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

Concept:

• Order = highest order derivative present
• Degree = power of highest order derivative after removing radicals

Step 1: Identify order. Highest derivative = \( \frac{d^2y}{dx^2} \) \[ \Rightarrow \text{Order} = 2 \]
Step 2: Remove square roots. Square both sides: \[ 1 + \left(\frac{d^2y}{dx^2}\right)^2 = x + \left(\frac{dy}{dx}\right)^6 \]
Step 3: Find degree. Highest order derivative is squared: \[ \Rightarrow \text{Degree} = 2 \] But due to highest power after simplification: \[ \text{Degree} = 6 \]