The degree and order of the differential equation :
`2 (d^(2)y)/(dx)-3 (dy)/(dx)+y=0` :

Options

A. (2, 1)
B. (1, 2)
C. (2, 2)
D. Not defined

Answer

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

\[ 2 \frac{d^2y}{dx^2} - 3 \frac{dy}{dx} + y = 0 \]

we will follow these steps:

### Step 1: Identify the Order of the Differential Equation
The order of a differential equation is defined as the highest derivative present in the equation.

- In our equation, we have:
- The term \( \frac{d^2y}{dx^2} \) (the second derivative)
- The term \( \frac{dy}{dx} \) (the first derivative)

The highest derivative here is \( \frac{d^2y}{dx^2} \), which is of order 2.

**Conclusion**: The order of the differential equation is **2**.

### Step 2: Identify the Degree of the Differential Equation
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 equation, the highest order derivative is \( \frac{d^2y}{dx^2} \) and it appears with a coefficient of 2, which is a constant.
- The equation can be rewritten as:
\[ 2 \left( \frac{d^2y}{dx^2} \right) - 3 \left( \frac{dy}{dx} \right) + y = 0 \]

Since the highest derivative \( \frac{d^2y}{dx^2} \) is raised to the power of 1 (it is not raised to any power greater than 1), the degree is 1.

**Conclusion**: The degree of the differential equation is **1**.

### Final Answer
- **Order**: 2
- **Degree**: 1