Question

The order and degree of the following differential equation: \( \frac{d^2 y}{dx^2} - 2x = \sqrt{y} + \frac{dy}{dx} \), respectively, are:

• A. 2, 2
• B. 2, 1
• C. 1, 2
• D. 4, 2
• E. 1, 1

Hint:

To determine the order and degree of a differential equation, focus on the highest derivative and ensure the equation is in polynomial form for degree.

Answer 1

The Correct Option is A

Step 1: The order of a differential equation is the highest derivative with respect to the independent variable. In this case, the highest derivative is \( \frac{d^2 y}{dx^2} \), so the order is 2. 
Step 2: The degree of a differential equation is the power of the highest derivative after making the equation polynomial (i.e., eliminating radicals or fractions involving derivatives). 
Here, the highest derivative is \( \frac{d^2 y}{dx^2} \), and it is raised to the first power, so the degree is 2. Thus, the order and degree are 2 and 2, respectively.