tangent and $$x$$ coordinate of the point is equal to the $$y$$ coordinate of the point, then the curve also passes through the point