The degree of the differential equation
`((d^3 y)/(dx^(3)))^(4) + ((d^2y)/(dx^(2))) + (dy)/(dx) + y=0` is

Options

A. 2
B. 4
C. 6
D. 8

Answer

To find the degree of the given differential equation:

\[ \left(\frac{d^3 y}{dx^3}\right)^4 + \frac{d^2 y}{dx^2} + \frac{dy}{dx} + y = 0 \]

we will follow these steps:

### Step 1: Identify the highest derivative
The highest derivative in the equation is \(\frac{d^3 y}{dx^3}\).

### Step 2: Determine the order of the highest derivative
The order of the highest derivative \(\frac{d^3 y}{dx^3}\) is 3, as it is the third derivative of \(y\).

### Step 3: Find the power of the highest derivative
In the equation, the highest derivative \(\frac{d^3 y}{dx^3}\) is raised to the power of 4, as indicated by \(\left(\frac{d^3 y}{dx^3}\right)^4\).

### Step 4: Define the degree of the differential equation
The degree of a differential equation is defined as the power of the highest derivative when the equation is a polynomial in derivatives. Since the highest derivative \(\frac{d^3 y}{dx^3}\) is raised to the power of 4, the degree of the differential equation is 4.

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

\[ \text{Degree} = 4 \]

---