Write the order and degree of the following differential equations :
`((d^(2)y)/(dx^(2)))^(2)+((dy)/(dx))^(3)+2y=0`

Answer

To find the order and degree of the given differential equation:

\[ \left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^3 + 2y = 0 \]

### Step 1: Identify the highest order derivative
The first step is to identify the highest order derivative present in the equation. In this case, we have:

- \(\frac{d^2y}{dx^2}\) which is the second derivative of \(y\) with respect to \(x\).
- \(\frac{dy}{dx}\) which is the first derivative of \(y\) with respect to \(x\).

Among these, \(\frac{d^2y}{dx^2}\) is the highest order derivative.

### Step 2: Determine the order
The order of a differential equation is defined as the highest order of the derivative present in the equation. Since the highest order derivative here is \(\frac{d^2y}{dx^2}\), the order of the differential equation is:

\[ \text{Order} = 2 \]

### Step 3: Determine the degree
The degree of a differential equation is defined as the power of the highest order derivative when the equation is a polynomial in derivatives. In our equation, the term \(\left(\frac{d^2y}{dx^2}\right)^2\) indicates that the highest order derivative \(\frac{d^2y}{dx^2}\) is raised to the power of 2.

Thus, the degree of the differential equation is:

\[ \text{Degree} = 2 \]

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

---