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

Answer

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

### Step 1: Identify the highest derivative
The equation involves the term \( y' \), which represents the first 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. In this case, the highest derivative is \( y' \), which is the first derivative. Therefore, the order of the equation is:

\[ \text{Order} = 1 \]

### Step 3: Identify 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 term \( y'^{2} \) is the highest derivative, and it is raised to the power of 2.

Thus, the degree of the equation is:

\[ \text{Degree} = 2 \]

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

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