Find the order and degree, if defined, of the following differential equation :
`y'''+5y''+y'=0`.

Answer

To find the order and degree of the given differential equation \( y''' + 5y'' + y' = 0 \), we will follow these steps:

### Step 1: Identify the highest derivative
The given differential equation is:
\[ y''' + 5y'' + y' = 0 \]
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 present 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 expressed as a polynomial in derivatives.

In our equation, the highest derivative \( y''' \) appears with a power of 1 (since it is not raised to any power other than 1).

Thus, the degree of the differential equation is:
\[ \text{Degree} = 1 \]

### Final Answer
The order of the differential equation is 3, and the degree is 1.