For the ODE y'' + 4y = 0, the general solution is:

A y = Ae^(2x) + Be^(−2x)

B y = A cos(2x) + B sin(2x)

C y = (A+Bx)e^(2x)

D y = Ax² + Bx

✓ Correct Answer: Option B

Characteristic equation: r² + 4 = 0, r = ±2i. Complex roots → y = A cos(2x) + B sin(2x).

💡 Why is B) the correct answer?

The correct answer to the question "For the ODE y'' + 4y = 0, the general solution is:" is Option B: y = A cos(2x) + B sin(2x).

The other options — A) y = Ae^(2x) + Be^(−2x), C) y = (A+Bx)e^(2x), D) y = Ax² + Bx — are incorrect for this FE Exam Prep question. As explained above: Characteristic equation: r² + 4 = 0, r = ±2i. Complex roots → y = A cos(2x) + B sin(2x).

📚 About This FE Exam Prep Practice Question

This 2-level FE Exam Prep question from the Mathematics topic is part of BrainForge Quiz's free exam preparation library. Each question includes the correct answer and a detailed explanation to help you understand the underlying concept, not just memorize the answer.

How to use this page: Read the question above, consider all four options (A through D), then check the highlighted correct answer and explanation. For active timed practice, start a free FE Exam Prep practice test or use flashcards for spaced repetition review.

Practice FE Exam Prep Quizzes → Browse All Questions Study Flashcards

For the ODE y'' + 4y = 0, the general solution is:

✓ Correct Answer: Option B

📚 About This FE Exam Prep Practice Question

Related FE Exam Prep Questions