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

QB_PH_028: Differential equations

Question Statement

The Wronskian $W(y_1, y_2)$ of two solutions $y_1 = \cos(3x)$ and $y_2 = \sin(3x)$ of $y'' + 9y = 0$ is:
Correct Answer
3, 3
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $W = \cos(3x)(3\cos 3x) - (-3\sin 3x)\sin 3x = 3(\cos^2 3x + \sin^2 3x) = 3$.
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