Form the differential equation representing the family of curves $y = mx$,where $m$ is an arbitrary constant.

The differential equation of the family of curves $y=e^{x}(A \cos x+B \sin x)$ where $A, B$ are arbitrary constants is

Let $f(x)$ be a positive function such that the area bounded by $y=f(x), y=0$ from $x=0$ to $x=a>0$ is $e^{-a}+4a^2+a-1$. Then the differential equation,whose general solution is $y=c_1 f(x)+c_2$,where $c_1$ and $c_2$ are arbitrary constants,is :

The differential equation of the family of curves ${y^2} = 4a(x + a)$,where $a$ is an arbitrary constant,is

The differential equation of all parabolas,whose axes are parallel to the $Y$-axis,is

The curve $y=(\cos x+y)^{1 / 2}$ satisfies the differential equation