In each of the following differential equations, indicate its degree, wherever possible. Also, give the order of each of them
`y'''+y''+y'+y sin y = 0`.

Answer

To solve the given differential equation and determine its order and degree, we will follow these steps:

### Step 1: Identify the given differential equation
The given differential equation is:
\[ y''' + y'' + y' + y \sin y = 0 \]

### Step 2: Determine the order of the differential equation
The order of a differential equation is defined as the highest derivative present in the equation.

In the given equation:
- \( y''' \) is the third derivative of \( y \)
- \( y'' \) is the second derivative of \( y \)
- \( y' \) is the first derivative of \( y \)

The highest derivative here is \( y''' \), which is the third derivative.

**Thus, the order of the differential equation is 3.**

### Step 3: Determine the degree of the differential equation
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 the given equation:
- The highest order derivative is \( y''' \), which appears to the first power (i.e., \( (y''')^1 \)).
- The other derivatives \( y'' \) and \( y' \) also appear to the first power.
- The term \( y \sin y \) does not involve derivatives and does not affect the degree.

Since the highest order derivative \( y''' \) is raised to the power of 1, the degree of the differential equation is:

**Thus, the degree of the differential equation is 1.**

### Final Answer:
- **Order:** 3
- **Degree:** 1