The degree of the differential equation :
`(1+ (dy)/(dx))^(5)=((d^(2)y)/(dx^(2)))^(2)` is :

Options

A. 1
B. 2
C. 3
D. 4

Answer

To find the degree of the given differential equation

\[ (1 + \frac{dy}{dx})^5 = \left(\frac{d^2y}{dx^2}\right)^2, \]

we will follow these steps:

### Step 1: Identify the highest order derivative
In the given equation, we have two derivatives:
- The first derivative \(\frac{dy}{dx}\)
- The second derivative \(\frac{d^2y}{dx^2}\)

The highest order derivative present in the equation is \(\frac{d^2y}{dx^2}\).

### Step 2: Determine the power of the highest order derivative
The degree of a differential equation is defined as the power of the highest order derivative after the equation has been made polynomial in derivatives.

In our case, the highest order derivative is \(\frac{d^2y}{dx^2}\), and it appears in the equation raised to the power of 2, as seen in \(\left(\frac{d^2y}{dx^2}\right)^2\).

### Step 3: Conclude the degree of the differential equation
Since the highest order derivative \(\frac{d^2y}{dx^2}\) is raised to the power of 2, the degree of the differential equation is:

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

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

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