Question

The solution of \( D^2 + 16y = \cos 4x \) is:

• A. \( A \cos 4x + B \sin 4x \)
• B. \( A \cos 4x + B \sin 4x + \frac{x}{8} \sin 4x \)
• C. \( A \cos 4x + B \sin 4x + \frac{x}{4} \sin 4x \)
• D. \( A \cos 4x + B \sin 4x + \frac{x}{4} \sin 4x \)

Hint:

For second-order linear differential equations, first solve the homogeneous part, then find a particular solution using the method of undetermined coefficients.

Answer 1

The Correct Option is A

Step 1: Solve the equation. Solve the non-homogeneous second-order differential equation by using complementary and particular solution methods.
Step 2: Conclusion. Thus, the solution is \( A \cos 4x + B \sin 4x \).