Question

Degree of the differential equation \[ \frac{dy}{dx} e^x + \left( \frac{dy}{dx} \right)^3 = x \]

• A. 2
• B. 1
• C. not defined
• D. 3

Hint:

For differential equations, make sure to check if the equation is polynomial in the highest derivative to determine its degree.

Answer 1

The Correct Option is C

Step 1: Identifying the degree of the equation.
The degree of a differential equation is the power of the highest derivative after eliminating any fractional or negative powers. In this case, the term \( \left( \frac{dy}{dx} \right)^3 \) indicates that the degree of the equation is not defined since the equation has a cubic power of a derivative, and the equation is not polynomial in the highest derivative.

Step 2: Conclusion.
Thus, the degree of the differential equation is not defined, making option (C) the correct answer.