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

Answer

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

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

- \( y''' \) (third derivative of \( y \))
- \( y'' \) (second derivative of \( y \))
- \( y' \) (first derivative of \( y \))
- \( y \) (the function itself)

The highest derivative here is \( y''' \).

### Step 2: Determine the order
The order of a differential equation is defined as the highest order of derivative present in the equation. Since the highest derivative is \( y''' \), which is the third derivative, the order of the differential equation is:

**Order = 3**

### Step 3: Determine the degree
The degree of a differential equation is defined as the power of the highest order derivative when the equation is a polynomial in derivatives.

In our equation, the highest derivative \( y''' \) appears to the first power (i.e., it is not raised to any power other than 1).

Thus, the degree of the differential equation is:

**Degree = 1**

### Final Answer:
- **Order = 3**
- **Degree = 1** (if defined)