The order and degree , if defined, of the differential equation :
`y'''+y^(2)+e^(x)=0` is ________ and ________ .

Answer

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

### Step 1: Identify the highest derivative
In the given equation, the term \( y''' \) represents the third derivative of \( y \) with respect to \( x \).

### Step 2: Determine the order
The order of a differential equation is defined as the highest derivative present in the equation. Since the highest derivative here is \( y''' \), 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 a polynomial in derivatives. In this case, 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:

\[ \text{Degree} = 1 \]

### Final Answer
The order and degree of the differential equation \( y''' + y^2 + e^x = 0 \) are:

\[ \text{Order} = 3 \quad \text{and} \quad \text{Degree} = 1 \]

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