The differential equation of the family of curves $y = a \cos(x + b)$ is

The order of the differential equation of the family of all concentric circles centered at $(h, k)$ is

Let $a$ and $b$ be arbitrary constants and $C$ be a fixed constant. If $y = a e^{2x} + b x e^{2x} + C$ is the general solution of a differential equation,then the order of that differential equation is

The differential equation of a family of hyperbolas whose axes are parallel to coordinate axes, centres lie on the line $y=2x$ and eccentricity is $\sqrt{3}$ is

The differential equation of $y = A{e^{2x}} + B{e^{ - 2x}}$ is (where $A$ and $B$ are arbitrary constants):

Statement $I$: The differential equation corresponding to the family of circles having their centres on $Y$-axis and fixed radius $k$ is $(x^2-k^2)(\frac{dy}{dx})^2+x^2=0$.
Statement $II$: The differential equation corresponding to the family of circles passing through the origin and having their centres on $X$-axis is $x^2-y^2+2xy \frac{dy}{dx}=0$.
Which of the above statements is (are) true?