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 $r^2 = a^2 \cos 2\theta$,where '$a$' is an arbitrary constant,is:

The differential equation of the family of all circles of radius $a$ is

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

Let $f(x)$ be a positive function such that the area bounded by $y=f(x), y=0$ from $x=0$ to $x=a>0$ is $e^{-a}+4a^2+a-1$. Then the differential equation,whose general solution is $y=c_1 f(x)+c_2$,where $c_1$ and $c_2$ are arbitrary constants,is :

The curve $y=(\cos x+y)^{1 / 2}$ satisfies the differential equation