Question

The solution of the differential equation \[ \log x \frac{dy}{dx} + x = \sin 2x \] is

• A. \( \log |x| = C - \cos x \)
• B. \( \log |x| = C - \frac{1}{2} \cos 2x \)
• C. \( \log |x| = C - \cos 2x \)
• D. \( \log |x| = C - \frac{1}{2} \cos 2x \)

Hint:

In solving differential equations, always try separating variables to integrate both sides.

Answer 1

The Correct Option is B

Step 1: Solve the differential equation.
Separate the variables and integrate both sides of the equation.
Step 2: Conclusion.
The solution is \( \log |x| = C - \frac{1}{2} \cos 2x \).
Final Answer: \[ \boxed{\log |x| = C - \frac{1}{2} \cos 2x} \]