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The Differential equation by eliminating the arbitrary constants from y = Acos3x + Bsin3x is

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$\frac{d^{2} y}{{dx}^{2}} + 9 y = 1$

$\frac{d^{2} y}{{dx}^{2}} + 9 y = 0$

$\frac{d^{2} y}{{dx}^{2}} - 9 y = 0$

$\frac{d^{2} y}{{dx}^{2}} + y = 0$

answer is B.

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Detailed Solution

$\begin{array}{rcl} y & = & A \cos 3 x + B \sin 3 x \\ y^{1} & = & - 3 a \sin 3 x + 3 B \cos 3 x \\ y^{11} & = & - 9 A \cos 3 x - 9 B \sin 3 x \\ = & - 9 y \\ y^{11} + 9 y & = & 0 \end{array}$

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