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

Assertion $(A)$: The degree of the differential equation $y'' + 2xy' + \log_e\left(\frac{dy}{dx}\right) = 0$ is $2$.
Reason $(R)$: The degree of a differential equation is the highest power of the highest order derivative occurring in the equation, after the equation is expressed in the form of a polynomial in differential coefficients.
The correct option among the following is:

The sum of the degree and order of the differential equation $(1+y_1^2)^{2/3} = y_2$ is

The degree of the given differential equation $\left( \frac{d^2y}{dx^2} \right)^3 = \left( 1 + \frac{dy}{dx} \right)^{1/2}$ is:

The order and degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^3+\left(\frac{d y}{d x}\right)=\int y d x$ are . . . . . . and . . . . . . respectively.

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