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

The general solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{3 x+y}{x-y}$$ is (where $$C$$ is a constant of integration.)