Question

The order and the degree of the differential equation \[ \sqrt{1 + \left(\frac{d^2y}{dx^2}\right)^2} = \sqrt{x + \left(\frac{dy}{dx}\right)^6} \] are respectively _____ and _____

• A. 2, 3
• B. 1, 6
• C. 3, 2
• D. 2, 6

Hint:

Always remove radicals and fractions before determining degree of differential equation.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Order is the highest derivative present. Degree is the power of the highest order derivative after removing radicals and fractions.
Step 2: Formula Application:
Square both sides to remove the square roots (radicals): $$1 + \left( \frac{d^{2}y}{dx^{2}} \right)^{2} = x + \left( \frac{dy}{dx} \right)^{6}$$
Step 3: Explanation:
1. The highest order derivative is $\frac{d^2y}{dx^2}$, so the Order = 2. 2. The power of this highest derivative is 2, so the Degree = 2.
Step 4: Final Answer:
The order is 2 and the degree is 2.