The order of the differential equation of all parabolas,whose latus rectum is $4a$ and axis is parallel to the $x$-axis,is

The order of the differential equation whose solution is $y=a \cos x+b \sin x+c e^{-x}$ is

The differential equation of all straight lines passing through the point $(1, -1)$ is

The differential equation of all parabolas having vertex at the origin and axis along the positive $Y$-axis 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 the family of curves $y = ax + \frac{1}{a}$, where $a (\neq 0)$ is an arbitrary constant, has the degree