The differential equation $\frac{d^3y}{dx^3} + 2\left[ 1 + \frac{d^2y}{dx^2} \right] = 1$ has order and degree as:

The degree and order of the differential equation $\left[1+\left(\frac{dy}{dx}\right)^3\right]^{\frac{7}{3}}=7\left(\frac{d^2y}{dx^2}\right)$ respectively are

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:

For the differential equation given below,determine its order and degree (if defined):
$\frac{d^{2} y}{d x^{2}}+5 x\left(\frac{d y}{d x}\right)^{2}-6 y=\log x$

Determine the order and degree (if defined) of the differential equation $y^{\prime} + 5y = 0$.

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