Q118 / 160 · AP EAMCET 2024 (21 May Shift 2) · Mathematics

The differential equation formed by eliminating arbitrary constants $\mathrm{A}, \mathrm{B}$ from the equation $y=A \cos 3 x+\mathrm{B} \sin 3 x$ is

  • A
    $\frac{d^2 y}{d x^2}+y=0$
  • Correct answer
    B
    $\frac{d^2 y}{d x^2}+9 y=0$
  • C
    $\frac{d^2 y}{d x^2}-9 y=0$
  • D
    $\frac{d^2 y}{d x^2}-y=0$

Solution

$\begin{aligned} & y=A \cos 3 x+B \sin 3 x \Rightarrow \frac{d y}{d x}=-3 A \sin 3 x+3 B \cos 3 x \\ & \frac{d^2 y}{d x^2}=-9 A \cos 3 x-9 B \sin 3 x=-9 y \\ & \Rightarrow \frac{d^2 y}{d x^2}+9 y=0 \text {. }\end{aligned}$

Hence, the correct answer is option: 'B'.

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