The differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{\sqrt{1-y^2}}{y}$$ determines a family of circles with

General solution of the differential equation $$\cos x(1+\cos y) \mathrm{d} x-\sin y(1+\sin x) \mathrm{d} y=0$$ is

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