The difference of the order and degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^{-\frac{7}{2}}\left(\frac{d^3 y}{d x^3}\right)^2-\left(\frac{d^2 y}{d x^2}\right)^{-\frac{5}{2}}\left(\frac{d^4 y}{d x^4}\right)=0$ is

The order and the degree of the differential equation $\sqrt{1 + (\frac{d^2y}{dx^2})^2} = \sqrt[3]{x + (\frac{dy}{dx})^3}$ are respectively . . . . . . and . . . . . . .

The order and degree of the differential equation $\sqrt[4]{\left(\frac{d^3 y}{d x^3}\right)^5} = \sqrt[3]{\left(\frac{d^2 y}{d x^2}\right)^4}$ are . . . . . . and . . . . . . respectively.

The order and degree of the differential equation $(\frac{d^3y}{dx^3})^{2/3} - 3 \frac{d^2y}{dx^2} + 5 \frac{dy}{dx} + 4 = 0$ are respectively:

Determine the order and degree (if defined) of the differential equation $y'' + (y')^2 + 2y = 0$.

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: