Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as
Assertion (A): The degree of the differential equation given by `(dy)/(dx)=(x^4-y^4)/((x^2+y^2)xy)` is 1.
Reason (R): The degree of a differential equation is the degree of the highest order derivative when differential coefficients are free from radicals and fraction
The given differential equation has first order derivative which is free from radical and fraction with power = 1, thus it has a degree of 1.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is NOT the correct explanation of A
C. A is true but R is false
D. A is false but R is True

Answer

To solve the problem, we need to analyze the statements of Assertion (A) and Reason (R) regarding the degree of the given differential equation.

### Step-by-Step Solution:

1. **Identify the Differential Equation:**
The given differential equation is:
\[ \frac{dy}{dx} = \frac{x^4 - y^4}{(x^2 + y^2)xy} \]

2. **Determine the Order of the Differential Equation:**
The highest order derivative in the equation is \(\frac{dy}{dx}\), which is a first-order derivative.

3. **Check for Radicals and Fractions:**
The expression on the right side of the equation is a fraction, but we need to focus on the derivative itself. The derivative \(\frac{dy}{dx}\) is not under any radical or exponentiation that would complicate its degree.

4. **Calculate the Degree of the Differential Equation:**
The degree of a differential equation is defined as the power of the highest order derivative when it is expressed in a polynomial form. In this case, \(\frac{dy}{dx}\) appears to the first power (1):
\[ \text{Degree} = 1 \]

5. **Evaluate Assertion (A) and Reason (R):**
- Assertion (A): "The degree of the differential equation is 1." This is **true**.
- Reason (R): "The degree of a differential equation is the degree of the highest order derivative when differential coefficients are free from radicals and fractions." This is also **true**.

6. **Determine the Relationship Between A and R:**
Since both statements are true, and the reason correctly explains the assertion, we conclude that both A and R are true, and R is the correct explanation of A.

### Conclusion:
The correct choice is:
**Option 1: Both A and R are true. R is the correct explanation of A.**