What are the order and degree respectively of the differential equation `y = x "" (dx)/(dy) + (dx)/(dy) `?

Options

A. `1,1`
B. 1,2
C. 2,1
D. 2,2

Answer

To determine the order and degree of the differential equation given by:

\[ y = x \frac{dx}{dy} + \frac{dx}{dy} \]

we will follow these steps:

### Step 1: Identify the Derivatives
First, we need to identify the derivatives present in the equation. In this case, we have the term \(\frac{dx}{dy}\), which is the first derivative of \(x\) with respect to \(y\).

### Step 2: Determine the Order
The order of a differential equation is defined as the highest order of derivative present in the equation. Here, the only derivative present is \(\frac{dx}{dy}\), which is a first derivative. Therefore, the order of the differential equation is:

**Order = 1**

### Step 3: Determine the Degree
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 our case, the highest derivative is \(\frac{dx}{dy}\), and it appears to the power of 1. Thus, the degree of the differential equation is:

**Degree = 1**

### Final Answer
So, the order and degree of the differential equation are:

**Order = 1, Degree = 1**

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