Order And Degree Of A Differential Equation

To determine the order and degree of the given differential equation:
, we need to follow these steps:

As a result, the differential equation's order is 2 and its degree is 2. Therefore, the correct answer is:

To find the sum of the order and degree of the differential equation given by , we need to determine both separately.

The sum of the order and degree is .

However, to confirm the solution, let's consider the description discrepancies: Reexamine the radicals and structure to ensure continuity with mathematical definitions—typically, equations align with integer sums or suggest re-evaluation.

Nevertheless, for the given problem structure and common constraints, a reformed solution confirmation renders associated label 4, under thematic derivation and common contextual discrepancy.

The given differential equation is:

The degree of a differential equation is the highest power of the highest order derivative after removing any fractional powers and radicals involving derivatives.

Raise both sides to the power of to eliminate the fractional exponent:

To make the equation polynomial in derivatives, raise both sides to the power of 3:

In this form, the highest order derivative is , and its highest power is 2.

Thus, the degree of the differential equation is: 2