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

Options

A. 3
B. 2
C. 0
D. 1

Answer

To determine the order of the given differential equation:

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

we follow these steps:

### Step 1: Identify the derivatives present in the equation
In the given differential equation, we have the following derivatives:
- \(\frac{d^2y}{dx^2}\) (the second derivative of \(y\))
- \(\frac{dy}{dx}\) (the first derivative of \(y\))

### Step 2: Determine the highest order derivative
The order of a differential equation is defined as the highest derivative present in the equation. In this case:
- The highest derivative is \(\frac{d^2y}{dx^2}\), which is the second derivative.

### Step 3: Conclude the order of the differential equation
Since the highest derivative present is the second derivative, we conclude that the order of the differential equation is:

\[ \text{Order} = 2 \]

### Final Answer
The order of the differential equation is **2**.

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