Question:
Degree of the differential equation
\[
\frac{dy}{dx} e^x + \left( \frac{dy}{dx} \right)^3 = x
\]
Degree of the differential equation
\[
\frac{dy}{dx} e^x + \left( \frac{dy}{dx} \right)^3 = x
\]
Show Hint
For differential equations, make sure to check if the equation is polynomial in the highest derivative to determine its degree.
Updated On: Mar 28, 2026
- 2
- 1
- not defined
- 3
Show Solution
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The Correct Option is C
Solution and Explanation
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.
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.
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