What is the degree of the differential equation
`(d^(2)y)/(dx^(2)) - sqrt(1+((dy)/(dx))^(3))=0` ?

Options

A. 1
B. 2
C. 3
D. 6

Explanation

To find the degree of the given differential equation

\[ \frac{d^2y}{dx^2} - \sqrt{1 + \left(\frac{dy}{dx}\right)^3} = 0, \]

we will follow these steps:

### Step 1: Rewrite the equation
We start by rewriting the equation in a more manageable form:

\[ \frac{d^2y}{dx^2} = \sqrt{1 + \left(\frac{dy}{dx}\right)^3}. \]

### Step 2: Eliminate the square root
To eliminate the square root, we will square both sides of the equation:

\[ \left(\frac{d^2y}{dx^2}\right)^2 = 1 + \left(\frac{dy}{dx}\right)^3. \]

### Step 3: Identify the highest order derivative
In the equation

\[ \left(\frac{d^2y}{dx^2}\right)^2 = 1 + \left(\frac{dy}{dx}\right)^3, \]

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

### Step 4: Determine the degree
The degree of a differential equation is defined as the power of the highest order derivative when the equation is expressed as a polynomial in derivatives. In this case, the term \(\left(\frac{d^2y}{dx^2}\right)^2\) indicates that the degree of the differential equation is 2.

### Conclusion
Thus, the degree of the given differential equation is:

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