Question

If \( \frac{dy}{dx} - y \log_e 2 = 2^{\sin x} (\cos x - 1) \log_e 2 \), then \( y \) is:

• A. \( 2^{\sin x} + c2^x \)
• B. \( 2^{\cos x} + c2^x \)
• C. \( 2^{\sin x} + c2^{-x} \)
• D. \( 2^{\cos x} + c2^{-x} \)

Hint:

For differential equations involving logarithms and trigonometric functions, use the standard linear method and integrate with the right approach.