Write the order and degree of the following differential equations.
`(d^4y)/(dx^4)+sinx = ((d^2y)/(dx^2))^5`

Options

A. order=4, degree =1
B. order=4, degree =2
C. order=4, degree =3
D. order=4, degree =4

Answer

To determine the order and degree of the given differential equation

\[ \frac{d^4y}{dx^4} + \sin x = \left( \frac{d^2y}{dx^2} \right)^5, \]

we will follow these steps:

### Step 1: Identify the highest order derivative
The order of a differential equation is defined as the highest derivative of the dependent variable with respect to the independent variable.

In the given equation, we have:
- The term \(\frac{d^4y}{dx^4}\) which is a fourth-order derivative.
- The term \(\frac{d^2y}{dx^2}\) which is a second-order derivative.

The highest order derivative present in the equation is \(\frac{d^4y}{dx^4}\).

### Step 2: Determine the order
Since the highest order derivative is the fourth derivative, the order of the differential equation is:

\[ \text{Order} = 4. \]

### Step 3: Identify the degree of the highest order derivative
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 highest order derivative \(\frac{d^4y}{dx^4}\) appears to the first power (it is not raised to any power).

### Step 4: Determine the degree
Thus, the degree of the differential equation is:

\[ \text{Degree} = 1. \]

### Conclusion
Therefore, the order and degree of the given differential equation are:

- **Order**: 4
- **Degree**: 1

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