The order and the degree of the differential equation $y=px+\sqrt{a^2p^2+b^2}$,(where $p=\frac{dy}{dx}$) are respectively.

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

The order and degree of the differential equation $y = x \frac{dp}{dx} + \sqrt{a^{2} p^{2} + b^{2}}$,where $p = \frac{dy}{dx}$ (here $a$ and $b$ are arbitrary constants) respectively are:

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 order of the differential equation $2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0$ is

The degree of the differential equation $y(x) = 1 + \frac{dy}{dx} + \frac{1}{2!} \left( \frac{dy}{dx} \right)^2 + \frac{1}{3!} \left( \frac{dy}{dx} \right)^3 + \dots$ is