In each of the following differential equations, indicate its degree, wherever possible. Also, give the order of each of them
`y(y')^(2)+y^(2)-1=0`.

Answer

To solve the given differential equation \( y(y')^2 + y^2 - 1 = 0 \), we need to determine its order and degree.

### Step 1: Identify the highest order derivative
The given equation can be rewritten in terms of derivatives. Here, \( y' \) represents the first derivative of \( y \) with respect to \( x \), which is \( \frac{dy}{dx} \).

### Step 2: Determine the order of the differential equation
The order of a differential equation is defined as the highest order of the derivative present in the equation. In our case, the only derivative present is \( y' \) (or \( \frac{dy}{dx} \)), which is of order 1.

**Order = 1**

### 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 after the equation has been expressed in a polynomial form in terms of the derivatives.

In the equation \( y(y')^2 + y^2 - 1 = 0 \), the term \( (y')^2 \) indicates that the highest order derivative \( y' \) is raised to the power of 2.

**Degree = 2**

### Conclusion
Thus, for the differential equation \( y(y')^2 + y^2 - 1 = 0 \):
- **Order = 1**
- **Degree = 2**