In each of the following differential equations, indicate its degree, wherever possible. Also, give the order of each of them
`y^(v)+y^(2)+e^(v')=0`

Answer

To solve the given differential equation \( y^{(5)} + y^{2} + e^{(y')} = 0 \), we need to determine its order and degree.

### Step 1: Identify the highest derivative
The first step in determining the order of a differential equation is to identify the highest derivative present in the equation.

In the equation \( y^{(5)} + y^{2} + e^{(y')} = 0 \):
- \( y^{(5)} \) represents the fifth derivative of \( y \).
- \( y^{2} \) is a function of \( y \) but does not involve any derivatives.
- \( e^{(y')} \) involves the first derivative of \( y \).

The highest derivative in this equation is \( y^{(5)} \).

### 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 the fifth derivative, we conclude that:

**Order = 5**

### 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. However, if the equation involves transcendental functions (like exponential, logarithmic, etc.) of the derivatives, the degree is considered to be undefined.

In our equation:
- The term \( e^{(y')} \) involves the first derivative \( y' \) in an exponential function, which is not a polynomial.

Thus, we conclude that:

**Degree = Not Defined**

### Final Answer
- **Order:** 5
- **Degree:** Not Defined