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

If $l$ and $m$ are the degree and the order respectively of the differential equation of the family of all circles in the $XY$ plane with radius $5$ units,then $2l + 3m =$

The degree of the differential equation obtained from the equation $(y - a)^2 = 4(x - b)$ [where $a$ and $b$ are arbitrary constants] is

The differential equation for the family of curves ${x^2} + {y^2} - 2ay = 0,$ where $a$ is an arbitrary constant,is

The family of curves $y = e^x(A\cos x + B\sin x)$ represents the differential equation:

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