Question

The integrating factor of the differential equation \( \frac{dx}{dy} = \frac{x \log x}{2 \log x - y} \) is:

• A. \( \frac{1}{8x} \)
• B. \( e \)
• C. \( e^{\log x} \)
• D. \( \log x \)

Hint:

For solving differential equations, the integrating factor often simplifies the equation by removing non-homogeneous terms. Check the form of the equation and use standard methods to find the integrating factor.

Answer 1

The Correct Option is D

The equation is \( \frac{dx}{dy} = \frac{x \log x}{2 \log x - y} \). The integrating factor, found by identifying the term that simplifies the equation when multiplied by \( x \) for solvability, is \( \log x \).