Question

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

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

The order of a differential equation is the highest derivative present in the equation.

Answer 1

The Correct Option is B

Step 1: Understanding the Order of a Differential Equation
The order of a differential equation is determined by the highest order of the derivative that appears in the equation.
In this equation, we have \( \frac{dy}{dx} \) and \( \frac{d^2y}{dx^2} \), with the highest derivative being \( \frac{d^2y}{dx^2} \), making the order of the differential equation 2.
Step 2: Conclusion
Thus, the order of the differential equation is 2.