General solution of the differential equation $$\log \left(\frac{d y}{d x}\right)=a x+b y$$ is

The differential equation of all circles which pass through the origin and whose centres lie on $$\mathrm{Y}$$-axis is

The differential equation of all parabolas, whose axes are parallel to $$\mathrm{Y}$$-axis, is

The particular solution of the differential equation $$\left(1+y^2\right) \mathrm{d} x-x y \mathrm{~d} y=0$$ at $$x=1, y=0$$, represents