Question

Choose the most appropriate options. 
The degree of the differential equation \[ x = 1 + \frac{dy}{dx} + \frac{1}{2!} \left( \frac{d^2y}{dx^2} \right) + \frac{1}{3!} \left( \frac{d^3y}{dx^3} \right) + ... \]

• A. 3
• B. 1
• C. not defined
• D. None of these

Hint:

The degree of a differential equation is the power of the highest derivative in the equation.

Answer 1

The Correct Option is B

The degree of a differential equation is the highest power of the highest order derivative.
In the given series expansion, the highest order derivative term is \( \frac{dy}{dx} \), and there is no exponent other than 1 for each derivative.
Thus, the degree is \( 1 \).