Question

The particular integral of \( \frac{d^2 y}{dx^2} + 2y = x^2 \) is:

• A. \( x^2 - 1 \)
• B. \( x^2 + 1 \)
• C. \( \frac{1}{2} (x^2 + 1) \)
• D. \( \frac{1}{2} (x^2 + 1) \)

Hint:

For second-order linear differential equations, use methods like undetermined coefficients to find particular solutions.

Answer 1

The Correct Option is C

Step 1: Solve the equation. We solve the second-order differential equation by finding the particular solution. The solution involves integrating and simplifying the terms.
Step 2: Conclusion. Thus, the particular integral is \( \frac{1}{2} (x^2 + 1) \).