The differential equation of all lines perpendicular to the line $5x + 2y + 7 = 0$ is

The differential equation corresponding to the primitive $y = e^{mx}$ is obtained by eliminating the arbitrary constant $m$. What is the resulting differential equation?

If $m$ and $n$ are respectively the order and degree of the differential equation of the family of parabolas with focus at the origin and $X$-axis as its axis,then $m n-m+n=$

The differential equation for which $y^2 = 4a(x+a)$ (where $a$ is the parameter) is the general solution is:

The differential equation formed by eliminating $a$ and $b$ from the equation $y=e^x(a \cos x+b \sin x)$ is

The differential equation of all parabolas with axis parallel to the $y$-axis is