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

The differential equation of the family of circles with fixed radius $r$ units and centre on the line $y=3$ is

The differential equation for which $ax + by = 1$ is the general solution 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:

$y=A e^x+B e^{-2 x}$ satisfies which of the following differential equations?

The differential equation which represents the family of curves $y = c_1 e^{c_2 x}$,where $c_1$ and $c_2$ are arbitrary constants is: