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:

• A
  $(A)$ is true, $(R)$ is true and $(R)$ is the correct explanation for $(A)$
• B
  $(A)$ is true, $(R)$ is true but $(R)$ is not the correct explanation for $(A)$
• C
  $(A)$ is true but $(R)$ is false
• D
  $(A)$ is false but $(R)$ is true