Question

The degree of the differential equation \( \left[ 1 + \left(\frac{dy}{dx}\right)^{2} \right]^{3/2} = \frac{d^{2}y}{dx^{2}} \) is:

• A. 3
• B. 2
• C. 1
• D. 3/2

Hint:

Order = highest derivative; Degree = power of that derivative in polynomial form.

Answer 1

The Correct Option is B

Step 1: Concept
Degree is the power of the highest order derivative after removing radicals/fractions.
Step 2: Analysis
Square both sides to remove the fractional power: $[1 + (y')^2]^3 = (y'')^2$.
Step 3: Conclusion
The highest order derivative is $y''$ and its power is 2. So, degree is 2.
Final Answer: (B)