Question

The degree of differential equation \[ 9 \frac{d^2y}{dx^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{\frac{1}{3}} \text{ is} \]

• A. 1
• B. 6
• C. 3
• D. 2

Hint:

To find the degree of a differential equation, first eliminate all radicals and fractions. Then identify the highest order derivative and note its power. That power is the degree.

Answer 1

The Correct Option is C

To find the degree of the given differential equation:

The differential equation is given by:

\(9 \frac{d^2y}{dx^2} = \left\{ 1 + \left( \frac{dy}{dx} \right)^2 \right\}^{\frac{1}{3}}\)

Step 1: Identify the order of the differential equation.

The highest order derivative present in the equation is \(\frac{d^2y}{dx^2}\), which indicates that the order of the differential equation is 2.

Step 2: Determine the degree of the differential equation.

The degree of a differential equation is defined as the power of the highest order derivative in the equation when it is free from fractions and radicals involving derivatives.

First, we need to eliminate the fractional exponent \(\frac{1}{3}\) by raising both sides to the power of 3:

\(\left( 9 \frac{d^2y}{dx^2} \right)^3 = 1 + \left( \frac{dy}{dx} \right)^2\)

This expression is now free from any fractional powers of derivatives.

The power of the highest order derivative term after raising to the power of 3 is 3, thus:

The degree of the differential equation is 3.

Conclusion: The correct option is 3.