Find the order and degree ( if defined) of each of the following equations :
`y''+3y'+2y=0`

Answer

To find the order and degree of the given differential equation \( y'' + 3y' + 2y = 0 \), we will follow these steps:

### Step 1: Identify the highest derivative
The equation is given as:
\[ y'' + 3y' + 2y = 0 \]
Here, \( y'' \) is the second derivative of \( y \), and \( y' \) is the first derivative of \( y \).

### Step 2: Determine the order
The order of a differential equation is defined as the highest order of derivative present in the equation. In this case, the highest derivative is \( y'' \), which is the second derivative. Therefore, the order of the differential equation is:
\[ \text{Order} = 2 \]

### 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 \( y'' \) has a power of 1 (since it is not raised to any power). Therefore, the degree of the differential equation is:
\[ \text{Degree} = 1 \]

### Final Answer
Thus, the order and degree of the differential equation \( y'' + 3y' + 2y = 0 \) are:
- Order: 2
- Degree: 1