If $\frac{d^2y}{dx^2} = 0$,then:

The differential equation for which $l x^2+m y^2=x+y$ is the general solution is

Verify that the given function $y = Ax$ is a solution of the differential equation $xy' = y$ $(x \neq 0)$.

The differential equation obtained by eliminating the arbitrary constant from the equation $y^2 = (x + c)^3$ is

The normal form of the equation of a straight line is $x \cos \alpha + y \sin \alpha = p$. Find the differential equation of the family of all such lines where $p$ and $\alpha$ are arbitrary constants.

The differential equation of the family of parabolas with focus at the origin and the $X$-axis as axis,is