Order And Degree Of Differential Equation

The correct answer is: (B): 6.

We are tasked with determining the degree of the differential equation:

Step 1: Express the equation in terms of derivatives

To find the degree, we need to ensure that the equation is polynomial in the derivatives of . Start by clearing the cube root by raising both sides of the equation to the power of 3:

Step 2: Eliminate the cube root and simplify

By simplifying both sides of the equation, we can rewrite the equation in a form where the derivatives are only raised to integer powers. This step essentially removes the fractional powers and simplifies the equation to a polynomial in and . The left side of the equation becomes a polynomial, while the right side has only the second derivative of , ensuring that we have a polynomial equation in terms of the derivatives.

Step 3: Identify the degree of the equation

The degree of a differential equation is defined as the highest power of the highest order derivative in the equation. In this case, after simplifying the equation, the highest order derivative is , and the highest power of this derivative is 6, making the degree of the equation 6.

Conclusion:
The degree of the differential equation is (B): 6.