Determine the order and degree (if defined) of the differential equation $\frac{d^4y}{dx^4} + \sin(y''') = 0$.

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

The differential equation whose solution is $Ax^2 + By^2 = 1$,where $A$ and $B$ are arbitrary constants,is of:

If the order and degree of the differential equation $\left(\frac{d^2 y}{dx^2}\right)^5 + 4 \frac{\left(\frac{d^2 y}{dx^2}\right)^5}{\left(\frac{d^3 y}{dx^3}\right)} + \frac{d^3 y}{dx^3} = \sin x$ are $m$ and $n$ respectively,then the value of $(m^2 + n^2)$ is equal to

The number of arbitrary constants in the particular solution of a differential equation of third order is:

For the differential equation $\frac{d^3 y}{d x^3}=0$,$y=a x^2+b x+c$ is