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

Options

A. 2
B. 1
C. 0
D. not defined

Answer

To determine the order of the given differential equation

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

we will follow these steps:

### Step 1: Identify the highest derivative present in the equation.

In the given equation, we have the following derivatives:

- \(\frac{d^2y}{dx^2}\) (the second derivative of \(y\))
- \(\frac{dy}{dx}\) (the first derivative of \(y\))
- \(y\) (the function itself, which is a 0th derivative)

### Step 2: Determine the order.

The order of a differential equation is defined as the highest order of derivative present in the equation.

- The highest derivative present in our equation is \(\frac{d^2y}{dx^2}\), which is the second derivative.

### Step 3: Conclude the order.

Since the highest derivative is the second derivative, the order of the differential equation is:

\[ \text{Order} = 2. \]

Thus, the order of the differential equation

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

is **2**.

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