The degree of the differential equation
`(d^2y)/(dx^2)+((dy)/(dx))^2+6y^5=0` is

Options

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

Answer

To find the degree of the given differential equation

\[ \frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 + 6y^5 = 0, \]

we need to follow these steps:

### Step 1: Identify the highest order derivative
The highest order derivative in the equation is \(\frac{d^2y}{dx^2}\), which is the second derivative of \(y\) with respect to \(x\).

**Hint:** Look for the term with the highest derivative in the equation.

### Step 2: Write the equation in polynomial form
The equation is already in a polynomial form with respect to the derivatives. We can see that it contains the second derivative \(\frac{d^2y}{dx^2}\) and the first derivative \(\frac{dy}{dx}\) squared.

**Hint:** Ensure that the equation is expressed as a polynomial in the derivatives.

### Step 3: Determine the degree of the highest order derivative
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 its derivatives. In this case, the highest order derivative \(\frac{d^2y}{dx^2}\) appears to the power of 1.

**Hint:** Check the exponent of the highest order derivative to find the degree.

### Conclusion
Since the highest order derivative \(\frac{d^2y}{dx^2}\) appears to the power of 1, the degree of the given differential equation is:

\[ \text{Degree} = 1. \]

### Final Answer
The degree of the differential equation is **1**.