Differential Equations

To determine the degree and order of the given differential equation , :
- The order of a differential equation is the highest derivative present in the equation.
- The degree of a differential equation is the highest power of the highest-order derivative after the equation has been made free of fractions and radicals (if any) in terms of the derivatives.
Step 1: Identify the Order
- The given equation contains , which is the second derivative of with respect to .
- There are no higher derivatives present.
- Therefore, the order ( ) is 2.
Step 2: Identify the Degree
- The highest-order derivative in the equation is .
- The equation is .
- To find the degree, we need to express the equation such that the highest derivative is isolated and check the power of that derivative.
- Rearrange the equation:
- Here, is raised to the power of 1, and there are no fractions or radicals involving . - The presence of (first derivative) does not affect the degree, as the degree is determined by the highest power of the highest-order derivative.
- Thus, the degree ( ) is 1.
Step 3: Compute
- (degree)
- (order)
- Therefore, .
Verification
- The equation is already in a form where the highest derivative is of degree 1, and the order is 2. The problem likely intends and to represent degree and order, and the sum is 3, matching option (B).