Determine order and degree ( if defined) of differential equations :
`y'''+2y''+y'=0`.

Answer

To determine the order and degree of the given differential equation \( y''' + 2y'' + y' = 0 \), we will follow these steps:

### Step 1: Identify the highest derivative
The first step is to identify the highest derivative present in the equation. The given equation is:

\[ y''' + 2y'' + y' = 0 \]

Here, \( y''' \) represents the third derivative of \( y \), \( y'' \) represents the second derivative, and \( y' \) represents the first derivative.

### Step 2: Determine the order
The order of a differential equation is defined as the highest derivative that appears in the equation. In this case, the highest derivative is \( y''' \), which is the third derivative.

Thus, the order of the differential equation is:

\[ \text{Order} = 3 \]

### Step 3: Determine the degree
The degree of a differential equation is defined as the power of the highest derivative when the equation is a polynomial in derivatives. In our equation, the highest derivative \( y''' \) appears to the first power (it is not raised to any power other than 1).

Thus, the degree of the differential equation is:

\[ \text{Degree} = 1 \]

### Final Result
In conclusion, for the differential equation \( y''' + 2y'' + y' = 0 \):
- The order is \( 3 \).
- The degree is \( 1 \).