Indicate the order of each of the following differential equations :
`y^(''''')+y=0`.

Answer

To determine the order of the given differential equation \( y^{(5)} + y = 0 \), we follow these steps:

### Step-by-Step Solution:

1. **Identify the Differential Equation**:
The given differential equation is \( y^{(5)} + y = 0 \).

2. **Understand the Notation**:
The notation \( y^{(5)} \) represents the fifth derivative of \( y \) with respect to \( x \). This means that we are differentiating \( y \) five times.

3. **Determine the Order**:
The order of a differential equation is defined as the highest derivative present in the equation. In this case, the highest derivative is \( y^{(5)} \), which is the fifth derivative.

4. **Conclusion**:
Therefore, the order of the differential equation \( y^{(5)} + y = 0 \) is **5**.