The order of the differential equation whose solution is $a e^{x} + b e^{2x} + c e^{3x} + d = 0$ is:

The differential equation of the family of curves for which the length of the normal is equal to a constant $k$,is given by

The differential equation of the family of circles touching $y$-axis at the origin is

$A$ differential equation representing the family of parabolas with axis parallel to the $y$-axis and whose length of latus rectum is the distance of the point $(2, -3)$ from the line $3x + 4y = 5$,is given by:

If $y = c{e^{{{\sin }^{ - 1}}x}}$,then the corresponding differential equation is:

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