If m, n are order and degree of differential equation `y(dy)/(dx) + x^(3)((d^(2)y)/(dx^(2)))-xy = cos x` then

Options

A. `m lt n`
B. m= n
C. `m gt n`
D. m-n = 3

Answer

To solve the problem, we need to determine the order and degree of the given differential equation:

\[ y \frac{dy}{dx} + x^3 \frac{d^2y}{dx^2} - xy = \cos x \]

### Step 1: Identify the highest order derivative
The highest order derivative in the equation is \( \frac{d^2y}{dx^2} \). This indicates that the order of the differential equation is 2.

### Step 2: Determine the degree of the highest order derivative
The degree of a differential equation is defined as the power of the highest order derivative when the equation is a polynomial in derivatives. In this case, the highest order derivative \( \frac{d^2y}{dx^2} \) appears to the first power (i.e., it is not raised to any power other than 1).

### Step 3: Conclusion on order and degree
From the analysis:
- The order \( m \) of the differential equation is 2.
- The degree \( n \) of the differential equation is 1.

### Final Result
Thus, we have:
- \( m = 2 \)
- \( n = 1 \)