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

Answer

To solve the problem, we need to analyze the given differential equation:

\[ y'' + y^2 = 0 \]

### Step 1: Identify the Order of the Differential Equation
The order of a differential equation is determined by the highest derivative present in the equation.

In this case, we have:

- \( y'' \) is the second derivative of \( y \) with respect to \( x \).

Thus, the highest derivative is \( y'' \), which is of order 2.

**Order = 2**

### Step 2: Identify the Degree of the Differential Equation
The degree of a differential equation is defined as the power of the highest derivative after the equation has been expressed in a polynomial form in terms of the derivatives.

In our equation:

\[ y'' + y^2 = 0 \]

We can rearrange it to:

\[ y'' = -y^2 \]

Here, the highest derivative \( y'' \) is raised to the power of 1 (since it appears as \( y'' \) and not \( (y'')^n \) for \( n > 1 \)).

Thus, the degree of the differential equation is:

**Degree = 1**

### Final Answer
- **Order**: 2
- **Degree**: 1

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