The order and degree of the differential equation $\{1+(\frac{dy}{dx})^2\}^{\frac{3}{2}}=\frac{d^2y}{dx^2}$ are $p$ and $q$ respectively. Then,$p+q=$ . . . . . . .

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:

Determine the order and degree (if defined) of the differential equation $y^{\prime \prime} + 2y^{\prime} + \sin(y) = 0$.

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

The differential equation $\left( \frac{d^2y}{dx^2} \right)^2 - \left( \frac{dy}{dx} \right)^{1/2} = y^3$ has the degree

The order and degree of the differential equation $3 x^2 \frac{d^2 y}{d x^2}-\sin \left(\frac{d^3 y}{d x^3}\right)+\cos (x y)=0$ are