Question Bank NAT • 2 Marks Section 1: Mathematical Physics Differential equations

QB_PH_007: Differential equations

Question Statement

For the differential equation $\frac{d^2 y}{dx^2} + 4y = 0$ with $y(0) = 0$ and $y'(0) = 6$, the value of $y(\pi/8)$ (rounded to two decimal places) is:
Correct Answer
2.1, 2.15
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $y(x) = 3 \sin(2x) \implies y(\pi/8) = 3 \sin(\pi/4) = 3/\sqrt{2} \approx 2.12$.
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