The order of the differential equation of all circles of radius $r$,having centre on the $y$-axis and passing through the origin is:

The order and the degree of the differential equation $\left( \frac{d^2s}{dt^2} \right)^2 + 3\left( \frac{ds}{dt} \right)^3 + 4 = 0$ are

The degree of the differential equation $x\left(\frac{d^2 y}{d x^2}\right)^{\frac{1}{3}}+2 x^2\left(\frac{d^2 y}{d x^2}\right)^{\frac{5}{3}}+7 \frac{d y}{d x}+y=0$ is:

If $y=a^3 e^{b^2 x+c}$ is the general solution of a differential equation,where $a$ and $c$ are arbitrary constants and $b$ is a fixed constant,then the order of the differential equation is

For the differential equation $\frac{d^3y}{dx^3} + \cos \left( \frac{d^2y}{dx^2} \right) = 0$, which of the following is true?

The order and degree of the differential equation $\frac{d^2 y}{d x^2}=\sqrt{\frac{d y}{d x}}$ are respectively